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Population dynamics and damage effects of the citrus rust mite, Phyllocoptruta oleivora (Ashmead)(Acari:eriophyidae)

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Title:
Population dynamics and damage effects of the citrus rust mite, Phyllocoptruta oleivora (Ashmead)(Acari:eriophyidae)
Creator:
Yang, Yubin, 1962-
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English
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xviii, 192 leaves : ill. ; 29 cm.

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Subjects / Keywords:
Cumulative damage ( jstor )
Figs ( jstor )
Flood damage ( jstor )
Fruits ( jstor )
Groves ( jstor )
Mites ( jstor )
Orange fruits ( jstor )
Pathogens ( jstor )
Population dynamics ( jstor )
Population growth ( jstor )
Alachua County ( local )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1994.
Bibliography:
Includes bibliographical references (leaves 178-191).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Yubin Yang.

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University of Florida
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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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002030136 ( ALEPH )
AKL7768 ( NOTIS )
33038031 ( OCLC )

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POPULATION DYNAMICS AND DAMAGE EFFECTS OF THE CITRUS RUST
MITE, PHYLLOCOPTRUTA OLEIVORA (ASHMEAD)(ACARI: ERIOPHYIDAE)













By

YUBIN YANG


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


1994










ACKNOWLEDGMENTS


I would like to extend the deepest gratitude to my major professor, Dr. Jon C. Allen, for

his clear guidance, advice, patience, encouragement, and superb teaching throughout my study.

Jon's broad knowledge enriched me, and his kind and pleasant personality comforted me all the

time. Thanks are also extended to Dr. J.L. Knapp, cochairman of my committee, and to Drs.

H.L. Cromroy, J.W. Jones, J.E. Lloyd, and P.A. Stansly for serving on the supervisory

committee and contributing to the completion of the dissertation. It has always been such a great

pleasure to work with my committee members. What I have learned is not only a way of

profession but also a way of life, and it will last forever along with my deep gratitude and

wonderful memory.

I am also extremely grateful to Dr. R.E. Rouse and Sally Davenport (Southwest Florida

Research and Education Center), to Mark Colbert, Tommy Duda, and Danny Jones (A. Duda

& Sons, Inc.), to Dr. Frederick S. Davies (University of Florida Horticultural Sciences

Department), and to the Coca-Cola Corporation for allowing us to conduct research in their

citrus groves and for their assistance and cooperation during the study. I am indebted to Elmo

B. Whitty, Harold E. Hannah, Y.J. Tsai and Harry E. Anderson (University of Florida) for

providing the weather data essential to my research.






I would also like to thank many American friends who have been so kind and nice to me,

and so patient with me.

I will be forever indebted to my parents for their unfailing love and support.

Finally, a very special thanks to my wife, Yu Lin, and my son, Danhong Yang for their

love, their encouragement, their patience, and their sacrifice.












TABLE OF CONTENTS


ACKNOWLEDGMENTS ................................... ii

LIST OF TABLES ....................................... x

LIST OF FIGURES......................................... xi

ABSTRACT .......................................... xvii

CHAPTERS

1. LITERATURE REVIEW ......................... 1

Distribution and Production of Citrus .................. 1
Origin and Distribution of the Citrus Rust Mite ............ 2
Taxonomic History ............................. 3
Host Preference ............................... 4
Life History and Habitat .......................... 4
Rearing Methods .......................... 4
Reproduction ............................ 5
Stages and Development ...................... 5
Economic Importance ............................ 8
History of Economic Importance ................ 8
Rust Mite Injury .......................... 9
Feeding and food ..................... 9
Injury to leaves ....................... 10
Injury to fruit ........................ 11
Injury to young twigs ................... 12
Leaf injury and greasy spot .............. 12
Economic Loss ........................... 13
Leaf drop and size in relation to damage ....... 13
Fruit damage in relation to mite density ........ 14
Fruit growth in relation to damage ........... 14
Fruit drop in relation to damage ........... 15
Fruit internal quality in relation to damage 15
Calculation of economic loss from rust mite
damage ....................... 16






Behavior and Ecology ........................... 16
Behavior and Distribution ..................... 16
Population Dynamics vs. Season ................. 18
Population Dynamics vs. Climatic Factors ........... 19
Mite-Pathogen Interaction .................... 21
Management of Citrus Rust Mite .................... 24
Chemical Control .......................... 24
Pesticides .......................... 24
Fungicides vs. H. thompsonii .............. 25
Cultural Control ........................... 25
Biological Control ......................... 26
Predators and parasitoids ................. 26
Pathogens .......................... 27
Integrated Control ........................ 27
Survey Methodology ....................... 28
Study Objectives and Methodology . 28

2. RELATIONSHIP BETWEEN MITE POPULATION DENSITY
AND FRUIT DAMAGE .......................... 31

Statement of the Problem and Study Objective ............. 31
Materials and Methods ........................... 32
M ite Damage ............................ 32
Study 1 ........................... 33
Study 2, 3, 4 ........................ 33
Study 5 ........................... 33
Study 6 ........................... 33
Fruit Growth ............................. 35
Data Analysis ............................ 35
Damage (Damage rate) .................. 35
Fruit growth ........................ 38
Results ..................................... 38
Cumulative Damage vs. Cumulative Mite Days ....... 38
Cumulative Mite Days vs. Time ................. 39
Damage Rate vs. Fruit Maturity ................. 39
Damage vs. Tree Age and Location ............... 40
Discussion ................................... 41
Why Damage Rate Increases with Increasing Cumulative
M ite Days? ......................... 41
Zero Damage Mite Density .................... 42
What is the Recommendation? ................. 43







3. RELATIONSHIP BETWEEN MITE DAMAGE AND FRUIT
GROWTH AND DROP ..........................


Statement of the Problem and Study Objective .
Materials and Methods ...............
Data Analysis .................
Fruit drop and mite damage ....
Fruit growth and mite damage .
Results ..........................
Fruit Drop and Mite Damage .......
Fruit Growth and Mite Damage ......
Discussion ...... .................


4. FREQUENCY DISTRIBUTION OF MITE DAMAGE ON
FRUIT ....................................

Statement of the Problem and Study Objective .............
Materials and Methods ...........................
Data Analysis ............................
Results .......................................
Quadrant Distribution of Damaged Fruit on a Tree .....
Distribution of Damaged Fruit .................
Discussion .............................. ... .
Properties of the Cumulative Frequency Distribution
Function ...........................
Application of the Cumulative Frequency Distribution
Function ...........................

5. MITE POPULATION DYNAMICS ON FRUIT AND LEAVES .


Statement of the Problem and Study Objective .
Materials and Methods ...............
Budwood Foundation Grove, 1991 .
Research Grove, 1992, 1993 .......
Commercial Grove, 1993 .........
Results .........................
Budwood Foundation Grove, 1991 .
Research Grove, 1992 ...........
Research Grove, 1993 ...........
Commercial Grove, 1993 .........
Discussion .......................


Mite Population vs.
Mite Population vs.


Fungal Pathogen
Food Availability


............ 84
. .. 84
............ 84
............ 85
. .. 88
. .. 88
. .. 89
. .. 89
. .. 89
. .. 90
. .. 90
. .. 91


Mite Population vs. Tree Age and Location ..........


.






Mite Population vs. Weather . 94
Mite Population on Upper vs. Lower Leaf Surface ..... 96
Quantification of Effects of Biotic and Abiotic Factors on
Mite Population Dynamics ................ 97

6. MITE POPULATION PREDICTION: AN AGE-STRUCTURED
MODEL OF THE FRUIT-MITE PATHOGEN SYSTEM ..... 107

Statement of the Problem and Study Objective ............ 107
Materials and Methods .......................... 107
The Fruit-Mite-Pathogen System ................ 107
Model Development ....................... 110
The age-stage-structure matrix ............ 110
Age-stage-specific growth rate, developmental rate,
mortality rate and fecundity .......... 113
Mite and pathogen population growth ........ 114
Mite and pathogen population density adjustment
due to fruit growth ............... 116
Model Parameter Specification ................ 117
Determination of the number of age groups .... 117
Elements for the mortality matrix M ......... 119
Elements for the growth rate matrix G and
developmental rate matrix D ......... 120
Elements for the fecundity matrix F ......... 124
Matrix Element Calculation Varying Temperature .... 127
Model Parameter Estimation ................. 129
Results .................................... 130
Parameter Estimates ....................... 130
Observed vs. Simulated Mite/Pathogen/Damage
Dynamics ......................... 131
Polk County 1993 .................... 131
Alachua County 1993 ................. 132
Alachua County 1992 .................. 132
Collier County 1991 ................... 132
Discussion .................................. 133
Need for a Maximization Tool ................ 133
Need for Pathogen Biology ................... 134
Modeling Pesticide-Induced Mortality ........... 134
Parameter Calibration and Model Application ........ 135

7. CALCULATION OF ECONOMIC LOSS FROM RUST MITE
DAM AGE ................................. 148

Statement of the Problem and Study Objective ............ 148






Materials and Methods .......................... 149
Mite Population Prediction .................. 149
Fruit Surface Damage Prediction .............. 149
Frequency Distribution of Mite Damage to Fruit ...... 150
Volume and Value Loss from Increased Fruit Drop and
Reduced Fruit Growth ................ 151
Fruit growth and drop vs. damage .......... 151
Total proportional volume loss ............ 153
Proportional volume and value loss for fresh and
processed fruit .................. 154
Adjustment for mean damage ............ 156
Value Loss from Reduced Fruit Grade ........... 157
Total Value Loss from Increased Fruit Drop, Reduced
Fruit Growth, and Reduced Fruit Grade ....... 158
Results .................................... 158
Volume Loss without New Damage .............. 158
Volume Loss with New Damage ................ 159
Discussion .................................. 160
Volume Loss for Fresh Fruit vs. Processed Fruit ..... 160
Mite Control Decision ..................... 160
Looking into the Future ..................... 162

8. SUMMARY and Discussion ....................... 168

Important Results ............................. 168
Fruit Damage vs. Mite Population Density ........ 168
Fruit Growth and Drop vs. Mite Damage .......... 169
Frequency Distribution of Mite Damage to Fruit ...... 169
Mite and Pathogen Population Dynamics ........... 170
Fruit-Mite-Pathogen System Simulation .......... 171
Calculation of Volume Loss from Mite Damage ...... 171
Practical Applications ........................... 172
Prediction of Fruit Surface Damage .............. 172
Prediction of Mite Population Trend ............. 172
Control Strategies for Fresh Fruit Groves and Processed
Fruit Groves ....................... 173
Further Studies ............................... 175
Model Calibration and Implementation ............ 175
Effect of Mite Population Discontinuity of Damage Rate 176
Standardized Survey Method ................. 176







APPENDIX RELATION BETWEEN VOLUME AND PERCENT
DIAMETER GROWTH ......................... 177

LITERATURE CITED ................................... 178

BIOGRAPHICAL SKETCH ................................ 192












LIST OF TABLES


Table page

2-1. Summary of experimental designs ................... 36

2-2. Parameter estimates for power curve, equation 2-3 .......... 44

4-1. Relationship between mean fruit surface damage and estimates for
parameters a and b in equation 4-1 .................. 76

4-2. Parameter estimates for equations 4-2 and 4-3 using two different
methods .................................... 77

5-1. Summary of experimental designs ................... 87

6-1. Parameter estimates for equations describing the relationship
between cumulative emergence (F(t,T)) and temperature (T) 136

6-2. Parameter estimates for the pathogen transmission rate and
density-dependence equations ..................... 137












LIST OF FIGURES


Figure pag

2-1. Relationships between mite population and fruit damage (Study
1. Alachua County, Florida, 1992). (a) Fruit surface
damage/damage rate vs. cumulative mite days; (b) Cumulative
mite days/damage rate vs. time; (c) Mite population
dynamics/cumulative fruit surface damage vs. time .......... 45

2-2. Relationships between mite population and fruit damage (Study
2. Alachua County, Florida, 1992). (a) Fruit surface
damage/damage rate vs. cumulative mite days; (b) Cumulative
mite days/damage rate vs. time; (c) Mite population
dynamics/cumulative fruit surface damage vs. time .......... 46

2-3. Relationships between mite population and fruit damage (Study
3. Alachua County, Florida, 1992). (a) Fruit surface
damage/damage rate vs. cumulative mite days; (b) Cumulative
mite days/damage rate vs. time; (c) Mite population
dynamics/cumulative fruit surface damage vs. time .......... 47

2-4. Relationships between mite population and fruit damage (Study
4. Alachua County, Florida, 1992). (a) Fruit surface
damage/damage rate vs. cumulative mite days; (b) Cumulative
mite days/damage rate vs. time; (c) Mite population
dynamics/cumulative fruit surface damage vs. time .......... 48

2-5. Relationships between mite population and fruit damage (Study
5. Alachua County, Florida, 1993). (a) Fruit surface
damage/damage rate vs. cumulative mite days; (b) Cumulative
mite days/damage rate vs. time; (c) Mite population
dynamics/cumulative fruit surface damage vs. time .......... 49






2-6. Relationships between mite population and fruit damage (Study
6. Polk County, Florida, 1993). (a) Fruit surface
damage/damage rate vs. cumulative mite days; (b) Cumulative
mite days/damage rate vs. time; (c) Mite population
dynamics/cumulative fruit surface damage vs. time .......... 50

2-7. Relationships between fruit surface area growth and time
(Alachua County, Florida, 1992) .................... 51

3-1. Observed cumulative fruit drop (percentage) for 'Hamlin'
orange fruit with different amounts of rust mite damage (Hendry
County, FL.,1991) ............................. 59

3-2. Predicted cumulative fruit drop (percentage) for 'Hamlin' orange
fruit with different amounts of rust mite damage (see equation 3-5
in text) FL., 1991) ............................. 60

3-3. Prediction error for the percent fruit drop of 'Hamlin' orange fruit
with different of amounts rust mite damage (Hendry County, FL,
1991). ...................................... 61

3-4. Observed transverse diameter increase (percentage) of 'Hamlin'
orange fruit with different amounts of rust mite damage (Hendry
County, FL, 1991) ............................. 62

3-5. Predicted transverse diameter increase (percentage) of 'Hamlin'
orange fruit with different amounts of rust mite damage (see
equation 3-6 in text) ............................. 63

3-6. Prediction error for the percent diameter increase of 'Hamlin'
orange fruit with different of amounts rust mite damage (Hendry
County, FL, 1991) ............................. 64

3-7. Mean fruit surface damage plotted against mean fruit diameter
by tree for nine 'Hamlin' orange trees (Gainesville, FL,
January 1992) ................................ 65

4-1. Observed distribution of damaged fruit on a tree (Polk County,
Florida, 1993) ............................... 78

4-2. Observed relative cumulative frequency of mite damage on fruit
(Polk County, Florida, 1993) ....................... 79






4-3. Relationship between parameter a (b) in the logistic equation
(equation 4-1) and mean fruit surface damage ............. 80

4-4. Predicted cumulative frequency distribution of mite damage on
fruit (Polk County, Florida, 1993) ................... 81

4-5. Predicted probability density function of mite damage on fruit
(Polk County, Florida, 1993) . 82

5-1. Mite population dynamics. (a) Population dynamics of citrus
rust mite and its fungal pathogen on fruit; (b) Dynamics of
citrus rust mite population and fruit surface damage on fruit;
(c) Population dynamics of citrus rust mite on leaves. ('Valencia'
orange, Collier County, Florida, 1991) ................ 98

5-2. Mite population dynamics. (a) Population dynamics of citrus rust
mite and its fungal pathogen on fruit; (b) Dynamics of citrus
rust mite population and fruit surface damage on fruit;
(c) Population dynamics of citrus rust mite on leaves. ('Hamlin'
orange, Collier County, Florida, 1991) ................ 99

5-3. Mite population dynamics. (a) Population dynamics of citrus rust
mite and its fungal pathogen on fruit; (b) Dynamics of citrus rust
mite population and fruit surface damage on fruit; (c) Population
dynamics of citrus rust mite on leaves. ('Hamlin' orange, Alachua
County, Florida, 1992) ......................... 100

5-4. Mite population dynamics. (a) Population dynamics of citrus rust
mite and its fungal pathogen on fruit; (b) Dynamics of citrus rust
mite population and fruit surface damage on fruit; (c) Population
dynamics of citrus rust mite on leaves. ('Hamlin' orange, Alachua
County, Florida, 1993) ......................... 101

5-5. Mite population dynamics. (a) Population dynamics of citrus rust
mite and its fungal pathogen on fruit; (b) Dynamics of citrus rust
mite population and fruit surface damage on fruit; (c) Population
dynamics of citrus rust mite on leaves. ('Hamlin' orange, Polk
County, Florida, 1993) .......................... 102

5-6. Weather data. (a) Daily mean temperature; (b) Daily leaf wetness
duration (hrs); (c) Daily rainfall (cm) (Immokalee, Collier County,
1991) .. .. .. ... .. 103






5-7. Weather data. (a) Daily mean temperature; (b) Daily rainfall (cm)
(Gainesville, Alachua County, 1992) ................. 104

5-8. Weather data. (a) Daily mean temperature; (b) Daily rainfall (cm)
(Gainesville, Alachua County, 1993) .................. 105

5-9. Weather data. (a) Daily mean temperature; (b) Daily leaf wetness
duration (hrs); (c) Daily rainfall (cm) (Lake Alfred, Polk County,
1993). ..................................... 106

6-1. The age-stage-structure matrix (N) of the citrus rust mite and
its fungal pathogen. n. = number of individuals in age i and
stage j; Egg = egg stage; N, = protonymph stage; N2 =
deutonymph stage; Adult = adult stage; P, = latent pathogen
stage; Pi = infectious pathogen stage .................. 111

6-2. The age-stage-specific growth rate matrix (G), developmental rate
matrix (D), mortality matrix (M), and fecundity matrix (F).
gV = probability that an individual from age i and stage j will
grow to age i+1 of the same stage after one age interval (day);
dj = probability that an individual from age i and stage j will
develop to the first age class of stage j+1 after one age interval
(day); m,, = probability that an individual in age i and stage j
will die after one age interval (day); f/ = number of offspring
that will be produced by every individual in age i and stage j
during one age interval (day) ...................... 112

6-3. Density-dependent egg-laying curve for the citrus rust mite .... 138

6-4. Effect of temperature and leaf wetness duration on pathogen
transmission rate... ............................. 139

6-5. Observed fruit-mite-pathogen system dynamics. (a) mite and
pathogen population; (b) fruit surface damage; (c) cumulative
mite days (Polk County, Florida, 1993) ................ 140

6-6. Predicted fruit-mite-pathogen system dynamics. (a) mite
(thick solid line) and pathogen (thin solid line) population;
(b) fruit surface damage; (c) cumulative mite days (Polk County,
Florida, 1993) ............................... 141






6-7. Observed fruit-mite-pathogen system dynamics. (a) mite and
pathogen population; (b) fruit surface damage; (c) cumulative
mite days (Alachua County, Florida, 1993) 142

6-8. Predicted fruit-mite-pathogen system dynamics. (a) mite
(thick solid line) and pathogen (thin solid line) population;
(b) fruit surface damage; (c) cumulative mite days (Alachua
County, Florida, 1993) .......................... 143

6-9. Observed fruit-mite-pathogen system dynamics. (a) mite and
pathogen population; (b) fruit surface damage; (c) cumulative
mite days (Alachua County, Florida, 1992) 144

6-10. Predicted fruit-mite-pathogen system dynamics. (a) mite
(thick solid line) and pathogen (thin solid line) population;
(b) fruit surface damage; (c) cumulative mite days (Alachua
County, Florida, 1992) ......................... 145

6-11. Observed fruit-mite-pathogen system dynamics. (a) mite and
pathogen population; (b) fruit surface damage; (c) cumulative
mite days (Collier County, Florida, 1991) 146

6-12. Predicted fruit-mite-pathogen system dynamics. (a) mite
(thick solid line) and pathogen (thin solid line) population;
(b) fruit surface damage; (c) cumulative mite days (Collier
County, Florida, 1991) ......................... 147

7-1. Volume loss from rust mite damage. (a) total volume loss;
(b) volume loss for processed fruit; (c) volume loss for fresh
fruit (mu=25% at t=200) ....................... 163

7-2. Effect of mite damage on fruit growth and drop. (a) volume
change (dashed line) and number (dashdot line) (mu=0);
(b) volume change (dashed line) and number (dashdot line)
(mu=25% at t=200); (c) mean damage change due to drop
(mu=25% at t=200) ........................... 164

7-3. Volume loss from rust mite damage. (a) total volume loss;
(b) volume loss for processed fruit; (c) volume loss for fresh
fruit (mu=50% at t=200) ....................... 165






7-4. Effect of mite damage on fruit growth and drop. (a) volume
change (dashed line) and number (dashdot line) (mu=0);
(b) volume change (dashed line) and number (dashdot line)
(mu=50% at t=200); (c) mean damage change due to drop
(mu=50% at t=200) ........................... 166

7-5. Predicted volume loss from rust mite damage. (a) total volume
loss; (b) volume loss for processed fruit; (c) volume loss for
fresh fruit (mu=0% at t= 160) (Polk County, Florida, 1993) ... 167












Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

POPULATION DYNAMICS AND DAMAGE EFFECTS OF THE CITRUS RUST
MITE, PHYLLOCOPTRUTA OLEIVORA (ASHMEAD)(ACARI: ERIOPHYIDAE)


By

YUBIN YANG

AUGUST 1994


Chairperson: Dr. Jon C. Allen
Major Department: Entomology and Nematology


The citrus rust mite, Phyllocoptruta oleivora, is one of the most important

pests of citrus in Florida. Mite population dynamics and effects of mite damage on

'Hamlin' orange fruit were studied.

There was an accelerating increase in fruit surface damage in relation to

cumulative mite days. Fruit surface damage was fitted to a power function of

cumulative mite days. Fruit drop increased with increasing damage. The data

showed a slightly negative relationship between fruit size and mite damage.

Cumulative percent drop and percent diameter increase were fitted to two-variable

logistic functions of damage and time. With the increase of mean fruit surface

damage, the relative frequency distribution of fruit damage changed from an


xvii







exponential decay curve to a symmetrical unimodal curve, with the peak shifting

toward higher damage classes. The cumulative frequency distribution of fruit damage

was fitted to a two-variable logistic function of mean fruit damage and damage class.

Mite populations on fruit began to build up from early May to early June,

reached the highest levels in the rainy season (June, July, and August), and then

quickly declined. Mite populations on leaves followed the same pattern as on fruit.

The high humidity favored the epizootic development of the fungal pathogen

Hirsutella thompsonii, the major factor responsible for rapid mite population decline.

An age-structured model of the fruit-mite-pathogen system was developed.

Mean squared errors of prediction for rust mite populations on fruit in three cases

were 658.6, 306.6 and 1114.0, respectively, for a period of 5 months. High errors

were caused by high mite population densities, and a slight shift in predicted mite

population peaks as compared to the observed data.

A model was established to estimate volume loss from rust mite damage. The

model also allows us to determine volume loss for fresh fruit as well as for processed

fruit. The loss model was coupled with the population model. The coupled model

can predict: (1) mite/pathogen population trend; (2) fruit size growth; (3) fruit surface

damage; and (4) volume loss. The coupled model needs to be further tested for use

in rust mite management.


xviii












CHAPTER 1
LITERATURE REVIEW


Distribution and Production of Citrus

Citrus is thought to have originated in Southeast Asia. It is currently grown in

over 100 countries on six continents (Saunt 1990). It distributes in a belt spreading

approximately 40 latitude on each side of the Equator and is found in tropical and

sub-tropical regions where favorable soil and climatic conditions occur. The most

commercial citrus production, however, is restricted to two narrower belts in the sub-

tropics roughly between 200 and 400 N and S of the Equator (Saunt 1990). The area

planted to citrus has been estimated at 2 million hectares and present-day production

of all types at 63 million tons, of which 71 per cent are oranges, 13 per cent

mandarins, 9 per cent lemons and limes, and 7 per cent grapefruit (Saunt 1990). The

United States once led in world production but now has been overtaken by Brazil.

These two countries produce about 42 per cent of the world's citrus crop. The

majority of their citrus crop is processed, with 52 per cent in Brazil, and 66% in the

USA (Saunt 1990). In Florida, round oranges constitute 70% of the total citrus

acreage, and over 90% of the round oranges are used in processed products where

purchases of this type of fruit are usually based upon pounds of soluble solids per box

(Townsend & Abbitt 1978).






2
Origin and Distribution of the Citrus Rust Mite

The citrus rust mite (CRM), Phyllocoptruta oleivora (Ashmead) (Acari:

Eriophyidae), is thought to have originated in Southeast Asia--the indigenous habitat

of citrus (Yothers & Mason 1930, van Brussel 1975). It now occurs in almost all

citrus-growing areas in the world, including Europe, Africa, southern Asia, Australia

and Pacific Islands, North, Central and South America, and the West Indies

(Commonwealth Institute of Entomology 1970). The species probably was introduced

into many citrus-growing countries on imported fruit or planting material (van Brussel

1975), and is now considered as a serious pest of citrus in most humid regions of the

world where the crop is grown (McCoy & Albrigo 1975, Davidson & Lyon 1987).

The citrus rust mite was first reported and described in Florida by Ashmead

(1879), and for over 50 years it was the only species of eriophyid mites reported from

citrus in the world (Burditt et al. 1963). The citrus bud mite, Aceria sheldoni

(Ewing) was first reported and described from California in 1937 (Ewing 1937) and

was found in Florida in 1959 (Attiah 1959). Between 1955 and 1963, several new

species of eriophyid mites were collected from citrus around the world (Burditt et al.

1963). One of these is the pink citrus rust mite, Aculus pelekassi Keifer. This

species was first described by Keifer (1959) from specimens collected in Greece, and

was first found in Florida in 1962 in laboratory colonies of citrus rust mites (Burditt

et al. 1963) and subsequently in citrus nurseries and groves (Denmark 1963). The

name of the pink rust mite was later amended to Aculops pelekassi (Keifer).








The citrus rust mite, the citrus bud mite, and the pink citrus rust mite are the

only eriophyid species reportedly occurring on citrus in the United States. Among

them, the citrus rust mite is the most economically important. Others & Mason

(1930) proposed that the citrus rust mite was probably introduced on nursery trees

when they were first brought into Florida for propagation, and the spread of the citrus

rust mite over Florida, and probably in other citrus-growing states, was principally

through infested nursery stock. The citrus rust mite is currently one of the most

common and serious pests of citrus in Florida, Texas, Louisiana, and the costal areas

of California (Farmer's Bulletin 1950, Davidson & Lyon 1987). The citrus rust mite

is more injurious in the south-central and west coastal areas than elsewhere in Florida

(Muma 1955b).

Taxonomic History

The citrus rust mite was first mentioned and described by Ashmead (1879) as

Typhlodromus oiliioorus. However, Ashmead a year later (1880) emended his first

spelling to Typhlodromus oleivorus. According to Ewing (1923), the genus

Typhlodromus is a synonym of Phytoptus, which in turn is a synonym of Eriophyes,

consequently the rust mite had long been placed in the genus Eriophyes (Yothers &

Mason 1930). Banks (1907) was the first to mention it under the name of

Phyllocoptes oleivorus (Ashmead). In 1938, Keifer erected a new genus,

Phyllocoptruta, and since then the citrus rust mite has been called Phyllocoptruta

oleivora (Ashmead) (van Brussel 1975).








Host Preference

Citrus rust mite infests plants of genera Citrus and Fortunella (family

Rutaceae) (Commonwealth Institute of Entomology 1970). Others & Mason (1930),

who listed many citrus species and varieties grown in Florida, observed the following

order of severity of infestation: lemon > lime > citron > grapefruit > sweet

orange > Tangerine > Mandarin. They reported that the nearer varieties and

hybrids are related to a 'true' Citrus species, the more favorable these plants are for

mite development, van Brussel (1975) also observed higher overall mite populations

in grapefruit groves than in orange groves in Surinam.

Life History and Habitat

Rearing Methods

The earliest attempts to rear citrus rust mite in the laboratory were made by

Others & Mason (1930) in Florida. They used a No. 0 gelatin capsule cage for the

confinement of the mites and attached the cage to the fruit surface with melted

paraffin. The stem of the fruit was placed in a vial of water to keep the fruit in good

condition. Adult mites were transferred to fresh fruit every few days as the older

fruit began to dry. Swirski & Amitai (1958) reared citrus rust mites on the fruit of

rooted lemon branches. Mites were confined in celluloid cells 2-3cm in diameter.

This method permitted rearing several generations of mites on the same fruit. Reed et

al. (1964) used Murcott Honey orange seedlings for rearing both citrus rust mites and

pink citrus rust mites in plastic screen cages in greenhouses. A ring of lanolin was

used to confine mites within a restricted area, by dipping a warm cork borer of the








required size into hot lanolin and stamping the lanolin onto a leaf or fruit.

Reproduction

Citrus rust mite reproduction was originally thought to be entirely by

parthenogenesis, and without males (Yothers & Mason 1930). Males were first

reported and described by Keifer (1938). The mode of reproduction was later found

to be arrhenotokous parthenogenesis (a type of haplodiploidy), in which unfertilized

eggs become males and fertilized eggs become females. This was proved by the fact

that isolated virgin females produced only male offspring while mixed groups of

males and females produced both sexes (Swirski & Amitai 1958, Oldfield et al. 1970,

Jeppson et al. 1975). Sperm transfer in this and closely related species is

accomplished by means of spermatophores which the males deposit on the fruit and

leaf surfaces at a rate of about 16 per day (Oldfield et al. 1970, Oldfield 1973,

Oldfield & Newell 1973a, 1973b). Sperm viability in the spermatophore was

observed to drop by the third day and all were inviable by the fifth day. Annual

oscillations in the sex ratio of the citrus rust mite natural populations have been

reported from Israel (Swirski & Amitai 1960).

Stages and Development

The adult citrus rust mite has an elongated and wedge-shaped body about three

times as long (150-180 /m) as wide. Its color varies from light yellow to straw color

(Knapp 1983). It can be seen only with the aid of a hand lens of lOx or 20x

magnification. Due to its yellow color the mite can be seen more easily on green

leaves and fruit than on fruit already colored. The adult mite is composed of a








gnathosoma and a thanosoma which is the slender, tapering abdomen. The abdomen

is transversely striated and has the appearance of a number of rings which .

grow smaller toward the posterior end. There are usually 28 thanosomal rings

appearing on the dorsal surface, but on the ventral surface there are twice as many

(Yothers & Mason 1930). The mite has two pairs of short, anterior legs and a pair of

lobes on the posterior end which assist in movement and clinging to plant surfaces

(Yothers & Mason 1930, Knapp 1983). Egg deposition begins within a day or two

after the female reaches maturity and continues throughout her life, about 20 days

(Knapp 1983). The morning hours seem to be the time of greatest activity in egg

laying (Yothers & Mason 1930). The female lays one to two eggs a day or as many

as 20-30 eggs during her lifetime (Knapp 1983).

Immature mites undergo two molts before becoming adults. Nymphs in both

the first and second stages resemble the adult in color and shape except for their

smaller size and lack of complete ring formation.

Eggs are spherical with a smooth regular surface ranging in color from

transparent to pale translucent yellow. It is about one-fourth the size of the adult mite

(Knapp 1983). In spite of their small size, the eggs are relatively large for the size of

the female, and only one or two developed eggs occur in the abdomen at one time.

The eggs are laid, both singly and in groups, on the surface of leaves, fruit, and

young twigs (Knapp 1983). Eggs are usually found in the pits or depressions of the

surface. By far the largest percentage hatch out in the early morning. Bright, sunny,

warm mornings will cause the eggs to hatch in greater numbers, and cloudy or cool








weather retards their development (Yothers & Mason 1930).

Hubbard (1885) noted that the breeding continued throughout the year. Frost,

which was sometimes severe enough to kill adult mites, did no injury to the eggs, and

the severity of a winter had little if any effect on the prevalence of the mites during

the following summer. In droughts, however, there was some evidence that many of

the eggs dried from dessication (Hubbard 1885).

Developmental durations for egg, protonymph, deutonymph, preoviposition

period, and adult were found to be 3.05, 1.82, 1.34, 2.66, and 6.89 days in summer,

and 5.07, 4.3, 6.4, 5, and 11.3 in winter, respectively (Yothers & Mason 1930).

Bodenheimer (1951) calculated the developmental threshold for the citrus rust mite as

200C based on the data of Yothers & Mason (1930). This threshold seems to be too

high (Swirski & Amitai 1958). Swirski & Amitai (1958) reported a developmental

threshold of 9.2 C for both egg and nymphal stages. They also established

regression functions between developmental rate and temperature for both eggs and

larvae.

Hobza & Jeppson (1974) reported that the theoretical optimal temperature for

the citrus rust mite was 24.50C, and the limiting temperatures were between 17.6C

and 31.4C. They quickly pointed out that the calculated developmental threshold of

17.60C may be too high due to unfavorable fruit conditions at low temperatures

(20C), and indicated that the actual temperature threshold should be between 15 and

17.6( PC). They also found a strong linear relationship between citrus rust mite

population growth rate and humidity within the temperature range permitting growth,







8
and a strong quadratic relationship between population growth rate and temperature at

any fixed relative humidity. They developed a regression model to quantify the

relationship between population growth rate and constant conditions of temperature

and relative humidity.

Allen et al. (1994b) did the most comprehensive study on the effect of constant

temperatures on rust mite development and reproduction. They also established

equations to quantify the temperature effects on mite development and reproduction.

They calculated a developmental threshold of 110C for the citrus rust mite.

Seki (1979) reported that a developmental threshold of 11.2*C for the pink

citrus rust mite, and that no oviposition was observed at 150C.

Economic Importance

History of Economic Importance

Several years prior to 1879 in which the citrus rust mite was first reported and

described (Ashmead 1879), Florida orange growers were very much concerned about

the cause of russeted fruit. Some growers attributed it to a fungus; others to adverse

soil conditions (Yothers & Mason, 1930). According to Yothers & Mason (1930),

J.K. Gates was the first to find the mites on oranges and immediately ascribed

russeting to their presence. This discovery eventually led to the description of the

species by Ashmead (1879).

During the first 50 or so years after its first discovery, the citrus rust mite was

considered the third most injurious citrus pest in Florida, being exceeded in amount of

damage only by purple scale (Lepidosaphes beckii Newm.) and citrus whitefly








(Dialeurodes citri Ashm.) (Yothers & Mason 1930). Watson & Berger (1937) listed

citrus pests in order of importance as purple scale, rust mite, and common citrus

whitefly. This change of citrus rust mite importance obviously resulted from the

reduction in whitefly populations due to the effectiveness of several species of

parasitic fungi which attack the immature stages of the citrus whitefly (McCoy 1985).

In 1957 and 1958, the hymenopterous parasite, Aphytis lepidosaphes, was found

fortuitously in Florida for the first time (Clancy & Muma 1959). It was established

in all citrus areas in a short time and effectively controlled the purple scale

populations (Selhime & Brooks 1977). As a result, the citrus rust mite emerged as

the most important economic arthropod pest of Florida citrus, and it remains so

(Knapp 1983). According to McCoy et al. (1976a), 87% of the citrus acreage in

Florida received from 3-5 pesticidal sprays per year for citrus rust mite control at an

estimated cost of 40-50 million dollars in 1973. This estimate is probably too high.

The premier economic importance of the citrus rust mite is currently being challenged

by the citrus leafminer, Phyllocnistis citrella Stainton, which was first discovered in

late May 1993 in southern Florida (Heppner 1993a, 1993b), and is now all over

Florida citrus growing areas. This moth causes severe damage to citrus plants and

great concern among Florida citrus growers (Knapp et al. 1993).

Rust Mite Injury

Feeding and food. Hubbard (1885) reported that the food of the citrus rust

mite consisted of the essential oil that abounds in all succulent parts of the orange,

and they did not feed on chlorophyll. It was once widely believed among citrus








growers that fruit injury was the result of the puncture of oil cells, although this

apparently is incorrect (Spencer and Osbum 1950). Others & Mason (1930)

demonstrated that the epidermal cells of the fruit were damaged by citrus rust mite .

McCoy and Albrigo (1975) further confirmed that citrus rust mite can only feed on

the epidermal cell layer of leaves and fruit, since the length of its piercing chelicerae

is on the order of 7 pm which is less than the depth of one cell The diameter of the

puncture is about 0.5 1.0 im, and is thus so small as to raise the question of

whether one puncture wound results in cell death or if more than one puncture in

some time period is required to kill an epidermal cell (Allen et al. 1992). This

question becomes potentially important when we attempt to construct models which

couple the mite feeding to fruit or leaf damage and loss.

Injury to leaves. Visible leaf injury is less common than fruit injury.

However, leaf injury can occasionally be severe (McCoy 1976). Injury to the upper

leaf surface is confined to epidermal cells and appears as small brownish spots or

blotches resembling the russetingg" condition common to immature fruit (Albrigo and

Mccoy 1974); severe injury can cause the upper leaf surface to lose its glossy

character taking on a dull bronze-like color and a rough texture that can be detected

by touch (Hubbard 1885, Yothers & Mason 1930). In many cases of severe injury,

localized degreening of the upper leaf cuticle may also develop, causing these

degreened areas to become a yellowish color similar to the condition occurring on

immature fruit (McCoy and Albrigo 1975). Injury to the lower leaf surface is

confined to epidermal cells which include the stomatal guard cells (Albrigo and







11

McCoy 1974). Lower surfaces often show 'leaf mesophyll collapse' appearing first as

yellow degreened patches and later as necrotic spots (Thompson 1946, Albrigo and

McCoy 1974). However, lower leaf surface injury frequently stops with a browning

of the epidermal cells (Yothers and Mason 1930, Griffiths and Thompson 1957).

Albrigo et al. (1987) and Achor et al. (1991) reported that upper leaf surface lesions

on 'Sunburst' mandarin by rust mite are more severe than those on other citrus

cultivars.

Injury to fruit. Damage to citrus fruit caused by citrus rust mites normally

affects only the surface layer of epidermal cells on the fruit (McCoy & Albrigo

1975). Fruit surface injury differs, depending on time of injury and variety of fruit

injured (Griffiths & Thompson 1957). In the case of grapefruit and lemons or limes,

injury during the early months of the fruit's growth will cause a silvering of the peel

and, if severe, may result in a condition knows as "sharkskin". When this occurs

early enough fruit size is reduced. Such fruit will not take a sheen when polished. In

the case of oranges, early injury results in a brown cracking and scarring of the

surface. When the fruit is mature, this injury is called russetingg". Late injury takes

a high polish and is called "bronzing" (Griffiths & Thompson 1957). Early rust mite

injury was observed more on early and mid-season fruit than on the late varieties

(Thompson 1937). The terms "russet", "russetting", or "discoloration" are currently

referred to fruit surface damage regardless of the time the damage occurs.

A typical aspect of rust mite injury on an infested tree is that only some of the

fruit are heavily attacked, whereas others are damaged only slightly or not at all.






12
Even on a single fruit, the rust mite tends to infest only a portion of the fruit, leaving

the rest undamaged. This partial russeting on fruit also occurs on leaves, and the

mite spatial distribution is consistent with these damage patterns. Rust mites on citrus

fruit tend to avoid the bright sunlit area of a fruit in the direct solar beam where the

temperature may reach 45*C. The formation of rings of high mite density around the

solar exposed area often leads to halo damage patterns (russet) around these areas

(Hubbard 1885, Yothers and Mason 1930, Albrigo and McCoy 1974, Van Brussel

1975), while in the center of the solar hot-spot not a single mite can be found (Allen

and McCoy 1979). The rust mites are usually present in great abundance from one

to two weeks before extensive injury appears (Yothers and Mason 1930).

Injury to young twigs. Others & Mason (1930) observed that rust mites were

also found on the branches just after they had become reasonably mature, in some

cases so abundantly as to cause russeting on the bark. But high mite populations on

branches are seldom seen, and possible mite injury to branches is not of much

concern to growers.

Leaf injury and greasy spot. Griffiths & Thompson (1957) suspected the

possible effects of rust mite injury to the leaves on the development of greasy spot, a

disease caused by the fungus, Mycosphaerella citri Whiteside. In several field

experiments, van Brussel (1975) demonstrated that rust mite injury to leaves was

correlated with increasing severity of greasy spot infections.








Economic Loss

Although the citrus rust mite causes injuries to fruit, leaves, branches, and

may even be related to greasy spot infections, its most economic importance is due to

fruit surface damage. Heavy infestation of rust mites causes not only fruit surface

discoloration but also increased fruit drop and size reduction, with an associated loss

in fruit quality and yield (Yothers 1918, Yothers & Miller 1934, McCoy & Albrigo

1975, Allen 1976, 1978, 1979, McCoy et al. 1976). This section reviews previous

studies on economic effects of mite damage to leaves and fruit.

Leaf drop and size in relation to damage. The literature presents conflicting

reports as to whether citrus rust mite injury to leaves, even when severe, will cause

defoliation. According to Hubbard (1885), leaves never drop no matter how severe

the rust mite attack, but growth and vitality of the tree can be affected. This was

especially noticeable in young trees, which were frequently overrun by the rust mite

in early summer, and during the remainder of the year made little progress (Hubbard

1885). According to Griffiths and Thompson (1957), however, high populations on

leaves and green twigs can cause a general defoliation similar to that caused by citrus

red mite, particularly during periods of dry, windy weather in late fall, winter, and

early spring. McCoy (1976) reported that the overall defoliation of both healthy and

injured leaves was 9.5 %, being significantly greater on summer flush. McCoy

(1976) further indicated that citrus rust mite injury to the lower leaf surface appeared

to be associated with defoliation. Increased water loss through the destruction of

epidermal cells of the lower leaf surface may possibly be enough, particularly during









the dry periods, to cause leaf abscission (McCoy 1976). McCoy (1976) further

suggested that leaf abscission may not be severe enough to affect tree vigor and

subsequent yield of 'Valencia' orange.

Others & Mason (1930) noted that in some instances, rust mites were so

abundant in the spring that the size of the leaves was reduced, and they further

commented that the devitalization caused by the presence of thousands of rust mites

on citrus foliage was much greater than the average grower realized. Unfortunately,

this lack of attention to leaf damage is still the case and most research has been

focused on fruit.

Fruit damage in relation to mite density. Allen (1976) made the first attempt

to establish a quantitative relationship between fruit surface damage and mite density

over the fruit growth season. The study showed that accumulated mite days (area

under the mite population graph) was almost linearly related to accumulated percent

damage on Valencia orange fruit surface. The study also indicated that damage rate

(percent per mite per day) was an increasing function of fruit age. The damage rate

on mature fruit in winter is higher than on young fruit in spring by about a factor of

10. The maximum damage rate for 'Valencia' oranges was found to be 0.000115

(proportion mite' cm'2 d') (Allen 1976). A detailed review can be found in Allen et

al. (1994a).

Fruit growth in relation to damage. Hubbard (1885) noted that fruit heavily

damaged by citrus rust mite were smaller than undamaged fruit. Others (1918)

found that "russet' grade (damaged) oranges were 12.5% smaller than undamaged









oranges prior to shipment. Allen (1979) made the first attempt to establish a cause

and effect relationship between citrus rust mite damage and small fruit size at harvest.

The study showed that damaged 'Duncan' grapefruit with the same initial diameter

grew slower, and their final diameter was less than that for undamaged fruit. A

detailed review can be found in Allen et al. (1994a).

Fruit drop in relation to damage. Ismail (1971) showed that after picking,

fruit were found to lose water faster and abscise more readily if they had rust mite

damage. Ismail (1971) further demonstrated that rust mite damaged fruit lost more

than twice as much fresh weight as did sound, green fruit, and most of the loss in

fresh weight was due to moisture loss. Allen (1978) showed that water loss rate for

on-tree 'Valencia' oranges was about 3 times higher for rust mite-damaged fruit than

for undamaged fruit regardless of fruit age, sun exposure or type of damage. Fruit

drop were increased by rust mite damage on 'Valencia' and 'Pineapple' oranges and

also 'Duncan' grapefruit. Fruit with the highest amount of damage showed the

highest drop and those with no damage showed the lowest drop in all 3 varieties.

Since fruit drop is cumulative, the earliest damage can have the greatest total effect.

A model has been developed to quantify the effect of damage on fruit drop (Allen

1978, Allen et al. 1994a).

Fruit internal quality in relation to damage. It was believed that russeted fruit

was sweeter than undamaged fruit. Chemical analyses of undamaged and russetted

oranges indicated that russetted fruit was not so sweet as the undamaged fruit, and

that rust mite injury retarded the ripening to a considerable extent (Yothers & Mason







16
1930). The sweeter taste, according to Yothers (1918) and Yothers & Mason (1930),

probably occurred because russeted fruit were not sold before the holidays, and had

ample opportunity to fully ripen so no russet fruit was ever sour. McCoy et al.

(1976) showed that at harvest, fruit with localized and extensive surface bronzing

(damage) and peel shrinkage had a lower juice volume, higher soluble solids, higher

acids, and higher concentrations of acetaldehyde and ethanol than normal fruit. Allen

(1979) also reached similar conclusions, indicating that weight per fruit at harvest was

negatively correlated with damage by citrus rust mite for 'Valencia' and 'Pineapple'

oranges and for 'Duncan' grapefruit. For all 3 varieties, soluble solids and percent of

acid were positively correlated with citrus rust mite damage (Allen 1979). Similar

results have also been reported on the pink citrus rust mite Aculops pelekassi (Kato

1977, Tono et al. 1978).

Calculation of economic loss from rust mite damage. Economic loss caused by

rust mite damage includes three major components: (1) fruit surface damage; (2)

reduced fruit growth; and (3) increased fruit drop. Models combining the three

aspects of economic loss have been developed by Allen et al. (1994a) for 'Valencia'

orange.

Behavior and Ecology

Behavior and Distribution

Citrus rust mites tend to aggregate within trees and on individual fruit as a

result of environmental factors, notably sunlight and temperature. Rust mites can

endure hot sun but tend to avoid direct sunlight. Shaded groves and the shaded side








of fruit do not usually exhibit mite densities as high as semishade areas. Hubbard

(1885) observed that although the rust mite cannot long endure the direct light and

heat of the sun, they also avoid dark shade. As a result of this behavior, a rust ring

might be formed on the fruit between the proportion of the orange most directly

exposed to the sun's rays and that in the densest shadow. Hubbard (1885) also

observed that the proportion of the fruit facing directly to the sun frequently presented

a bright spot, and the opposite side an area of lighter bronze, with less sharply

defined boundaries. A laboratory observation made by Yothers & Mason (1930)

showed that rust mites tended to aggregate to the light during the day and scatter

during the night, but mites appeared to avoid direct sunlight. A similar phenomenon

has also been observed by later researchers (Albrigo & McCoy 1974, van Brussel

1975, Allen & McCoy 1979, Allen & Stamper 1979). Allen & Syvertsen (1979)

reported that a model of fruit temperature in relation to solar radiation indicated

strong temperature and water vapor concentration deficit gradients on fruit surface.

Therefore, mite distribution on the fruit surface might be a response to differences in

temperature and humidity on different parts of the fruit surface. It was also observed

that the degree of aggregation generally increases with mite density (Hall et al. 1991).

Aggregation generally complicates sampling, and a variety of sampling methods have

been used by researchers to estimate levels of citrus rust mites (Yothers & Miller

1934, Pratt 1957, Allen 1976, Bullock 1981, Knapp et al. 1982, Childers & Selhime

1983, Pefia & Baranowski 1990, Hall et al. 1991, Rogers 1992, Rogers et al. 1993).

McCoy (1979) reported that there was a tendency for the rust mite to migrate









to newly formed stem growth and the under surface of leaves near the base of the

spring flush in late-march mainly by crawling, and that development on spring flush

during April is generally slow but more rapid than corresponding development on old

(previous year) flush. Dean (1959b) reported that citrus rust mites on grapefruit

leaves were more numerous on the east as well as the north side of the tree, being

most numerous in the northeast quadrant.

Population Dynamics vs. Season

The seasonal abundance of the citrus rust mite has been discussed by numerous

researchers. In Florida, rust mite is present on citrus trees throughout the year

(Yothers & Mason 1930). The lowest population occurs in January and February.

During March and April their numbers increase rapidly. During May and the first

part of June the rate of increase is much more rapid than at any other time of the

year. The period of maximum infestation usually occurs during late June or July or

even August, well after the beginning of rainy season. During the later part of the

rainy season, mite populations diminish almost to the point of extinction (Hubbard

1885, Yothers and Mason 1930, Pratt 1957, Simanton 1960). A second but much

smaller population peak usually occurs between November and early January (Yothers

and Mason, Pratt 1957, Knapp 1983). After this they very slowly and gradually

increase until the following June (Pratt 1957, Simanton 1960). The period of

maximum infestation occurs first on lemon and then on grapefruit and about one

month later on orange (Yothers & Mason, 1930).

Rust mite population is usually higher on fruit than on leaves, and citrus rust









mite prefers the lower leaf surface to the upper surface (Yothers & Mason 1930,

Thompson 1937, Swirski 1962).

Although the seasonal abundance of citrus rust mite appears to follow a

distinct patten of two population peaks, weather, natural enemies, and particularly

horticultural practices will cause atypical population fluctuations to the extent that

damage may occur any time of the year (McCoy et al. 1976, McCoy 1979). McCoy

et al. (1976) found typical mite population dynamics under unsprayed conditions;

however, peak densities varied in time and intensity under sprayed conditions.

Population Dynamics vs Climatic Factors

For many years it had been thought by citrus growers that heavy rains of

summer were directly responsible for the scarcity of rust mites during the rainy

season. They had thought that the heavy rains washed the mites from the foliage and

fruit. But Yothers & Mason (1930) reported that rust mites seemed to have the power

of sticking to the foliage in spite of the rains, although heavy driving rains did wash a

few mites from the foliage and fruit. This diminution in numbers was not appreciable

and had little or no bearing either on methods of control or on subsequent abundance

of the mites. This scarcity of rust mites was later attributed to the fungus disease,

Hirsutella thompsonii (Fisher et al. 1949, McCoy & Kanavel 1969).

Humid weather, as measured by the number of hours at the dew point

temperature, is favorable to the increase in rust mite population. Maximum

population levels are reached during the summer rainy season, and the winter period

of moderate rain, fog, and heavy dew. Dean (1959a) reported that rust mite









populations increased particularly during periods of high relative humidity while

periods of low relative humidity and very windy weather seemed unfavorable. Rust

mites increased generally following periods of greater precipitation, which appeared to

be associated with higher humidity, and Dean (1959a) further stated that relative

humidity appeared to be the most important weather factor influencing citrus rust mite

populations.

In Surinam, van Brussel (1975) reported that during rainy season, counts of

rust mites were low, and mite population increased at the beginning of the dry

seasons. Maximum counts were reached in 4-5 weeks, and then dropped to a low

level in a similar period. Low mite counts during the rainy seasons were not entirely

attributable to the entomophagous fungus H. thompsonii, despite the favorable moist

conditions for fungal growth. They were neither the result of washing-off by rain,

nor of drowning (the adult can survive 12 hours in water). They seemed to be the

result of larval mortality, which increased when larvae were wetted and a water film

was present on the food plant. A moist substrate seemed to interfere with molting,

and rain also interfered in oviposition since rust mites avoided egg-laying on wetted

parts of the food plants. The part of fruit exposed directly to sunlight were less

attractive to the rust mite than others, but these areas were also exposed to dew

condensation at night.

Others & Mason (1930) reported that although the freeze in February 1917

killed more than 99% of the mites in almost all Florida citrus groves due to low

temperature and heavy infestation, the only results of the reduction of mites by the








freeze in February was the postponement of the time of maximum infestation for a

about one month or six weeks. Others & Mason (1930) also reported that the

drought of the spring of 1922 effectively prevented mite population growth.

Mite-Pathogen Interaction

H. thompsonii Fisher (Fisher 1950a), is a specific fungal pathogen of Acari,

particularly eriophyid and tetranychid mites inhabiting citrus and other plants

throughout the world. It is recognized as the most important natural enemy attacking

citrus rust mite in Florida (Speare & Yothers 1924, Yothers & Mason 1930, Fisher et

al. 1949, Muma 1955b, 1958, McCoy & Kanavel 1969, McCoy et al 1976, Lipa

1971, McCoy 1981).

Spears and Yothers (1924), who studied the citrus rust mite in citrus orchards

in Florida, were the first to suggest that the marked decrease in mite numbers--a

phenomenon which occurred annually with the onset of the rainy season at the end of

June or early July was probably due to a fungal disease. High mite populations per

grapefruit in the hundred thousands dropped to almost zero by the end of September.

Spears and Yothers (1924) observed hyphal bodies in abnormally dark-colored

sluggish mites. Furthermore they noticed mycelia on dead mites with hyphae

protruding from the cadavers. It was also noted that rust mites were more abundant

on trees sprayed with fungicides (copper sprays or compounds) than on unsprayed

trees (Winston et al. 1923), and the use of such fungicides evidently eliminated the

fungus disease which, under normal conditions, would have attacked the rust mites.

Others & Mason (1930), in reporting similar data, concluded that the reduction in








mite numbers could not have been the result of food scarcity, since on average only

half the untreated fruit were severely infested with rust mites. Fisher et al. (1949)

tentatively identified the fungus, which was regularly associated with dead mites as a

Hirsutella species, and later described as H. thompsonii (Fisher 1950a). Muma

(1955b) found that about 70% of the mites were infected with H. thompsonii, and that

the severity and duration of the fungal outbreak was proportional to mite density

(Muma 1958). Both Fisher et al. (1949) and Burditt et al. (1963) described color

changes of the citrus rust mite infected with H. thompsonii. McCoy and Kanavel

(1969) isolated the fungus on an artificial medium and confirmed its pathogenicity

against citrus rust mite. The biology and pathogenicity of H. thompsonii were further

studied by McCoy (1978a), Gerson et al. (1979), and Kenneth et al. (1979).

Both of the two nymphal stages and the adult can be infected by the pathogen

under field conditions (personal communication, C. W. McCoy), and the infectivity is

dependent on the presence of free water and high humidity (McCoy 1978a, Gerson et

al. 1979, Kenneth et al. 1979). In Florida, epizootics caused by interaction of

weather, mite and fungus occur regularly in summer, and diseased mites can be found

on fruit and foliage throughout the year (McCoy 1978a, McCoy 1981). Epizootics

lasting 2-3 weeks develop regularly in summer, and elimination of the mites results in

a high fungal residue that usually prevents further mite build-up during the fall and

winter (McCoy 1981).

H. thompsonii produces a conidium on conidiophores found on an external

mycelium outside the host on the plant substrate. Infection appears to be highest on a







23
substrate with free water; however, it will also occur at 90 to 100% relative humidity

(McCoy 1978). Once inside the host, the hyphae form a ramifying growth within the

hemocoel and after death erupt through the host cuticle onto the plant surface where

they reproduce asexually. It takes less than 4 hours for a spore to penetrate the mite

cuticle and about 2 days for the total infection process to be completed to sporulation

at 26-27C (McCoy 1978, Gerson et al. 1979, Kenneth et al. 1979).

H. thompsonii has been developed as a mycoacaricide for the control of the

citrus rust mite by workers in the USA (McCoy and Selhime 1977, McCoy 1978a,

Mccoy and Couch 1978, McCoy et al. 1978, McCoy 1981, McCoy & Couch 1982,

van Winkelhoff & McCoy 1984), Surinam (Van Brussel 1975), and China (Yen

1974), but is not presently available commercially.

In Florida, application of fragmented mycelia of H. thompsonii resulted in

decreased mite numbers on the leaves and increased rate of mite infection at 1 week

post-treatment, and mite populations remained at low levels for 10-14 weeks (McCoy

et al. 1971, McCoy & Selhime 1977, McCoy 1978). These studies also showed that

the disease spread rapidly to untreated areas once the fungal epizootic reached a peak

in treated trees (McCoy 1978a). In Texas, different concentrations of Hirsutella

mycelia gave 40% infection of citrus rust mites after 6 days under laboratory

conditions (Villalon & Dean 1974).

In Surinam, van Brussel (1975) achieved control of low citrus rust mite

populations by applying a mycelial suspension of H. thompsonii at a dosage of 0.05 to

1 g/liter.







24
In Chekiang Province, China, the application of H. thompsonii for citrus rust

mite resulted in 90% mortality after 3 days (Yen 1974).

The reliability of this control, however, appears to be related to the effect of

weather on the survival of the mycelia during the 48 h after application. Applications

applied on cloudy days or in the late afternoon or early evening gave best results

(McCoy 1978a).

In addition to its potential as a mycoacaricide, H. thompsonii is a great

resource as a natural enemy of the citrus rust mite in groves where fruit is grown for

processing (McCoy et al. 1976a, McCoy et al. 1976b). McCoy (1978b) reported that

the use of oil as a selective fungicide, and the maintenance of higher citrus rust mite

densities in the summer significantly increased the natural control of citrus rust mite

by the parasitic fungus H. thompsonii without greatly affecting external fruit quality.

The seasonal incidence of disease in mite populations was significantly higher and

more effective in the unsprayed plots where citrus rust mite populations were

maintained at high densities (McCoy 1978b).

Similar effects by H. thompsonii to the blueberry bud mite (Acalitus vaccinii)

were reported (Baker & Neunzig 1968)

Management of Citrus Rust Mite

Chemical Control

Pesticides. Before 1957, sulfur and lime-sulfur were the only materials used

in Florida to control citrus rust mite (Hubbard 1885, Johnson 1961). Fisher (1957)

reported that zineb (zinc ethylene-bis-dithiocarbamate) very effectively controlled








russeting of citrus fruit. Johnson et al. (1957) showed that zineb and maneb

(manganese ethylene-bis-dithiocarbamate) controlled citrus rust mite. Currently

pesticides used to control citrus rust mite includes Petroleum oil, Kelthane, Ethion,

Agrimek, and Vendex (Childers & Selhime 1983, Knapp 1992).

Fungicides vs. H. thompsonii. Winston et al. (1923) first reported that citrus

rust mite was more abundant on copper sprayed citrus than on unsprayed citrus.

Others & Mason (1930) also reported that rust mites were more abundant following

copper sprays than where these sprays were omitted. Thompson (1939) reached the

same conclusion, especially if mites are present in small numbers at the time the

spray was applied. Griffiths & Fisher (1949, 1950) further demonstrated that copper

and zinc containing sprays were reducing the number of H. thompsonii, the

unsprayed controls had the lowest numbers of rust mites and the zinc and copper plots

had the highest numbers of rust mite. However, Lye et al. (1990) reported that

copper sprays, applied when the mite population started to increase, slightly reduced

mite populations in most of the sampling dates, but they did not examine the possible

adverse effect of copper on H. thompsonii.

Cultural Control

Hubbard (1885) observed that fruit were less liable to rust on low lands

compared to high lands and that groves planted upon moist, rich hammock or clay

soils, as a rule, produced fruit with less damage than those on high, sandy pine lands.

This result was commonly attributed to the abundance of moisture in low ground; but

it may be more directly due to the denser shade afforded by a more vigorous foliage








and reduced radiation from a darker soil. Townsend & Abbitt (1978) reported that

the east coast recorded the lowest rust mite activity and the ridge and west coast area

the highest. Bodenheimer (1951) observed that groves planted on wide spacings were

heavily attacked, especially young groves. It was generally believed that the citrus

rust mite is ordinarily less abundant on citrus trees growing in a cover crop than in

groves without a cover crop. One theory is that parasites, and especially the fungal

pathogen H. thompsonii flourish under humid conditions and that the relative humidity

in a grove in cover crop is higher than in one kept clean-cultivated. But Osburn &

Mathis (1944) observed no difference in rust mite infestation between trees growing

under these two conditions; however there were very small differences between the

temperatures and humidities recorded under the two treatments. Muma (1961)

reached similar conclusions. Cultural control methods have not been extensively used

for mite control.

Biological Control

Predators and parasitoids. The strawberry mite, Agistemus floridanus

Gonzalez, was found to feed and complete its life cycle on at least four economically

injurious pests of citrus, the citrus rust mite, Phyllocoptruta oleivora, the Texas citrus

mite, Eutetranychus banksi (McG.), the cloudy-winged whitefly, Dialeurodes citrifolii

(Morgan), and the six-spotted mite, Eotetranychus sexmaculatus (Riley)(Muma &

Selhime 1971). Maximum populations normally occur during the winter and spring

but can occur during the summer and fall. Muma & Selhime (1971) noted that the

strawberry mite does not appear to have a biological control potential on citrus in






27
Florida. Other predator species reportedly attacking the citrus rust mite include adult

mealywing (Coniopteryx vicina Hagen) (Muma 1955b, Muma 1967), adult lady beetle

Stethorus nanus Lac. (Yothers & Mason 1930), black hunter thrips (Leptothrips mali

(Fitch) (Muma 1955a), the immature stage of a cecidomyid fly (Hubbard 1883,

Others & Mason 1930), syrphid flies and predaceous thrips (Aleurodothrips

fasciapennis) (Watson & Berger 1937). McCoy (1985) reported a new phytoseiid,

Euseius mesembrinus, which feeds on citrus rust mite. No internal parasite has ever

been found attacking the citrus rust mite (Yothers & Mason 1930). It is generally

believed that predators and parasitoids can not effectively control the citrus rust mite.

Pathogens. Except for the fungal pathogen H. thompsonii, no other pathogens

have been reported to attack the citrus rust mite. The parasitic fungus, H. thompsonii

Fisher, was the only significant natural enemy influencing citrus rust mite populations

(Spear & Yothers 1924, Yothers & Mason 1930, Fisher et al. 1949, Muma 1955,

McCoy & Kanavel 1969, van Brussel 1975, Gerson et al. 1979, Kenneth et al. 1979).

Integrated Control

Others (1918) reported that there was a very significant reduction in fruit

yield between sprayed and unsprayed plots from 1913 to 1915. But in a three year

study, Griffths (1951) found no significant yield differences in yield and internal

quality between sprayed and unsprayed groves, and the scales and citrus red mites

were less prevalent on the unsprayed grove. McCoy et al. (1976a, 1976b) reported

that the injury threshold for citrus rust mite was far above the current spray threshold,

medium oil spray was less detrimental than copper to the parasitic fungus of the citrus








rust mite and is preferable for greasy spot control in integrated systems. McCoy et

al. (1976a, 1976 b) further reported that the parasitic fungus, H. thompsonii, was

more effective in integrated systems where citrus rust mite populations were

maintained at high densities.

Survey Methodology

Various methods have been developed to estimate mite population density

(Yothers 1934, Turner 1975, Allen 1976, Hall et al. 1991, Rogers 1992, Rogers et

al. 1993). A hand lens is a very common instrument for estimating mite populations.

Those used usually have lOx or 20x magnification. With lOx magnification, only

immatures and adults can be seen; with 20x magnification, eggs, immatures, adults,

and visibly diseased mites are observable. An improvement made by Allen (1976) is

to mount a 10x or 20x magnifying lens over a piece of clear plastic upon which a cm2

grid has been etched. The grid is divided into 25 equal subdivisions, each having an

area of 4 mm2. All the mites under the grid or subdivisions are counted. This lens is

typically used for detailed studies. The most commonly used methods for quick

commercial scouting include the percent infested lens field (Yothers 1934, Knapp

1983) and the HB coding system (Rogers 1992, Rogers et al. 1993).

Study Objective and Methodology

Previous studies have made tremendous contributions to understanding the

citrus rust mite population system, and to the improved practices in rust mite control

(McCoy 1976a, 1976b, Allen 1980, 1981, Knapp 1983, Hall et al. 1991, Anonymous

1993, Rogers et al. 1993). As this review indicates, excellent quantitative studies








have been conducted on 'Valencia' and 'Pineapple' oranges and grapefruit (Allen

1976, 1977, 1978, 1979, 1980, 1981, Allen & Stamper 1979, Hall et al. 1991, Allen

et al. 1994). My study will be an extension of the quantitative studies by Allen, and

will be mainly concentrated on 'Hamlin' orange, especially on fruit. The overall

objective is to develop a system for predicting CRM populations and evaluating

resulting damage or loss which can help growers make the best control decision with

a reduction in control costs. In order to achieve this objective, my approach was to

design a general framework for the proposed system, study the individual

components, and finally incorporate the individual components into an interacting and

cohesive entity. There are two major components in the system: (1) damage

dynamics and (2) rust mite population dynamics. The damage dynamics component

includes four aspects of rust mite damage: (a) relationship between mite population

density and fruit surface damage; (b) frequency distribution of mite damage on fruit in

a grove; (c) relationship between fruit surface damage and fruit drop; (d) relationship

between fruit surface damage and fruit growth. This information will enable us to

determine quantitatively the pest status of the citrus rust mite. In practical citrus

production, pesticide application decisions require reliable prediction of potential mite

population trends and resulting damage. The rust mite population dynamics model

would help to predict short-term mite population trends. The major biological factors

affecting mite population dynamics are probably the fungal pathogen H. thompsonii

and undamaged fruit surface. The major climatic factors are probably temperature,

humidity, and rainfall. These factors will be included in the mite population








dynamics component.

By combining damage dynamics and mite population dynamics, one will be

able to (1) estimate total volume and value loss from rust mite damage; (2) predict

mite population trend; and (3) predict potential mite damage and volume/value loss.

These results will help growers to make necessary mite control decisions.

The following chapters report major results of my studies. Each chapter starts

with a brief statement of the problem and a statement of a specific objective,

continues on materials and methods, and then results and discussion. The last chapter

is a summary of major results from my studies.











CHAPTER 2
RELATIONSHIP BETWEEN MITE POPULATION
DENSITY AND FRUIT DAMAGE


Statement of the Problem and Study Objective


Predicting the dynamics of a crop-pest system is an important component of a

pest management program. In order to achieve this objective, we should at least

obtain the following information: 1) population dynamics (population prediction); 2)

damage dynamics (damage prediction); 3) yield loss (loss prediction). The citrus rust

mite, Phyllocoptruta oleivora (Acari: Eriophyidae), infests fruit, leaves, and young

twigs of all citrus species and varieties. It is a serious pest of citrus in Florida

(Knapp 1983), and most humid regions of the world (Davison & Lyon 1987). Its

economic importance is mainly due to damage to the fruit surface through extensive

feeding (McCoy & Albrigo 1975). Discolored fruit have less market value.

Furthermore, highly damaged fruit have a smaller growth rate and a higher drop rate,

if damage occurs early in the fruit growing season (Allen 1978, 1979, Yang et al.

1994). Mathematical models have already been established to relate fruit surface

damage to yield loss (Allen 1978, 1979, Yang et al. 1994). A study was conducted

to relate mite population density to rust mite damage on 'Valencia' orange fruit (Allen

1976). The current study was undertaken to determine a quantitative relationship







32
between population dynamics of citrus rust mite and damage to 'Hamlin' orange fruit,

which will be used as a damage prediction model of the mite IPM system.

Materials and Methods

Mite Damage

This study consists of six similar field studies, five of which were carried out

at a research citrus grove of the University of Florida Horticultural Sciences

Department, in Alachua County, FL., and the other at a commercial citrus grove in

Polk County, FL.

Studies 1-5 were located at the research grove consisted of an area of about 2

acres, with 8-yr-old 'Hamlin' orange trees. Eight rows of trees ran from south to

north, with each row consisting of 14 trees. The sampling area consisted of the six

central rows of the study plot. The grove was well- maintained, and was irrigated by

a drip irrigation system as needed. A petroleum oil spray was applied on 14 July

1993 to control citrus rust mites, causing a 56% mite mortality by July 16.

Study 6 was located at the commercial citrus grove in Polk County. The study

plot consisted of an area of about 5 acres, with eight rows of trees running from south

to north, with each row consisting of about 35 trees, with 4-yr-old 'Hamlin' orange

trees. The grove was also well-maintained. Irrigation was by overhead sprinklers.

A nutritional spray was applied on 12 June 1993, but the spray didn't have much

effect on citrus rust mite populations. Sampling plans for the six studies were as

follows:








Study 1. This study was designed to elucidate the relationship between mite

density and fruit surface damage at the grove level. Twenty five trees were randomly

selected, six fruit from each tree were then selected and tagged, a total of 150 fruit.

Fruit were chosen so that they were approximately evenly spaced around the tree.

The study period was from 8 May to 11 December 1992.

Study 2.3.4. Studies 2, 3, 4 were designed to determine the possible effect of

fruit maturity on mite damage rate. They were conducted in the same grove as in

study 1 but on different fruit. In each of these three studies, fruit already with low

mite populations were specifically (not randomly) chosen and tagged. Mite population

density and fruit surface damage were estimated until mite populations declined to a

very low level. The duration and sample size for each of the studies were as follows:

17 June to 14 August 1992 (study 2: n=30); 10 July to 11 September 1992 (study 3:

n=45); 4 September to 11 December 1992 (study 4: n=40).

Study 5. To obtain corroborating information on mite damage rate at the

grove level, a similar study was conducted from 24 May to 5 November 1993 in the

same grove as for the previous four studies. Thirty trees were randomly selected, six

fruit from each tree were then selected and tagged, for a total of 180 fruit. Fruit

were chosen so that they were evenly spaced around the tree.

Study 6. This study was designed to determine possible effects of tree age and

location on damage rate. It was conducted at the commercial citrus grove. The

sampling area was located at the center of the study plot. Twenty five trees were

randomly selected from each of the central 6 rows at every sampling, with one









fruitfrom each tree, for a total of 150 fruit. The study was conducted from 28 May

to 17 Nov. 1993.

In all the six studies, the sampling interval was 1-3 times a week. Rust mite

population density was determined with the help of a 20x hand lens mounted over a

piece of clear plastic upon which a one cm2 grid had been etched. The grid was

divided into 25 equal subdivisions, each having an area of 4 mm2. Only mites within

the middle 4 squares were counted, for a total area of 4*4 (i.e. 16 mm2) per count.

In the study at the research citrus grove, four counts were made for each fruit (i.e. a

total of 4*4*4=64 mm2 fruit surface area), with one count from each quadrant of the

fruit. In the study at the commercial citrus grove, eight counts were made for each

fruit (i.e. a total of 8*4*4=128 mm2 fruit surface area), with two counts from each

quadrant. Mite density was converted to mites/cm2 for data analysis. Fruit surface

damage was estimated visually at each sampling date. The method for damage

estimation was to visually examine the four quadrants of a damaged fruit, and then

estimate the percent damaged surface area. A comparative study by Allen (personal

communication) indicated that average variation in damage estimation for the same

person and among different people was about 5-10%. Allen's comparative study also

showed that this variation decreased with experience and with the increase in sample

size. Damage estimation usually is more accurate in the cases of both low and high

surface damage, and less accurate in the case of intermediate surface damage. This is

because of the nonlinear response of human eyes to object surface.








Fruit Growth

As part of the attempt to determine the possible effects of fruit maturity on

mite damage rate, measurement of fruit growth was conducted at the research grove

from 8 May 1992 to 17 February 1993. Fruit surface area growth was considered as

an indicator of fruit maturity. At the beginning of fruit growing season in early

spring, six fruit from each of the 25 tagged trees in study 1 were randomly selected

and tagged, a total of 150 fruit. Fruit were chosen so that they were about evenly

spaced around the tree. Fruit equatorial circumference was measured with a flexible

measuring tape. Measurements were taken every one to two weeks. These fruit were

kept from mite damage by applying abamectin (Agrimek, MSD Agvet, Merk & Co.,

Inc.) when mite populations on the fruit were high. Fruit with high mite populations

were dipped into a 1:5000 Agrimek solution twice during the study period: once on

16 July 1992, and again on 7 August 1992. A summary of all the experimental

designs can be found in Table 2-1.

Data Analysis

Damage (Damage Rate). To avoid excessive use of symbols, the same symbol

in different equations might have different meanings and values. Mite population

density was converted to mites/cm2. Since eggs were unlikely to do any damage to

the fruit, mite-days were calculated based on the nymphal and adult mite density.

The formula for calculating mite days is: Mite days = (Mean mite density between

two consecutive samplings) (Sampling interval). Working on 'Valencia' oranges,








Table 2-1. Summary of experimental designs.

Study Location Duration No. fruit Sampling

1 Alachua May 08-Dec 11, 1992 150 Random TP
2 Alachua Jun 17-Aug 14, 1992 30 Selectedb
3 Alachua Jul 10-Sep 11, 1992 45 Selected
4 Alachua Sep 04-Dec 11, 1992 40 Selected
5 Alachua May 24-Nov 05, 1993 180 Random T
6 Polk May 08-Nov 17, 1993 150 RandomW

Fruit Growth Alachua 08 May 1992-17 Feb 1993 150 Random T

* Fruit were randomly selected and tagged at the beginning of the study, and
subsequent sampling were conducted on the same tagged fruit.
b Fruit were specifically selected so that they all had moderately low mite populations
which would increase in a short period of time and cause fruit damage at about the
same time.
' Fruit were randomly selected at every sampling date.






37
Allen (1976) started with the assumption that the rate of damage was proportional to

mite density, i.e.


d = am(t) 2-1
dt

where y is cumulative % damage; m(t) is mite density, and a is instantaneous


damage rate per mite per day. If a is constant, equation 2-1 implies that dy is a
dt


linear function of mite density. Equation 2-1 is equivalent to


t
y =afm(t)dt
0 2-2

or

y = ax(t)

where x(t) = cumulative mite days (area under the mite population graph) at time t .

Data in Allen (1976) suggested that a is probably not constant (a function of time). I

adopted a pragmatic approach here of fitting the data to a power curve of the form


y = exp(a)xb 2-3

where y = cumulative percent damage; x = cumulative mite days; a and b =

constants. Equation 2-3 fitted the data well. By taking the derivative of equation 2-3

we obtain the instantaneous damage rate per mite day


dy = exp(a)bxb-1 2-4
dx









where y is equivalent to the "a" of equation 2-2 (i.e. the slope of mite days vs.
dx


damage graph). Here the damage per mite day ("a" of equation 2-2) is a nonlinear

function of mite days.

Fruit growth. Fruit was assumed to be spherical, and fruit surface area was

calculated based on measurements of fruit circumferences. We used a logistic growth

equation for fruit surface area (y g) in relation to time (t)


= c 2-5
Y =1 + exp(a-bt)

Where yg = cm2; t = time of the year (Julian days). The growth rate can be

obtained by taking the derivative of equation 2-5


dYg c*b*exp(a-bt) 2-6
dt (1 + exp(a-bt))2

Data-fitting to equations were performed with TableCurve (Jandel Scientific

1992). The predetermined significance level for testing R2 (coefficient of

determination) (Cornell & Berger 1987) for each equation was p =0.05.

Results

Cumulative Damage vs. Cumulative Mite Days

The relationships between damage and mite days, from six sets of data, are

illustrated in Figs. 2-la to 2-6a, the parameters for the data-fitted curves are

presented in Table 2-2. All data sets (Figs. 2-la to 2-6a) demonstrated similar trends,








i.e. with the increase of mite days, damage showed an accelerating increase. This

trend was clearly demonstrated by an almost linear increase in damage rate per mite

day in relation to mite days (Figs. 2-la to 2-6a). The result from study 4 also

showed a slightly accelerating increase in damage with mite days(Fig. 2-4a), but this

accelerating effect is very small as compared with the other studies. This is probably

due to low mite population density.

Cumulative Mite Days vs. Time

When mite days were plotted against time, they exhibited a sigmoid growth in

all six sets of data (Figs. 2-lb to 2-6b). Since mite days equals the area under the

mite population curve, the shape of the population curve determines the shape of

cumulative mite days. Mite population dynamics curves are more or less

symmetrically bell-shaped in all six sets of data (Figs. 2-1c to 2-6c), resulting in

sigmoid cumulative mite day curves (Figs. 2-lb to 2-6b). If there were two

population peaks, we would expect a double-sigmoid curve of cumulative mite days.

If mite population were constant for a rather long time, we would expect a linear

increase in cumulative mite days with regard to time.

Damage Rate vs. Fruit Maturity

The data-fitted function for fruit area growth is


146.3346 2-7
Yg 1 +exp(4.389115-0.023039t)


(R2 = 0.9930; P<0.05). The sigmoid trend of mite damage rate with time did not

closely correlate with fruit surface area growth which exhibited a more or less convex






40
growth during the study period (i.e. from 8 May 1992 to 17 February 1993) (Fig. 2-

7). This was clearly demonstrated by the results from studies 2, 3 and 4 (Figs. 2-2b

to 2-4b): The three sets of data obtained at different time of the year demonstrated

similar sigmoid trend in damage rate, which seemed to be more correlated with the

mite population peak than with fruit growth (Figs. 2-2b, c to 2-4b, c). In a study by

Allen (1976), the author suspected a possible relationship between the time-varying

damage rate and fruit maturity, both of which were sigmoid functions of time. The

current study indicated that damage rate was not necessarily related to fruit maturity,

but was an accelerating function of mite days. Although the damage rate was not

closely correlated with fruit maturity, time (i.e. fruit maturity) did affect the damage

rate, and therefore the damage. This effect was clearly demonstrated through the

results of studies 2, 3, and 4 (Figs. 2-2a to 2-4a): With increasing fruit maturity, it

took fewer and fewer mite days to cause the same amount of fruit surface damage.

For example, to cause a 10% fruit surface damage, it took about 3100, 2600, and

1500 mite days in June-August (study 2: Fig. 2-2a), July-September (study 3: Fig. 2-

3a), and September-November (study 4: Fig. 2-4a), respectively. In conclusion, the

original damage rate, equation 2-1, is probably a more complicated function involving

time-varying parameters and nonlinear mite density effects.

Damage vs. Tree Age and Location

Results from the research citrus grove (8-yr-old) and from the commercial

citrus grove (4-yr-old) showed similar trends in population dynamics (Fig. 2-5c vs. 2-

6c). The relationships between damage and mite days from the two studies were very






41

similar in 1993 (Fig. 2-5a vs. 2-6a). For example, 3000 mite days resulted in about

22% fruit surface damage in both groves (Fig. 2-5a vs. 2-6a). This was also

reflected in the similarity of the damage rate per mite day from the two studies (Fig.

2-5a vs. 2-6a). The results suggest that the general trend between mite days and

damage (equation 2-3) may hold true for trees with different ages and in different

areas, for the same citrus variety. This property of mite damage may greatly simplify

building damage models for rust mite management programs.

Discussion

Why Does Damage per Mite Day Increase with Mite Days? Results from this study

clearly demonstrated that damage rate increases with increasing mite days.

Observations on 'Valencia' orange by Allen (1976) also indicated similar trend,

though the author related the damage rate increase to time instead of cumulative mite

days. There are several possible reasons for this phenomenon. One is that mites

inject digestive enzymes into cells while feeding, these enzymes might have an

accumulated accelerating effect in causing the death of epidermal cells. Another

reason is that death of a cell might expedite the death of adjacent damaged cells.

Another reason is human limitation in seeing the damage. The mites are so small that

they feed on individual cells causing punctures that are much smaller than the cells

themselves (McCoy & Albrigo 1975, Allen et al. 1992). Thus damage accumulates

one cell at a time. As the accumulation of dead cells becomes visible to the eye, it

might give rise to an artificial nonlinearity, i.e. fewer and fewer mite punctures are

needed to cause visible fruit surface damage, resulting in a superficial phenomenon of







42

increasing damage per mite day with season and mite days. Alternatively, there may

actually be nonlinear and threshold effects of mite density. The observed increase in

damage per mite day is probably a combined result of these factors. Fortunately,

whatever the explanation or mechanismss, the derived empirical equations can still be

used in predicting mite-caused fruit surface damage.

Zero Damage Mite Density

It has been suggested (McCoy & Albrigo 1975, Allen et al. 1992) that cells

may recover from mite punctures, and if so, more than one puncture within a limited

time period may be needed to cause the death of a cell. This may be true since fruit

can support low mite populations without showing visible surface damage. We define

effective cumulative mite days (ECMD) as the total cumulative mite days minus the

cumulative mite days which have already recovered from mite feeding, and zero

damage density (ZDD) as the mite density at which the number of newly-punctured

cells equals to the number of cells recovered from mite feeding. The relationship

between Effective Cumulative Mite Days and Zero Damage Density can be described

by

t
ECMD(t) =f(m(t)-ZDD)dt 2-8
to

where m(t) = mite density at time t The zero damage density may be a function of

fruit maturity and damage. The effective cumulative mite days may give better

prediction of mite damage than cumulative mite days, especially when mite

populations are low for a long time. This subject is currently being studied.








What Is the Recommendation?

From the above analysis, it is clear that mite damage is affected by many

factors. The relationship between cumulative damage and cumulative mite days is

probably a combined result of these factors. It may take many years of research

before we can eventually elucidate the possible effects of different factors. Since

model parameter estimates for the six studies did not vary much (Table 2-2), I suggest

using an averaged model as a temporary damage prediction model, which can be

modified when more information is available. Since sampled fruit in studies 2, 3 and

4 were not randomly selected (see Materials and Methods), and may not represent the

fruit on a grove level, only results from studies 1, 5 and 6 were averaged. The

parameters for this damage prediction model is shown in Table 2-2. The prediction

model is


y = exp(-13.901008)*x2086012 2-9

This formula can be used in predicting fruit surface damage based on mite population

survey data or predicted mite populations.








Table 2-2. Parameter estimates for power curve, equation 2-3.

Study Parameter Parameter R2
(a) (b)

1 -11.120513 1.784393 0.9958*
2 -16.011120 2.273361 0.9895'
3 -17.912093 2.567227 0.9860*
4 -5.539264 1.066059 0.9621:
5 -15.654411 2.269957 0.9958*
6 -14.928099 2.203687 0.9973*

1,5,6 -13.901008' 2.086012"
combined 2.435209b 0.263303b

* Mean.
b SD.



















1000 2000 3000


- 0.016 1
CU
*R
0.012 0
E
0.008

0.004 g
CD
a E
0.000
4000


Cumulative mite days


. -I I I -
160 200 240 280 320 36


0.025 >

0.020 a

0.015 E
0)
0.010 "U
a)
0.005 I)
E
0.000 o
0


40
Mites )
Damage -30 E

120 L

10 m
C
0 U-
160 200 240 280 320 360


Julian day (1=1 Jan. 1992)


Fig. 2-1. Relationships between mite population and fruit damage (Study 1.
Alachua County, Florida, 1992). (a) Fruit surface damage/damage rate
vs. cumulative mite days; (b) Cumulative mite days/damage rate vs.
time; (c) Mite population dynamics/cumulative fruit surface damage vs.
time.


4000

3000

2000

1000


0 1-
120


100 -

80 -

60 -

40 -

20 -
0 -0
120








S40 0.016
OC 0 Damage rateP c
E 30 Fruit damage 0.012 e

8 20 0.008

10 -- 0.004 a
2a a
u- 0 ---- 0.000 E
0 1000 2000 3000 4000 5000 6000 0
Cumulative mite days

>, 6000 0.025
S5000 o Damage rate 0.020
E 4000 Mite days
B 0.015 E
> 3000 0 -
U 0.010 2
5 2000 U
| 1000 -- 0005 O
b cu
0 0.000 E
120 160 200 240 280 320 360 0


o 200 40
160 Mites a)
Ei Damage 30 E
e 120 ,2
= 20 8
"u 80- -
E t
40- L
0 0 -
< 120 160 200 240 280 320 360

Julian day (1=1 Jan. 1992)


Fig. 2-2. Relationships between mite population and fruit damage (Study 2.
Alachua County, Florida, 1992). (a) Fruit surface damage/damage rate
vs. cumulative mite days; (b) Cumulative mite days/damage rate vs.
time; (c) Mite population dynamics/cumulative fruit surface damage vs.
time.









0.025 Z
o Damage rate 0.020
Fruit damage
-* 0.015 E
0.010 c
0.005 0
a E
-0.000 CU
0 1000 2000 3000 4000 5000


Cumulative mite days


01
120


200 -
160 -
120 -
80 -
40 -
0 -
120


160 200 240 280 320 36


0.04 v
Cu
0.03
E
0.02 a

0.01 )
E
0.00 C
0 0


50
o Mites 40 )
Damage E
30
20
10 )
0 "
160 200 240 280 320 360


Julian day (1=1 Jan. 1992)


Relationships between mite population and fruit damage (Study 3.
Alachua County, Florida, 1992). (a) Fruit surface damage/damage rate
vs. cumulative mite days; (b) Cumulative mite days/damage rate vs.
time; (c) Mite population dynamics/cumulative fruit surface damage vs.
time.


5000
4000
3000

2000
1000


Fig. 2-3.



















0 500


-rate 0.010

mnage 0.008"

S- 0.006 E

~ 0.004
0.002
I I I 0.000
1000 1500 2000 2500


Cumulative mite days


0 1
120


0 1
120


1 I 240 280 320 36
160 200 240 280 320 36


0.020
"0
0.015
E
0.010 a
t-
0.005 e
CD
E
0.000 CU
0 0


20
Mites 0)
Damage I- 15 E

10
5u

I 0 U-
160 200 240 280 320 360


Julian day (1=1 Jan. 1992)


Relationships between mite population and fruit damage (Study 4.
Alachua County, Florida, 1992). (a) Fruit surface damage/damage rate
vs. cumulative mite days; (b) Cumulative mite days/damage rate vs.
time; (c) Mite population dynamics/cumulative fruit surface damage vs.
time.


2500

2000

1500

1000

500


Fig. 2-4.



















2000


3000


40


-


Cumulative mite days


160 200 240 280 320 36


0.025 "

0.020 a

0.015 E

0.010 |
L-
0.005 0)
E
0.000 CU
0 0


40 -
Mites _D
Damage 30 E

20 8

10
c 2
0 U-
160 200 240 280 320 360


Julian day (1=1 Jan. 1993)


Fig. 2-5. Relationships between mite population and fruit damage (Study 5.
Alachua County, Florida, 1993). (a) Fruit surface damage/damage rate
vs. cumulative mite days; (b) Cumulative mite days/damage rate vs.
time; (c) Mite population dynamics/cumulative fruit surface damage vs.
time.


o Damage rate
- Fruit damage





I Ia


20

10


1000


5000

4000

3000

2000

1000


0
120


100

80

60

40
20


0
120


0.016
"0
0.012 .

0.008 a

0.004 a)
E0
0.000 Ca
'00








W, 50
0)
E 40
a, 30
20

10
"L 0


0 1000 2000 3000 4000 50C


Cumulative mite days


0
120


100 -
80 -
60 -
40 -
20-
0
120


160 200 240 280 320 36
160 200 240 280 320 36


0.020
0.016
0.012 E
0.008 ]
0.004 E)
0.000 Co
)0



0.025
0.020 "
0.015 E

0.010
0.005 CD
E
0.000 Co
0


40
Mites 0 0
Damage 30 E

20 8

10 20

0 L
160 200 240 280 320 360


Julian day (1=1 Jan. 1993)


Fig. 2-6. Relationships between mite population and fruit damage (Study 6. Polk
County, Florida, 1993). (a) Fruit surface damage/damage rate vs.
cumulative mite days; (b) Cumulative mite days/damage rate vs. time;
(c) Mite population dynamics/cumulative fruit surface damage vs. time.


5000
4000
3000
2000
1000

















150


120


90


60


30


120


180 240 300 360


420


Julian day (1=1 Jan. 1992)











Fig. 2-7. Relationships between fruit surface area growth and time (Alachua
County, Florida, 1992).











CHAPTER 3
RELATIONSHIP BETWEEN MITE DAMAGE AND
FRUIT GROWTH AND DROP



Statement of the Problem and Study Objective

Reports on the economic importance of citrus rust mite refer not only to fruit

surface discoloration, but also to fruit drop and size reduction, with an associated loss

of fruit quality and yield. Hubbard (1885) noted that "...if severely attacked by the

rust mite before it has completed its growth, the orange does not attain its full size.

Very rusty fruit is always small." Yothers (1918) observed that "russet" grade

(damaged) oranges and grapefruit were 12.5% (volume) smaller than undamaged fruit

before shipment. Those studies did not indicate whether damaged and undamaged

fruit of the same initial size actually grow at different rates. Small size could

presumably be correlated with rust mite damage because of location effects on the tree

or because of higher mite densities on fruit that were initially small compared with

other fruit. Allen (1979a) made the first attempt to establish a cause-effect

relationship between rust mite damage and small fruit size at harvest, and showed that

damaged 'Duncan' grapefruit grew slower and their final diameter was smaller than

for undamaged fruit. Another effect of rust mite damage is increased fruit drop.

Ismail (1971) showed that, after picking, fresh fruit were found to lose water faster

and develop an abscision zone more readily if they had rust mite damage. Studies by

52








Allen (1978, 1979b) indicated that fruit drop rates were increased by rust mite

damage on 'Valencia' and 'Pineapple' oranges and also on 'Duncan' grapefruit.

The objective of this study was to measure the effects of rust mite damage on

'Hamlin' orange fruit growth and drop, and to construct loss models for this variety

for use in rust mite management programs.

Materials and Methods

This study was conducted at a commercial citrus grove in Hendry County, FL,

from 8 June to 17 December 1991 with 5-yr-old 'Hamlin' orange trees on Swingle

rootstock. Fruit were damaged by rust mites a week before the experiment was

started, and no subsequent damage occurred. Fruit were chosen to include a range of

rust mite damage from 0 to 100% of the fruit surface. Fruit with different amounts

of rust mite damage were tagged evenly around each tree to eliminate potential

location effects. Every 2-3 wk, transverse fruit diameters were measured with a

caliper, fruit surface damage was estimated visually, and fruit drop was recorded. A

total of 593 fruit were tagged on 55 trees (10-20 fruit per tree) for both growth and

drop studies. An additional 228 fruit (on another 10 trees) were tagged for the drop

study only. A follow-up study of correlation of fruit size with mite damage was

conducted in a 'Hamlin' orange grove of the University of Florida Horticultural

Sciences Department in Alachua County in January 1992. Nine trees were chosen,

and diameters and damage of all the fruit on each tree were recorded. Mean diameter

and mean damage of all the fruit on each tree were obtained.








Data Analysis

Fruit drop and mite damage. Fruit were grouped into five equal intervals of

percentage surface damage: 0-19, 20-39,..., 80-100%. Mean damage and cumulative

rate of fruit drop were calculated for each category based on all the fruit tagged

initially. Cumulative percentage fruit drop (F op) was fitted to a two-variable

logistic function of damage (x) and time (t) with the SAS-NLIN procedure (SAS

Institute 1985). The form of the logistic function is


F 100 3-1
D'P 1 +exp(a-(b+cx)t)

A positive value of parameter c would indicate increasing fruit drop with increasing

mite damage (x). This function assumes that cumulative percentage fruit drop (FD)

is logistic and that the rate (b + cx) within the logistic is a linear function of damage

(x).

Fruit growth and mite damage. To reduce the possible effects of initial

diameter differences on fruit growth, we used percentage diameter increase instead of

diameter as the growth indicator. Percent diameter increase (FGao) for each fruit

was obtained using the following formula:

Far.th = Diameter at sampling date Initial diameter (8 June) 100
Initial diameter (8 June)


Fruit were grouped into five equal intervals of percentage surface damage: 0-

19, 20-39,..., 80-100%. Mean damage and mean percentage diameter increase were






55

calculated for each category. Percent diameter increase (FG,.) from individual fruit

was fitted to a two-variable logistic function of damage (x) and time (t) with SAS-

NLIN procedure (SAS Institute 1985). The form of the logistic function is


FGm, = k+ p x 3-2
1 +exp(a-(b+cx)t)


A negative value of parameter p would indicate smaller final % fruit growth

(FGW) with increasing mite damage (x). A negative value of parameter c would

indicate a decreasing percent fruit growth (FoGo) with increasing mite damage (x).

This function assumes that percentage fruit growth (FGrow) is logistic and that both

the final percentage fruit growth (k + px) and the rate (b + cx) within the logistic are

linear functions of damage (x). The predetermined significance level for testing R2

(Cornell & Berger 1987) was P = 0.05. The predicted result was compared with

observed. Prediction error was calculated using the formula


Prediction error = Predicted value Observed value 3-3

Mean squared error of prediction (MSEP) was calculated using the formula (Wallach

& Goffinet 1989, Thornley & Johnson 1990)


MSEP = 'i) 3-4
i= m-n

where m = number of observations; n = number of model parameters; y =

predicted value; yi = observed value.








Results

Fruit Drop and Mite Damage

Fruit drop rate increased with increasing mite damage, and most drop occurred

late in the fruit growing season (Fig. 3-1). The cumulative drop by 17 December for

damage categories 0-19, 20-39, 40-59, 60-79, and 80-100% was 6.4, 9.3, 9.4, 12.6,

and 21.0%, respectively. These results were similar to those obtained by Allen

(1979b) on 'Valencia' and 'Pineapple' oranges and 'Duncan' grapefruit. Our results

also indicated an accelerating fruit drop with increasing mite damage and time (Fig.

3-1). This effect is illustrated more clearly by fitting equation 3-1 to the data (Fig. 3-

2). The data-fitted model is


100 3-5
F'op = 1 + exp (7.230067 (0.010659 + 0.00007473x) t)

where Fp = cumulative percent fruit drop, t = Julian day (1 = 1 January), x =

percentage fruit surface damage, R2 = 0.8197 (P < 0.05). Notice here that

parameter c of equation 3-1 is positive, indicating increasing fruit drop with

increasing mite damage as expected. The maximum prediction error was less than 6

(cumulative percent fruit drop) (Fig. 3-3). The mean squared error of prediction was

5.17.

Fruit growth and mite damage. Fruit with almost the same initial transverse

diameter and different amounts of rust mite damage grew at slightly different rates

and diverged slightly with time (Fig. 3-4). Diameter growth (percentage increase)

was always highest for the lowest damage category, and fruit diameters (by 17







57

December) for damage categories 20-39, 40-59, 60-79, and 80-100% grew 2.6, 2.5,

2.4, and 1.7% less, respectively, than that of the lowest category (Fig. 3-4). The

overall data suggested a slight negative relationship between final fruit size and mite

damage (Fig. 3-4). This effect is demonstrated in the data-fitted percentage diameter

increase model (Fig. 3-5). Fitting to the data, we obtained the following

parameterized form of equation 3-2


F a, = 33.73 0.0108x 3-6
1 + exp(7.994361 (0.039723 0.00000916x)t)

where Fo = percentage increase in fruit diameter, t = Julian day (1 = 1

January), x = percentage fruit surface damage, R2 = 0.8405 (P < 0.05). Notice

here that parameter p and c of equation 3-2 are both negative, indicating a negative

effect of mite damage on fruit growth. The maximum prediction error was less than

3 (percent diameter increase) (Fig. 3-6). The mean squared error of prediction was

1.62.

Discussion

A study by Allen (1979a) on the effect of mite damage on 'Duncan' grapefruit

growth showed a greater size reduction than in our 'Hamlin' orange study. In the

grapefruit study, size reduction resulted from growth divergence of the damage

categories during June, July, and August (the primary period of fruit expansion).

Timing of damage in relation to the fruit growth cycle is important. In our study,

most of the fruit growth terminated approximately 3 mo after damage had occurred

('Hamlin' is an early maturing variety), and differences in mean diameter among








damage categories were not as pronounced as in the case of 'Duncan' grapefruit

(Allen 1979a). One reason for this is that the remaining diameter growth following

the damage for the 'Hamlin' oranges in this study was approximately 30% as

compared with 50-80% remaining growth for the 'Duncan' grapefruit (Allen 1979a).

Late-season (January 1992) observations on 'Hamlin' oranges at the University of

Florida Horticultural Science Department grove showed a strong negative correlation

of fruit size with mite damage (Fig. 3-7). This is probably due to fruit shrinkage

from water loss. It is known that water loss from fruit is exacerbated (approximately

a 3-fold increase) by rust mite damage both on and off the tree (Ismail 1971, McCoy

et al. 1976, Allen 1978, 1979a) and is probably worse on small rootstock systems

than on large ones (Allen 1979a). Thus, water stress may be the mechanism

responsible for increased fruit drop with mite damage.

Because rust mite damage is associated with increased water loss, future

research might examine the possibility of reducing yield loss by minimizing water

stress on damaged fruit. That is, can we reduce pesticide usage and maintain yield by

substituting water management for rust mite management? Further studies should also

look for differences between early and late-season mite damage on fruit growth and

drop and on the effects of leaf damage on yield. The fruit growth and drop models

developed in this study will be used to estimate yield loss (percentage volume) from

rust mite damage. The difference between the yield loss and cost of mite control will

determine whether control action at a certain time is economically justified in a given

grove.





















S25
a.
"20
20

75 15

0 10

S 55
,400
aO 0 3 350 ,3
300 2
100 8 250
60
o0 150
Damage class (%)









Fig.3-1. Observed cumulative fruit drop (percentage) for 'Hamlin' orange fruit
with different amounts of rust mite damage (Hendry County,
FL.,1991).






60















30
0

co 20"
-5

a 10

%- 0
CL 350
300

100 20
80

0 150 1










Fig. 3-2. Predicted cumulative fruit drop (percentage) for 'Hamlin' orange fruit
with different amounts of rust mite damage (see equation 3 in text)
FL., 1991).






61












0









^ -5\ /400 16
-5



/ /350
SI300 4
100 80 250 b
60 40 / 200
20 0 150

Damage class (,








Fig. 3-3. Prediction error for the percent fruit drop of 'Hamlin' orange fruit with
different of amounts rust mite damage (Hendry County, FL, 1991).







62














cm 40

30


10


400
( 0 350 p
0 300 0
100 80 /-250
60 40-- /200 .^
20.
02 0 150

Darage ()








Fig. 3-4. Observed transverse diameter increase (percentage) of 'Hamlin' orange
fruit with different of amounts rust mite damage (Hendry County, FL,
1991).







63













40


0)20






400ge
30

i5 20











Da









Fig. 3-5. Predicted transverse diameter increase (percentage) of 'Hamlin' orange
fruit with different amounts of rust mite damage (see equation 4 in
text).







64
















CO







00
0 5100













Damage (%)








Fig. 3-6. Prediction error for the percent diameter increase of 'Hamlin' orange

fruit with different of amounts rust mite damage (Hendry County, FL,
1991).
1991).


























70 -





65 -


40 60


Mean % fruit surface damage by tree











Fig. 3-7. Mean fruit surface damage plotted against mean fruit diameter by tree
for nine 'Hamlin' orange trees (Gainesville, FL, January 1992).


R2 = 0.7819
P < 0.05


I












CHAPTER 4
FREQUENCY DISTRIBUTION OF MITE DAMAGE ON FRUIT


Statement of the Problem and Study Objective


Extensive feeding by the citrus rust mite, Phyllocoptruta oleivora (Ashmead)

(Acari: Eriophyidae) causes fruit surface discoloration (i.e. russet) (Albrigo & McCoy

1974, McCoy & Albrigo 1976), and it has been reported that heavy surface russet

reduces growth and increases drop of the damaged fruit (Allen 1978, 1979, Yang et

al. 1994). Mite damage is not equally distributed over all the fruit in a grove (Hall et

al. 1991), and furthermore, only high percentage surface damage shows obvious

effect on fruit growth and drop (Allen 1978, 1979). It is therefore important to know

the fraction of fruit in a grove that falls into the higher percentage russet categories.

More specifically, given the mean percentage fruit surface russet, one wants to know

the fractions of fruit that fall into various russet categories (i.e. the frequency

distribution). This would then permit us to calculate average losses over the

distribution from (1) reduced fruit grade, (2) reduced growth, and (3) increased drop

(Allen 1978, Allen et al. 1994a). Allen & Stamper (1979) reported that the relative

frequency distribution of mite damage on 'Valencia' and 'Pineapple' orange, and on

'Duncan' grapefruit can be described with a modified beta distribution, with the mean

as its only parameter. In this study I seek to develop a simpler, closed-form density

and cumulative distribution function which avoids the somewhat awkward beta









function in integral form. The purpose was two fold: 1) to determine the frequency

distribution of percentage russet on 'Hamlin' orange fruit, and 2) to express the

distribution in terms of the mean percentage russet with a simple mathematical

formula which will eventually be used in constructing loss models in rust mite

management programs.

Materials and Methods

This study was conducted at a commercial citrus grove in Polk County, FL,

from 24 August to 13 October 1993 with 4-yr-old 'Hamlin' orange trees. The study

plot consisted of an area of about 5 acres, with eight rows of trees running from north

to south, with each row consisting of about 35 trees. The sampling area was located

at the center of the study plot. Ten trees were tagged at each of the central 6 rows

before any visible mite damage occurred. Ten fruit were randomly selected from

each of the four quadrants (south, east, north, and west) of a tagged tree, with a total

of forty fruit per tree. Fruit surface damage was estimated visually. Sampling was

made every one to two weeks. The total number of fruit for each sampling was

40*10*6 (i.e. 2400). The study plot was under regular management during the study

except that pesticides were not applied.

Data Analysis.

Fruit were grouped into a zero class and 5% intervals of percentage surface

damage, i.e. 0, 1-5, 6-10, ..., 96-100%. Mean damage for each group was

calculated by averaging the damage of all the fruit included in the group. In the study

by Allen & Stamper (1979), group frequency was fitted directly to equations. In

attempts for simpler solutions, it was found that the logistic distribution function gave








excellent fit to the cumulative frequency distribution. The logistic distribution

function is

1
Feq(X) (-) 4-1
1 + exp(- )


The mean of the logistic distribution is a; the variance of the logistic distribution is


1.*b2 (Patel et al. 1976). The purpose is to use mean damage to determine the
3


relative frequency of different damage classes. Since damage class (x) can only be

from 0 to 100%, therefore, only the part of the logistic distribution which lies

between 0 and 100 is used. The mean of this data-fitted truncated logistic

distribution is the mean damage, which is different from the mean (a) of the actual

logistic distribution, as is the variance. Parameters a and b of our fitted distribution

were found to change with mean fruit surface damage (I). We therefore assumed

that parameters a and b were functions of mean fruit surface damage (IL), i.e. a(p)

and b(p). In order to determine the functional forms for a(pt) and b(pi), we first

fitted each of the six sets of observed data to the logistic distribution function

(equation 4-1) separately, and then fitted the estimated a and b values to functions of

the mean damage (l). The following function was found to give a good fit to

parameter a in relation to mean fruit surface damage (I)







69

a(p) = ao + alpL + a2exp(-g) 4-2

where a0, a1, a2 =parameters. The following function was found to give good fit to

parameter b(t)


b(ui)=1bo+bexp(-b2 p) 4-3

where bo, b, b2 =parameters. The above data-fitting process was accomplished with

TableCurve (Jandel Scientific 1992). The final form of the cumulative frequency

distribution is the following two-variable logistic function of mean fruit surface

damage (gI) and damage class (x)


1
FFreq(XI = 1 + exp(- x-a(L)) 4-4



where a(p) and b(i) are functions of pi as defined in equations 4-2 and 4-3. I

replaced a(p.) and b(V) in equation 4-4 with equations 4-2 and 4-3, and then used the

SAS-NLIN procedure (SAS Institute 1985) for simultaneous estimation of all six

parameters (a0, a,, a2, bo, bl, b2) based on the original six sets of data. The final

frequency distributions were based on these SAS-NLIN estimates.

The corresponding density function can be obtained by taking the partial

derivative of the cumulative frequency distribution (equation 4-4) with respect to

damage class (x), giving









1 x-a
aFq(X) *exp(--) 45
a (1 + exp(- -a))2
b

Although the density function (equation 4-5) describes a continuous distribution from

negative infinity to positive infinity, our damage classes are limited only to the range

of [0, 100] %. To make the density function (equation 4-5) integrate to one between

0 and 100%, we should divide equation 6-5 by the total area (A) between these

limits. This area can be found directly from equation 4-4, so that


1 1
A = F.q(100)-Freq(O) = 100-a 0- -- 4-6
1+exp(- ) 1+exp(--)
b b

Dividing equation 4-5 by A, we obtain


1 x-a
-exp( -- )
fFq(X) 1 b b 4-7
(1 + exp( -a))2
b

for our logistic density function where the dependence on g has been dropped for

simplicity. Mean squared error of prediction (MSEP) was calculated using the

formula (Wallach & Goffinet 1989, Thornley & Johnson 1990)


MSEP = 4-8
i-1 m-n

where m = number of observations; n = number of model parameters; =


predicted value; y. = observed value.









Results

Quadrant Distribution of Damaged Fruit on Trees.

Damaged fruit were not equally distributed among the four quadrants of the

tree (Fig. 4-1). In the early stage of mite damage when the mean fruit surface

damage was low, fruit on the east quadrant of the tree had the highest mean surface

damage, followed by the north quadrant. But in the late stage of mite damage when

the mean fruit surface damage was increased, fruit on the north quadrant of the tree

had the highest mean surface damage, followed by the east quadrant. The west

quadrant always had the lowest mean surface damage. By the time of the last

observation (i.e. October 13, 1993), mean damage for the north, east, south, and west

quadrants were 42, 39, 30 and 24%, respectively. Since fruit surface damage is

directly related to total mite population supported by the fruit, the north side of the

tree should have the highest mite population, followed by the east, south and west.

Rust mites prefer moderate temperatures, and avoid direct sun-lit fruit surface when

air temperature is high (Hubbard 1885, Yothers & Mason 1930, Albrigo & McCoy

1974, Allen & Mccoy 1979). The uneven distribution of mite damage is probably a

result of mite response to the differences in temperature and sunlight distributions

among the quadrants. Allen & McCoy (1979) studied the temperature and rust mite

distribution in the north top, north bottom, south top, and south bottom quadrant of a

tree. Their results indicated that the north bottom quadrant had the most favorable

temperatures and usually the most rust mites; the south bottom was also favorable and

had high mite densities. They also found that the south top quadrant was least

favorable, often having temperatures in the lethal range, and had the lowest rust mite








population, but no observations were made on the east and west quadrant (Allen &

McCoy 1979). Rust mite scouting programs could probably make use of these

difference in mite distribution.

Distribution of Damaged Fruit.

Distribution of damaged fruit over the damage classes changed tremendously,

depending on the overall mean damage. When the mean damage was low, most of

the fruit had no rust mite damage, and the cumulative distribution demonstrated a

convex rise to a saturation plateau at one (Fig. 4-2). With the increase of mean fruit

surface damage, the proportion of fruit without damage decreased, and the proportion

of fruit with higher damage correspondingly increased. As a result, the cumulative

distribution changed from convex to sigmoid (Fig. 4-2). Each of the six sets of

cumulative distribution data was fitted to the logistic equation (equation 1), and the

results are summarized in Table 4-1. Parameters a and b were then fitted to

equations 4-2 and 4-3, respectively, as functions of mean percent damage (iL). The

parameter estimates using the above two-step procedure and using SAS-NLIN

procedure (with equations 4-2 and 4-3 inserted into equation 4-4) are summarized in

Table 4-2. The relationships between parameters a(R) and b(pL) and mean fruit

surface damage are shown in Fig. 4-3. The cumulative frequency distribution can be

obtained by replacing parameters a(u) and b(R) in equation 4-4 with equations 4-2

and 4-3; the predicted results are shown in Fig. 4-4. The mean squared error of

prediction was 18.04.







73

The probability density function can be obtained by replacing parameters a(p)

and b(p) in equation 4-7 with equations 4-2 and 4-3. The predicted probability

density distribution is shown in Fig. 4-5. With increasing

mean damage, the probability density curve changes from an exponential decay to a

symmetrical unimodal curve, with the peak shifting toward higher damage classes

(Fig. 4-5).

Discussion

Properties of the Cumulative Frequency Distribution Function.

The logistic distribution function (equation 4-1) has been used to model insect

phenology (Dennis et al. 1986, Kemp et al. 1986, Dennis & Kemp 1988) as a

stochastic process. Here we used the truncated logistic for describing the frequency

distribution of rust mite damage on citrus fruit. As manifested in the equations 4-2

and 4-3, the mean and variance of the full (untruncated) logistic distribution are

functions of the mean of the truncated distribution (the data). Parameter a(L)

exhibits a sharp increase when the mean fruit surface damage is low, and a slower

linear increase with further increase in mean damage (equation 4-2, Fig. 4-3).

Parameter b(gi) also exhibited a sharp increase, but then approaches a constant value

with further increasing damage (equation 4-3, Fig. 4-3). This indicates that as the

peak of the density function shifts towards higher damage, there is little change in the

variance after the data mean exceeds about 20%. This is similar to shifting a normal

density curve to a higher mean without changing the variance.








Application of the Cumulative Frequency Distribution Function.

The cumulative frequency distribution function (equation 4-4) will enable us to

easily determine the proportion of fruit which falls into a specific damage class if the

mean fruit surface damage is known. For example, the proportion of fruit which falls

between damage class x. and x2 is FFrq(X2, ) FF E(Xl, I) In commercial citrus

production, it is often necessary to determine the proportion of fruit which can go to

fresh fruit market. If fruit with more than x percentage of the surface russetted is

damaged enough to be rejected from the fresh fruit market, then the proportion of

fruit which can go to the fresh fruit market (the 'pack-out') would simply be

1
F1eq(X, ) = 4-9
1 + exp(- x-a(L)
b(p.)

In Fig. 4-4, we can observe the proportion of 'pack-out', F,q(x,p), for any damage

class cut-off (x) as a function of the mean damage (p.).

Another intended application of the established equation is to determine yield

loss from rust mite damage. Rust mite damage reduces growth and increases drop of

damaged fruit (Allen 1978, 1979, Allen et al. 1994, Yang et al. 1994), but these

effects are not uniformly distributed over damage classes, with more obvious effects

on the more heavily damaged fruit. It is therefore necessary to integrate these effects

over the whole damage class, based on the frequency distribution of fruit to obtain

average effects as functions of damage. Mathematical models describing the

relationships between fruit growth and drop and fruit surface damage have been







75

developed (Allen 1978, 1979, Yang et al. 1994). Allen et al. (1994) have established

differential equations to estimate volume loss from reduced fruit growth and drop, by

combining the frequency distribution with growth and drop models. These models are

to be further improved and fine-tuned so that they can be used in predicting mite

damage losses. The established models in this paper should also prove useful in pest

management studies.








Table 4-1. Relationship between mean fruit surface damage and estimates for
parameters a and b in equation 4-1.

Date Mean damage Parameter Parameter R2
(%) (a) (b)

8-24-93 0.6 -19.45044 7.0134054 0.9730*
8-31-93 2.4 -9.677496 7.5374539 0.9703*
9-07-93 6.2 -5.032474 10.943753 0.9966'
9-14-93 12.2 5.224359 11.241025 0.9960*
9-27-93 25.0 21.19182 10.984929 0.9957*
10-13-93 34.0 29.79047 10.984405 0.9882*

Significant at p =0.05.







77

Table 4-2. Parameter estimates for equations 4-2 and 4-3 by two different methods.

Method Equation Parameter Parameter Parameter R2
ao a, a2
bo b, b2

TableCurve 4-2 -11.185925 1.2398129 -16.209061 0.9899'
4-3 11.207186 -5.365157 0.273146 0.7875

SAS-NLIN 4-4' -9.7211588 1.1878809 3.077703 0.9993*
11.3049751 -8.623718 0.228797

* Inserting equations 4-2 and 4-3 into equation 4-4 before data-fitting.
* Significant at p =0.05.
































240 250 260 270 280


Julian day (1=1 Jan. 1993)


Observed distribution of damaged fruit on trees (Polk County, Florida,
1993).


Fig. 4-1.


230


290







79











1.0

( 0.8


-o
0.6

S0.4
e 100
S 0.2 80 \
60 <
0 0.0 1 / 4 20 4 00p

S40 0
MU Mean damage (+











Fig. 4-2. Observed relative cumulative frequency of mite damage on fruit (Polk
County, Florida, 1993).
































10 20 30


- 12



8 -



-4 .



-0
40


mu = Mean damage (%)














Fig. 4-3. Relationship between parameter a (b) in the logistic equation (equation
4-1) and mean fruit surface damage.







81
















13
Cr
0)






05






















County, Florida, 1993).
County, Florida, 1993).




















0.1


C"


0.05,
0
II


0>
0
2100

2550
0 5



50 0 00)o'








Fig. 4-5. Predicted relative frequency of mite damage on fruit (Polk County,
Florida, 1993).




Full Text

POPULATION DYNAMICS AND DAMAGE EFFECTS OF THE CITRUS RUST
MITE, PHYLLOCOPTRUTA OLE1VORA (ASHMEAD)(ACARI: ERIOPHYIDAE)
By
YUBIN YANG
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1994

ACKNOWLEDGMENTS
I would like to extend the deepest gratitude to my major professor, Dr. Jon C. Allen, for
his clear guidance, advice, patience, encouragement, and superb teaching throughout my study.
Jon's broad knowledge enriched me, and his kind and pleasant personality comforted me all the
time. Thanks are also extended to Dr. J.L. Knapp, cochairman of my committee, and to Drs.
H.L. Cromroy, J.W. Jones, J.E. Lloyd, and P.A. Stansly for serving on the supervisory
committee and contributing to the completion of the dissertation. It has always been such a great
pleasure to work with my committee members. What I have learned is not only a way of
profession but also a way of life, and it will last forever along with my deep gratitude and
wonderful memory.
I am also extremely grateful to Dr. R.E. Rouse and Sally Davenport (Southwest Florida
Research and Education Center), to Mark Colbert, Tommy Duda, and Danny Jones (A. Duda
& Sons, Inc.), to Dr. Frederick S. Davies (University of Florida Horticultural Sciences
Department), and to the Coca-Cola Corporation for allowing us to conduct research in their
citrus groves and for their assistance and cooperation during the study. I am indebted to Elmo
B. Whitty, Harold E. Hannah, Y.J. Tsai and Harry E. Anderson (University of Florida) for
providing the weather data essential to my research.
11

I would also like to thank many American friends who have been so kind and nice to me,
and so patient with me.
I will be forever indebted to my parents for their unfailing love and support.
Finally, a very special thanks to my wife, Yu Lin, and my son, Danhong Yang for their
love, their encouragement, their patience, and their sacrifice.
in

TABLE OF CONTENTS
ACKNOWLEDGMENTS ii
LIST OF TABLES x
LIST OF FIGURES xi
ABSTRACT xvii
CHAPTERS
1. LITERATURE REVIEW 1
Distribution and Production of Citrus 1
Origin and Distribution of the Citrus Rust Mite 2
Taxonomic History 3
Host Preference 4
Life History and Habitat 4
Rearing Methods 4
Reproduction 5
Stages and Development 5
Economic Importance 8
History of Economic Importance 8
Rust Mite Injury 9
Feeding and food 9
Injury to leaves 10
Injury to fruit 11
Injury to young twigs 12
Leaf injury and greasy spot 12
Economic Loss 13
Leaf drop and size in relation to damage 13
Fruit damage in relation to mite density 14
Fruit growth in relation to damage 14
Fruit drop in relation to damage 15
Fruit internal quality in relation to damage 15
Calculation of economic loss from rust mite
damage 16
IV

Behavior and Ecology 16
Behavior and Distribution 16
Population Dynamics vs. Season 18
Population Dynamics vs. Climatic Factors 19
Mite-Pathogen Interaction 21
Management of Citrus Rust Mite 24
Chemical Control 24
Pesticides 24
Fungicides vs. H. thompsonii 25
Cultural Control 25
Biological Control 26
Predators and parasitoids 26
Pathogens 27
Integrated Control 27
Survey Methodology 28
Study Objectives and Methodology 28
2. RELATIONSHIP BETWEEN MITE POPULATION DENSITY
AND FRUIT DAMAGE 31
Statement of the Problem and Study Objective 31
Materials and Methods 32
Mite Damage 32
Study 1 33
Study 2, 3, 4 33
Study 5 33
Study 6 33
Fruit Growth 35
Data Analysis 35
Damage (Damage rate) 35
Fruit growth 38
Results 38
Cumulative Damage vs. Cumulative Mite Days 38
Cumulative Mite Days vs. Time 39
Damage Rate vs. Fruit Maturity 39
Damage vs. Tree Age and Location 40
Discussion 41
Why Damage Rate Increases with Increasing Cumulative
Mite Days? 41
Zero Damage Mite Density 42
What is the Recommendation? 43
v

3. RELATIONSHIP BETWEEN MITE DAMAGE AND FRUIT
GROWTH AND DROP 52
Statement of the Problem and Study Objective 52
Materials and Methods 53
Data Analysis 54
Fruit drop and mite damage 54
Fruit growth and mite damage 54
Results 56
Fruit Drop and Mite Damage 56
Fruit Growth and Mite Damage 56
Discussion 57
4. FREQUENCY DISTRIBUTION OF MITE DAMAGE ON
FRUIT 66
Statement of the Problem and Study Objective 66
Materials and Methods 67
Data Analysis 67
Results 71
Quadrant Distribution of Damaged Fruit on a Tree 71
Distribution of Damaged Fruit 72
Discussion 73
Properties of the Cumulative Frequency Distribution
Function 73
Application of the Cumulative Frequency Distribution
Function 74
5. MITE POPULATION DYNAMICS ON FRUIT AND LEAVES . 83
Statement of the Problem and Study Objective 83
Materials and Methods 84
Budwood Foundation Grove, 1991 84
Research Grove, 1992, 1993 84
Commercial Grove, 1993 85
Results 88
Budwood Foundation Grove, 1991 88
Research Grove, 1992 89
Research Grove, 1993 89
Commercial Grove, 1993 89
Discussion 90
Mite Population vs. Fungal Pathogen 90
Mite Population vs. Food Availability 91
Mite Population vs. Tree Age and Location 93
vi

Mite Population vs. Weather 94
Mite Population on Upper vs. Lower Leaf Surface 96
Quantification of Effects of Biotic and Abiotic Factors on
Mite Population Dynamics 97
6. MITE POPULATION PREDICTION: AN AGE-STRUCTURED
MODEL OF THE FRUIT-MITE PATHOGEN SYSTEM 107
Statement of the Problem and Study Objective 107
Materials and Methods 107
The Fruit-Mite-Pathogen System 107
Model Development 110
The age-stage-structure matrix 110
Age-stage-specific growth rate, developmental rate,
mortality rate and fecundity 113
Mite and pathogen population growth 114
Mite and pathogen population density adjustment
due to fruit growth 116
Model Parameter Specification 117
Determination of the number of age groups .... 117
Elements for the mortality matrix M 119
Elements for the growth rate matrix G and
developmental rate matrix D 120
Elements for the fecundity matrix F 124
Matrix Element Calculation - Varying Temperature .... 127
Model Parameter Estimation 129
Results 130
Parameter Estimates 130
Observed vs. Simulated Mite/Pathogen/Damage
Dynamics 131
Polk County 1993 131
Alachua County 1993 132
Alachua County 1992 132
Collier County 1991 132
Discussion 133
Need for a Maximization Tool 133
Need for Pathogen Biology 134
Modeling Pesticide-Induced Mortality 134
Parameter Calibration and Model Application 135
7. CALCULATION OF ECONOMIC LOSS FROM RUST MITE
DAMAGE 148
Statement of the Problem and Study Objective 148
vii

Materials and Methods 149
Mite Population Prediction 149
Fruit Surface Damage Prediction 149
Frequency Distribution of Mite Damage to Fruit 150
Volume and Value Loss from Increased Fruit Drop and
Reduced Fruit Growth 151
Fruit growth and drop vs. damage 151
Total proportional volume loss 153
Proportional volume and value loss for fresh and
processed fruit 154
Adjustment for mean damage 156
Value Loss from Reduced Fruit Grade 157
Total Value Loss from Increased Fruit Drop, Reduced
Fruit Growth, and Reduced Fruit Grade 158
Results 158
Volume Loss without New Damage 158
Volume Loss with New Damage 159
Discussion 160
Volume Loss for Fresh Fruit vs. Processed Fruit 160
Mite Control Decision 160
Looking into the Future 162
8. SUMMARY and Discussion 168
Important Results 168
Fruit Damage vs. Mite Population Density 168
Fruit Growth and Drop vs. Mite Damage 169
Frequency Distribution of Mite Damage to Fruit 169
Mite and Pathogen Population Dynamics 170
Fruit-Mite-Pathogen System Simulation 171
Calculation of Volume Loss from Mite Damage 171
Practical Applications 172
Prediction of Fruit Surface Damage 172
Prediction of Mite Population Trend 172
Control Strategies for Fresh Fruit Groves and Processed
Fruit Groves 173
Further Studies 175
Model Calibration and Implementation 175
Effect of Mite Population Discontinuity of Damage Rate . 176
Standardized Survey Method 176
viii

APPENDIX RELATION BETWEEN VOLUME AND PERCENT
DIAMETER GROWTH 177
LITERATURE CITED 178
BIOGRAPHICAL SKETCH 192
IX

LIST OF TABLES
Table page
2-1. Summary of experimental designs 36
2-2. Parameter estimates for power curve, equation 2-3 44
4-1. Relationship between mean fruit surface damage and estimates for
parameters a and b in equation 4-1 76
4-2. Parameter estimates for equations 4-2 and 4-3 using two different
methods 77
5-1. Summary of experimental designs 87
6-1. Parameter estimates for equations describing the relationship
between cumulative emergence (F(t,I)) and temperature (T) . . 136
6-2. Parameter estimates for the pathogen transmission rate and
density-dependence equations 137
x

LIST OF FIGURES
Figure
page
2-1. Relationships between mite population and fruit damage (Study
1. Alachua County, Florida, 1992). (a) Fruit surface
damage/damage rate vs. cumulative mite days; (b) Cumulative
mite days/damage rate vs. time; (c) Mite population
dynamics/cumulative fruit surface damage vs. time 45
2-2. Relationships between mite population and fruit damage (Study
2. Alachua County, Florida, 1992). (a) Fruit surface
damage/damage rate vs. cumulative mite days; (b) Cumulative
mite days/damage rate vs. time; (c) Mite population
dynamics/cumulative fruit surface damage vs. time 46
2-3. Relationships between mite population and fruit damage (Study
3. Alachua County, Florida, 1992). (a) Fruit surface
damage/damage rate vs. cumulative mite days; (b) Cumulative
mite days/damage rate vs. time; (c) Mite population
dynamics/cumulative fruit surface damage vs. time 47
2-4. Relationships between mite population and fruit damage (Study
4. Alachua County, Florida, 1992). (a) Fruit surface
damage/damage rate vs. cumulative mite days; (b) Cumulative
mite days/damage rate vs. time; (c) Mite population
dynamics/cumulative fruit surface damage vs. time 48
2-5. Relationships between mite population and fruit damage (Study
5. Alachua County, Florida, 1993). (a) Fruit surface
damage/damage rate vs. cumulative mite days; (b) Cumulative
mite days/damage rate vs. time; (c) Mite population
dynamics/cumulative fruit surface damage vs. time 49
xi

2-6. Relationships between mite population and fruit damage (Study
6. Polk County, Florida, 1993). (a) Fruit surface
damage/damage rate vs. cumulative mite days; (b) Cumulative
mite days/damage rate vs. time; (c) Mite population
dynamics/cumulative fruit surface damage vs. time 50
2-7. Relationships between fruit surface area growth and time
(Alachua County, Florida, 1992) 51
3-1. Observed cumulative fruit drop (percentage) for ’Hamlin’
orange fruit with different amounts of rust mite damage (Hendry
County, FL.,1991) 59
3-2. Predicted cumulative fruit drop (percentage) for ’Hamlin’ orange
fruit with different amounts of rust mite damage (see equation 3-5
in text) FL., 1991) 60
3-3. Prediction error for the percent fruit drop of ’Hamlin’ orange fruit
with different of amounts rust mite damage (Hendry County, FL,
1991) 61
3-4. Observed transverse diameter increase (percentage) of ’Hamlin’
orange fruit with different amounts of rust mite damage (Hendry
County, FL, 1991) 62
3-5. Predicted transverse diameter increase (percentage) of ’Hamlin’
orange fruit with different amounts of rust mite damage (see
equation 3-6 in text) 63
3-6. Prediction error for the percent diameter increase of ’Hamlin’
orange fruit with different of amounts rust mite damage (Hendry
County, FL, 1991) 64
3-7. Mean fruit surface damage plotted against mean fruit diameter
by tree for nine ’Hamlin’ orange trees (Gainesville, FL,
January 1992) 65
4-1. Observed distribution of damaged fruit on a tree (Polk County,
Florida, 1993) 78
4-2. Observed relative cumulative frequency of mite damage on fruit
(Polk County, Florida, 1993) 79
xii

4-3. Relationship between parameter a (b) in the logistic equation
(equation 4-1) and mean fruit surface damage 80
4-4. Predicted cumulative frequency distribution of mite damage on
fruit (Polk County, Florida, 1993) 81
4-5. Predicted probability density function of mite damage on fruit
(Polk County, Florida, 1993) 82
5-1. Mite population dynamics, (a) Population dynamics of citrus
rust mite and its fungal pathogen on fruit; (b) Dynamics of
citrus rust mite population and fruit surface damage on fruit;
(c) Population dynamics of citrus rust mite on leaves. (’Valencia’
orange, Collier County, Florida, 1991) 98
5-2. Mite population dynamics, (a) Population dynamics of citrus rust
mite and its fungal pathogen on fruit; (b) Dynamics of citrus
rust mite population and fruit surface damage on fruit;
(c) Population dynamics of citrus rust mite on leaves. (’Hamlin’
orange, Collier County, Florida, 1991) 99
5-3. Mite population dynamics, (a) Population dynamics of citrus rust
mite and its fungal pathogen on fruit; (b) Dynamics of citrus rust
mite population and fruit surface damage on fruit; (c) Population
dynamics of citrus rust mite on leaves. (’Hamlin’ orange, Alachua
County, Florida, 1992) 100
5-4. Mite population dynamics, (a) Population dynamics of citrus rust
mite and its fungal pathogen on fruit; (b) Dynamics of citrus rust
mite population and fruit surface damage on fruit; (c) Population
dynamics of citrus rust mite on leaves. (’Hamlin’ orange, Alachua
County, Florida, 1993) 101
5-5. Mite population dynamics, (a) Population dynamics of citrus rust
mite and its fungal pathogen on fruit; (b) Dynamics of citrus rust
mite population and fruit surface damage on fruit; (c) Population
dynamics of citrus rust mite on leaves. (’Hamlin’ orange, Polk
County, Florida, 1993) 102
5-6. Weather data, (a) Daily mean temperature; (b) Daily leaf wetness
duration (hrs); (c) Daily rainfall (cm) (Immokalee, Collier County,
1991)
xiii
103

5-7. Weather data, (a) Daily mean temperature; (b) Daily rainfall (cm)
(Gainesville, Alachua County, 1992) 104
5-8. Weather data, (a) Daily mean temperature; (b) Daily rainfall (cm)
(Gainesville, Alachua County, 1993) 105
5-9. Weather data, (a) Daily mean temperature; (b) Daily leaf wetness
duration (hrs); (c) Daily rainfall (cm) (Lake Alfred, Polk County,
1993) 106
6-1. The age-stage-structure matrix (N) of the citrus rust mite and
its fungal pathogen. n¡j = number of individuals in age i and
stage j ; Egg = egg stage; N, = protonymph stage; N2 =
deutonymph stage; Adult = adult stage; P[ = latent pathogen
stage; P¡ = infectious pathogen stage Ill
6-2. The age-stage-specific growth rate matrix (G), developmental rate
matrix (D), mortality matrix (M), and fecundity matrix (F).
gtj = probability that an individual from age i and stage j will
grow to age i+1 of the same stage after one age interval (day);
dy = probability that an individual from age i and stage j will
develop to the first age class of stage j+1 after one age interval
(day); = probability that an individual in age i and stage j
will die after one age interval (day); = number of offspring
that will be produced by every individual in age i and stage j
during one age interval (day) 112
6-3. Density-dependent egg-laying curve for the citrus rust mite .... 138
6-4. Effect of temperature and leaf wetness duration on pathogen
transmission rate 139
6-5. Observed fruit-mite-pathogen system dynamics, (a) mite and
pathogen population; (b) fruit surface damage; (c) cumulative
mite days (Polk County, Florida, 1993) 140
6-6. Predicted fruit-mite-pathogen system dynamics, (a) mite
(thick solid line) and pathogen (thin solid line) population;
(b) fruit surface damage; (c) cumulative mite days (Polk County,
Florida, 1993) 141
xiv

6-7. Observed fruit-mite-pathogen system dynamics, (a) mite and
pathogen population; (b) fruit surface damage; (c) cumulative
mite days (Alachua County, Florida, 1993) 142
6-8. Predicted fruit-mite-pathogen system dynamics, (a) mite
(thick solid line) and pathogen (thin solid line) population;
(b) fruit surface damage; (c) cumulative mite days (Alachua
County, Florida, 1993) 143
6-9. Observed fruit-mite-pathogen system dynamics, (a) mite and
pathogen population; (b) fruit surface damage; (c) cumulative
mite days (Alachua County, Florida, 1992) 144
6-10. Predicted fruit-mite-pathogen system dynamics, (a) mite
(thick solid line) and pathogen (thin solid line) population;
(b) fruit surface damage; (c) cumulative mite days (Alachua
County, Florida, 1992) 145
6-11. Observed fruit-mite-pathogen system dynamics, (a) mite and
pathogen population; (b) fruit surface damage; (c) cumulative
mite days (Collier County, Florida, 1991) 146
6-12. Predicted fruit-mite-pathogen system dynamics, (a) mite
(thick solid line) and pathogen (thin solid line) population;
(b) fruit surface damage; (c) cumulative mite days (Collier
County, Florida, 1991) 147
7-1. Volume loss from rust mite damage, (a) total volume loss;
(b) volume loss for processed fruit; (c) volume loss for fresh
fruit (mu=25% at t=200) 163
7-2. Effect of mite damage on fruit growth and drop, (a) volume
change (dashed line) and number (dashdot line) (mu=0);
(b) volume change (dashed line) and number (dashdot line)
(mu=25% at t=200); (c) mean damage change due to drop
(mu=25% at t=200) 164
7-3. Volume loss from rust mite damage, (a) total volume loss;
(b) volume loss for processed fruit; (c) volume loss for fresh
fruit (mu=50% at t=200) 165
xv

7-4. Effect of mite damage on fruit growth and drop, (a) volume
change (dashed line) and number (dashdot line) (mu=0);
(b) volume change (dashed line) and number (dashdot line)
(mu=50% at t=200); (c) mean damage change due to drop
(mu=50% at t=200) 166
7-5. Predicted volume loss from rust mite damage, (a) total volume
loss; (b) volume loss for processed fruit; (c) volume loss for
fresh fruit (mu=0% at t = 160) (Polk County, Florida, 1993) . . . 167
xvi

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
POPULATION DYNAMICS AND DAMAGE EFFECTS OF THE CITRUS RUST
MITE, PHYLLOCOPTRUTA OLEIVORA (ASHMEAD)(ACARI: ERIOPHYIDAE)
By
YUBIN YANG
AUGUST 1994
Chairperson: Dr. Jon C. Allen
Major Department: Entomology and Nematology
The citrus rust mite, Phyllocoptruta oleivora, is one of the most important
pests of citrus in Florida. Mite population dynamics and effects of mite damage on
’Hamlin’ orange fruit were studied.
There was an accelerating increase in fruit surface damage in relation to
cumulative mite days. Fruit surface damage was fitted to a power function of
cumulative mite days. Fruit drop increased with increasing damage. The data
showed a slightly negative relationship between fruit size and mite damage.
Cumulative percent drop and percent diameter increase were fitted to two-variable
logistic functions of damage and time. With the increase of mean fruit surface
damage, the relative frequency distribution of fruit damage changed from an
xvii

exponential decay curve to a symmetrical unimodal curve, with the peak shifting
toward higher damage classes. The cumulative frequency distribution of fruit damage
was fitted to a two-variable logistic function of mean fruit damage and damage class.
Mite populations on fruit began to build up from early May to early June,
reached the highest levels in the rainy season (June, July, and August), and then
quickly declined. Mite populations on leaves followed the same pattern as on fruit.
The high humidity favored the epizootic development of the fungal pathogen
Hirsutella thompsonii, the major factor responsible for rapid mite population decline.
An age-structured model of the fruit-mite-pathogen system was developed.
Mean squared errors of prediction for rust mite populations on fruit in three cases
were 658.6, 306.6 and 1114.0, respectively, for a period of 5 months. High errors
were caused by high mite population densities, and a slight shift in predicted mite
population peaks as compared to the observed data.
A model was established to estimate volume loss from rust mite damage. The
model also allows us to determine volume loss for fresh fruit as well as for processed
fruit. The loss model was coupled with the population model. The coupled model
can predict: (1) mite/pathogen population trend; (2) fruit size growth; (3) fruit surface
damage; and (4) volume loss. The coupled model needs to be further tested for use
in rust mite management.
xviii

CHAPTER 1
LITERATURE REVIEW
Distribution and Production of Citrus
Citrus is thought to have originated in Southeast Asia. It is currently grown in
over 100 countries on six continents (Saunt 1990). It distributes in a belt spreading
approximately 40° latitude on each side of the Equator and is found in tropical and
sub-tropical regions where favorable soil and climatic conditions occur. The most
commercial citrus production, however, is restricted to two narrower belts in the sub¬
tropics roughly between 20° and 40° N and S of the Equator (Saunt 1990). The area
planted to citrus has been estimated at 2 million hectares and present-day production
of all types at 63 million tons, of which 71 per cent are oranges, 13 per cent
mandarins, 9 per cent lemons and limes, and 7 per cent grapefruit (Saunt 1990). The
United States once led in world production but now has been overtaken by Brazil.
These two countries produce about 42 per cent of the world’s citrus crop. The
majority of their citrus crop is processed, with 52 per cent in Brazil, and 66% in the
USA (Saunt 1990). In Florida, round oranges constitute 70% of the total citrus
acreage, and over 90% of the round oranges are used in processed products where
purchases of this type of fruit are usually based upon pounds of soluble solids per box
(Townsend & Abbitt 1978).
1

2
Origin and Distribution of the Citrus Rust Mite
The citrus rust mite (CRM), Phyllocoptruta oleivora (Ashmead) (Acari:
Eriophyidae), is thought to have originated in Southeast Asia—the indigenous habitat
of citrus (Yothers & Mason 1930, van Brussel 1975). It now occurs in almost all
citrus-growing areas in the world, including Europe, Africa, southern Asia, Australia
and Pacific Islands, North, Central and South America, and the West Indies
(Commonwealth Institute of Entomology 1970). The species probably was introduced
into many citrus-growing countries on imported fruit or planting material (van Brussel
1975), and is now considered as a serious pest of citrus in most humid regions of the
world where the crop is grown (McCoy & Albrigo 1975, Davidson & Lyon 1987).
The citrus rust mite was first reported and described in Florida by Ashmead
(1879), and for over 50 years it was the only species of eriophyid mites reported from
citrus in the world (Burditt et al. 1963). The citrus bud mite, Aceña sheldoni
(Ewing) was first reported and described from California in 1937 (Ewing 1937) and
was found in Florida in 1959 (Attiah 1959). Between 1955 and 1963, several new
species of eriophyid mites were collected from citrus around the world (Burditt et al.
1963). One of these is the pink citrus rust mite, Aculus pelekassi Keifer. This
species was first described by Keifer (1959) from specimens collected in Greece, and
was first found in Florida in 1962 in laboratory colonies of citrus rust mites (Burditt
et al. 1963) and subsequently in citrus nurseries and groves (Denmark 1963). The
name of the pink rust mite was later amended to Aculops pelekassi (Keifer).

3
The citrus rust mite, the citrus bud mite, and the pink citrus rust mite are the
only eriophyid species reportedly occurring on citrus in the United States. Among
them, the citrus rust mite is the most economically important. Yothers & Mason
(1930) proposed that the citrus rust mite was probably introduced on nursery trees
when they were first brought into Florida for propagation, and the spread of the citrus
rust mite over Florida, and probably in other citrus-growing states, was principally
through infested nursery stock. The citrus rust mite is currently one of the most
common and serious pests of citrus in Florida, Texas, Louisiana, and the costal areas
of California (Farmer’s Bulletin 1950, Davidson & Lyon 1987). The citrus rust mite
is more injurious in the south-central and west coastal areas than elsewhere in Florida
(Muma 1955b).
Taxonomic History
The citrus rust mite was first mentioned and described by Ashmead (1879) as
Typhlodromus oiliioorus. However, Ashmead a year later (1880) emended his first
spelling to Typhlodromus oleivorus. According to Ewing (1923), the genus
Typhlodromus is a synonym of Phytoptus, which in turn is a synonym of Eriophyes,
consequently the rust mite had long been placed in the genus Eriophyes (Yothers &
Mason 1930). Banks (1907) was the first to mention it under the name of
Phyllocoptes oleivorus (Ashmead). In 1938, Keifer erected a new genus,
Phyllocoptruta, and since then the citrus rust mite has been called Phyllocoptruta
oleivora (Ashmead) (van Brussel 1975).

4
Host Preference
Citrus rust mite infests plants of genera Citrus and Fortunella (family
Rutaceae) (Commonwealth Institute of Entomology 1970). Yothers & Mason (1930),
who listed many citrus species and varieties grown in Florida, observed the following
order of severity of infestation: lemon > lime > citron > grapefruit > sweet
orange > Tangerine > Mandarin. They reported that the nearer varieties and
hybrids are related to a ’true’ Citrus species, the more favorable these plants are for
mite development, van Brussel (1975) also observed higher overall mite populations
in grapefruit groves than in orange groves in Surinam.
Life History and Habitat
Rearing Methods
The earliest attempts to rear citrus rust mite in the laboratory were made by
Yothers & Mason (1930) in Florida. They used a No. 0 gelatin capsule cage for the
confinement of the mites and attached the cage to the fruit surface with melted
paraffin. The stem of the fruit was placed in a vial of water to keep the fruit in good
condition. Adult mites were transferred to fresh fruit every few days as the older
fruit began to dry. Swirski & Amitai (1958) reared citrus rust mites on the fruit of
rooted lemon branches. Mites were confined in celluloid cells 2-3cm in diameter.
This method permitted rearing several generations of mites on the same fruit. Reed et
al. (1964) used Murcott Honey orange seedlings for rearing both citrus rust mites and
pink citrus rust mites in plastic screen cages in greenhouses. A ring of lanolin was
used to confine mites within a restricted area, by dipping a warm cork borer of the

5
required size into hot lanolin and stamping the lanolin onto a leaf or fruit.
Reproduction
Citrus rust mite reproduction was originally thought to be entirely by
parthenogenesis, and without males (Yothers & Mason 1930). Males were first
reported and described by Keifer (1938). The mode of reproduction was later found
to be arrhenotokous parthenogenesis (a type of haplodiploidy), in which unfertilized
eggs become males and fertilized eggs become females. This was proved by the fact
that isolated virgin females produced only male offspring while mixed groups of
males and females produced both sexes (Swirski & Amitai 1958, Oldfield et al. 1970,
Jeppson et al. 1975). Sperm transfer in this and closely related species is
accomplished by means of spermatophores which the males deposit on the fruit and
leaf surfaces at a rate of about 16 per day (Oldfield et al. 1970, Oldfield 1973,
Oldfield & Newell 1973a, 1973b). Sperm viability in the spermatophore was
observed to drop by the third day and all were inviable by the fifth day. Annual
oscillations in the sex ratio of the citrus rust mite natural populations have been
reported from Israel (Swirski & Amitai 1960).
Stages and Development
The adult citrus rust mite has an elongated and wedge-shaped body about three
times as long (150-180 ^m) as wide. Its color varies from light yellow to straw color
(Knapp 1983). It can be seen only with the aid of a hand lens of lOx or 20x
magnification. Due to its yellow color the mite can be seen more easily on green
leaves and fruit than on fruit already colored. The adult mite is composed of a

6
gnathosoma and a thanosoma which is the slender, tapering abdomen. The abdomen
is transversely striated and has the appearance of a number of rings which .
grow smaller toward the posterior end. There are usually 28 thanosomal rings
appearing on the dorsal surface, but on the ventral surface there are twice as many
(Yothers & Mason 1930). The mite has two pairs of short, anterior legs and a pair of
lobes on the posterior end which assist in movement and clinging to plant surfaces
(Yothers & Mason 1930, Knapp 1983). Egg deposition begins within a day or two
after the female reaches maturity and continues throughout her life, about 20 days
(Knapp 1983). The morning hours seem to be the time of greatest activity in egg
laying (Yothers & Mason 1930). The female lays one to two eggs a day or as many
as 20-30 eggs during her lifetime (Knapp 1983).
Immature mites undergo two molts before becoming adults. Nymphs in both
the first and second stages resemble the adult in color and shape except for their
smaller size and lack of complete ring formation.
Eggs are spherical with a smooth regular surface ranging in color from
transparent to pale translucent yellow. It is about one-fourth the size of the adult mite
(Knapp 1983). In spite of their small size, the eggs are relatively large for the size of
the female, and only one or two developed eggs occur in the abdomen at one time.
The eggs are laid, both singly and in groups, on the surface of leaves, fruit, and
young twigs (Knapp 1983). Eggs are usually found in the pits or depressions of the
surface. By far the largest percentage hatch out in the early morning. Bright, sunny,
warm mornings will cause the eggs to hatch in greater numbers, and cloudy or cool

7
weather retards their development (Yothers & Mason 1930).
Hubbard (1885) noted that the breeding continued throughout the year. Frost,
which was sometimes severe enough to kill adult mites, did no injury to the eggs, and
the severity of a winter had little if any effect on the prevalence of the mites during
the following summer. In droughts, however, there was some evidence that many of
the eggs dried from dessication (Hubbard 1885).
Developmental durations for egg, protonymph, deutonymph, preoviposition
period, and adult were found to be 3.05, 1.82, 1.34, 2.66, and 6.89 days in summer,
and 5.07, 4.3, 6.4, 5, and 11.3 in winter, respectively (Yothers & Mason 1930).
Bodenheimer (1951) calculated the developmental threshold for the citrus rust mite as
20°C based on the data of Yothers & Mason (1930). This threshold seems to be too
high (Swirski & Amitai 1958). Swirski & Amitai (1958) reported a developmental
threshold of 9.2 °C for both egg and nymphal stages. They also established
regression functions between developmental rate and temperature for both eggs and
larvae.
Hobza & Jeppson (1974) reported that the theoretical optimal temperature for
the citrus rust mite was 24.5°C, and the limiting temperatures were between 17.6°C
and 31.4°C. They quickly pointed out that the calculated developmental threshold of
17.6°C may be too high due to unfavorable fruit conditions at low temperatures
(20°C), and indicated that the actual temperature threshold should be between 15 and
17.6(± 1°C). They also found a strong linear relationship between citrus rust mite
population growth rate and humidity within the temperature range permitting growth,

8
and a strong quadratic relationship between population growth rate and temperature at
any fixed relative humidity. They developed a regression model to quantify the
relationship between population growth rate and constant conditions of temperature
and relative humidity.
Allen et al. (1994b) did the most comprehensive study on the effect of constant
temperatures on rust mite development and reproduction. They also established
equations to quantify the temperature effects on mite development and reproduction.
They calculated a developmental threshold of 11°C for the citrus rust mite.
Seki (1979) reported that a developmental threshold of 11.2°C for the pink
citrus rust mite, and that no oviposition was observed at 15°C.
Economic Importance
History of Economic Importance
Several years prior to 1879 in which the citrus rust mite was first reported and
described (Ashmead 1879), Florida orange growers were very much concerned about
the cause of russeted fruit. Some growers attributed it to a fungus; others to adverse
soil conditions (Yothers & Mason, 1930). According to Yothers & Mason (1930),
J.K. Gates was the first to find the mites on oranges and immediately ascribed
russeting to their presence. This discovery eventually led to the description of the
species by Ashmead (1879).
During the first 50 or so years after its first discovery, the citrus rust mite was
considered the third most injurious citrus pest in Florida, being exceeded in amount of
damage only by purple scale (Lepidosaphes beckii Newm.) and citrus whitefly

9
(Dialeurodes citri Ashm.) (Yothers & Mason 1930). Watson & Berger (1937) listed
citrus pests in order of importance as purple scale, rust mite, and common citrus
whitefly. This change of citrus rust mite importance obviously resulted from the
reduction in whitefly populations due to the effectiveness of several species of
parasitic fungi which attack the immature stages of the citrus whitefly (McCoy 1985).
In 1957 and 1958, the hymenopterous parasite, Aphytis lepidosaphes, was found
fortuitously in Florida for the first time (Clancy & Muma 1959). It was established
in all citrus areas in a short time and effectively controlled the purple scale
populations (Selhime & Brooks 1977). As a result, the citrus rust mite emerged as
the most important economic arthropod pest of Florida citrus, and it remains so
(Knapp 1983). According to McCoy et al. (1976a), 87% of the citrus acreage in
Florida received from 3-5 pesticidal sprays per year for citrus rust mite control at an
estimated cost of 40-50 million dollars in 1973. This estimate is probably too high.
The premier economic importance of the citrus rust mite is currently being challenged
by the citrus leafminer, Phyllocnistis citrella Stainton, which was first discovered in
late May 1993 in southern Florida (Heppner 1993a, 1993b), and is now all over
Florida citrus growing areas. This moth causes severe damage to citrus plants and
great concern among Florida citrus growers (Knapp et al. 1993).
Rust Mite Injury
Feeding and food. Hubbard (1885) reported that the food of the citrus rust
mite consisted of the essential oil that abounds in all succulent parts of the orange,
and they did not feed on chlorophyll. It was once widely believed among citrus

10
growers that fruit injury was the result of the puncture of oil cells, although this
apparently is incorrect (Spencer and Osbum 1950). Yothers & Mason (1930)
demonstrated that the epidermal cells of the fruit were damaged by citrus rust mite .
McCoy and Albrigo (1975) further confirmed that citrus rust mite can only feed on
the epidermal cell layer of leaves and fruit, since the length of its piercing chelicerae
is on the order of 7 /im which is less than the depth of one cell . The diameter of the
puncture is about 0.5 - 1.0 /¿m, and is thus so small as to raise the question of
whether one puncture wound results in cell death or if more than one puncture in
some time period is required to kill an epidermal cell (Allen et al. 1992). This
question becomes potentially important when we attempt to construct models which
couple the mite feeding to fruit or leaf damage and loss.
Injury to leaves. Visible leaf injury is less common than fruit injury.
However, leaf injury can occasionally be severe (McCoy 1976). Injury to the upper
leaf surface is confined to epidermal cells and appears as small brownish spots or
blotches resembling the "russeting" condition common to immature fruit (Albrigo and
Mccoy 1974); severe injury can cause the upper leaf surface to lose its glossy
character taking on a dull bronze-like color and a rough texture that can be detected
by touch (Hubbard 1885, Yothers & Mason 1930). In many cases of severe injury,
localized degreening of the upper leaf cuticle may also develop, causing these
degreened areas to become a yellowish color similar to the condition occurring on
immature fruit (McCoy and Albrigo 1975). Injury to the lower leaf surface is
confined to epidermal cells which include the stomatal guard cells (Albrigo and

11
McCoy 1974). Lower surfaces often show ’leaf mesophyll collapse’ appearing first as
yellow degreened patches and later as necrotic spots (Thompson 1946, Albrigo and
McCoy 1974). However, lower leaf surface injury frequently stops with a browning
of the epidermal cells (Yothers and Mason 1930, Griffiths and Thompson 1957).
Albrigo et al. (1987) and Achor et al. (1991) reported that upper leaf surface lesions
on ’Sunburst’ mandarin by rust mite are more severe than those on other citrus
cultivars.
Injury to fruit. Damage to citrus fruit caused by citrus rust mites normally
affects only the surface layer of epidermal cells on the fruit (McCoy & Albrigo
1975). Fruit surface injury differs, depending on time of injury and variety of fruit
injured (Griffiths & Thompson 1957). In the case of grapefruit and lemons or limes,
injury during the early months of the fruit’s growth will cause a silvering of the peel
and, if severe, may result in a condition knows as "sharkskin". When this occurs
early enough fruit size is reduced. Such fruit will not take a sheen when polished. In
the case of oranges, early injury results in a brown cracking and scarring of the
surface. When the fruit is mature, this injury is called "russeting". Late injury takes
a high polish and is called "bronzing" (Griffiths & Thompson 1957). Early rust mite
injury was observed more on early and mid-season fruit than on the late varieties
(Thompson 1937). The terms "russet", "russetting", or "discoloration" are currently
referred to fruit surface damage regardless of the time the damage occurs.
A typical aspect of rust mite injury on an infested tree is that only some of the
fruit are heavily attacked, whereas others are damaged only slightly or not at all.

12
Even on a single fruit, the rust mite tends to infest only a portion of the fruit, leaving
the rest undamaged. This partial russeting on fruit also occurs on leaves, and the
mite spatial distribution is consistent with these damage patterns. Rust mites on citrus
fruit tend to avoid the bright sunlit area of a fruit in the direct solar beam where the
temperature may reach 45°C. The formation of rings of high mite density around the
solar exposed area often leads to halo damage patterns (russet) around these areas
(Hubbard 1885, Yothers and Mason 1930, Albrigo and McCoy 1974, Van Brussel
1975), while in the center of the solar hot-spot not a single mite can be found (Allen
and McCoy 1979). The rust mites are usually present in great abundance from one
to two weeks before extensive injury appears (Yothers and Mason 1930).
Injury to young twigs. Yothers & Mason (1930) observed that rust mites were
also found on the branches just after they had become reasonably mature, in some
cases so abundantly as to cause russeting on the bark. But high mite populations on
branches are seldom seen, and possible mite injury to branches is not of much
concern to growers.
Leaf injury and greasy spot. Griffiths & Thompson (1957) suspected the
possible effects of rust mite injury to the leaves on the development of greasy spot, a
disease caused by the fungus, Mycosphaerella citri Whiteside. In several field
experiments, van Brussel (1975) demonstrated that rust mite injury to leaves was
correlated with increasing severity of greasy spot infections.

13
Economic Loss
Although the citrus rust mite causes injuries to fruit, leaves, branches, and
may even be related to greasy spot infections, its most economic importance is due to
fruit surface damage. Heavy infestation of rust mites causes not only fruit surface
discoloration but also increased fruit drop and size reduction, with an associated loss
in fruit quality and yield (Yothers 1918, Yothers & Miller 1934, McCoy & Albrigo
1975, Allen 1976, 1978, 1979, McCoy et al. 1976). This section reviews previous
studies on economic effects of mite damage to leaves and fruit.
Leaf drop and size in relation to damage. The literature presents conflicting
reports as to whether citrus rust mite injury to leaves, even when severe, will cause
defoliation. According to Hubbard (1885), leaves never drop no matter how severe
the rust mite attack, but growth and vitality of the tree can be affected. This was
especially noticeable in young trees, which were frequently overrun by the rust mite
in early summer, and during the remainder of the year made little progress (Hubbard
1885). According to Griffiths and Thompson (1957), however, high populations on
leaves and green twigs can cause a general defoliation similar to that caused by citrus
red mite, particularly during periods of dry, windy weather in late fall, winter, and
early spring. McCoy (1976) reported that the overall defoliation of both healthy and
injured leaves was 9.5 %, being significantly greater on summer flush. McCoy
(1976) further indicated that citrus rust mite injury to the lower leaf surface appeared
to be associated with defoliation. Increased water loss through the destruction of
epidermal cells of the lower leaf surface may possibly be enough, particularly during

14
the dry periods, to cause leaf abscission (McCoy 1976). McCoy (1976) further
suggested that leaf abscission may not be severe enough to affect tree vigor and
subsequent yield of ’Valencia’ orange.
Yothers & Mason (1930) noted that in some instances, rust mites were so
abundant in the spring that the size of the leaves was reduced, and they further
commented that the devitalization caused by the presence of thousands of rust mites
on citrus foliage was much greater than the average grower realized. Unfortunately,
this lack of attention to leaf damage is still the case and most research has been
focused on fruit.
Fruit damage in relation to mite density. Allen (1976) made the first attempt
to establish a quantitative relationship between fruit surface damage and mite density
over the fruit growth season. The study showed that accumulated mite days (area
under the mite population graph) was almost linearly related to accumulated percent
damage on Valencia orange fruit surface. The study also indicated that damage rate
(percent per mite per day) was an increasing function of fruit age. The damage rate
on mature fruit in winter is higher than on young fruit in spring by about a factor of
10. The maximum damage rate for ’Valencia’ oranges was found to be 0.000115
(proportion mite'1 cm'2 d'1) (Allen 1976). A detailed review can be found in Allen et
al. (1994a).
Fruit growth in relation to damage. Flubbard (1885) noted that fruit heavily
damaged by citrus rust mite were smaller than undamaged fruit. Yothers (1918)
found that "russet’ grade (damaged) oranges were 12.5% smaller than undamaged

15
oranges prior to shipment. Allen (1979) made the first attempt to establish a cause
and effect relationship between citrus rust mite damage and small fruit size at harvest.
The study showed that damaged ’Duncan’ grapefruit with the same initial diameter
grew slower, and their final diameter was less than that for undamaged fruit. A
detailed review can be found in Allen et al. (1994a).
Fruit drop in relation to damage. Ismail (1971) showed that after picking,
fruit were found to lose water faster and abscise more readily if they had rust mite
damage. Ismail (1971) further demonstrated that rust mite damaged fruit lost more
than twice as much fresh weight as did sound, green fruit, and most of the loss in
fresh weight was due to moisture loss. Allen (1978) showed that water loss rate for
on-tree ’Valencia’ oranges was about 3 times higher for rust mite-damaged fruit than
for undamaged fruit regardless of fruit age, sun exposure or type of damage. Fruit
drop were increased by rust mite damage on ’Valencia’ and ’Pineapple’ oranges and
also ’Duncan’ grapefruit. Fruit with the highest amount of damage showed the
highest drop and those with no damage showed the lowest drop in all 3 varieties.
Since fruit drop is cumulative, the earliest damage can have the greatest total effect.
A model has been developed to quantify the effect of damage on fruit drop (Allen
1978, Allen et al. 1994a).
Fruit internal quality in relation to damage. It was believed that russeted fruit
was sweeter than undamaged fruit. Chemical analyses of undamaged and russetted
oranges indicated that russetted fruit was not so sweet as the undamaged fruit, and
that rust mite injury retarded the ripening to a considerable extent (Yothers & Mason

16
1930). The sweeter taste, according to Yothers (1918) and Yothers & Mason (1930),
probably occurred because russeted fruit were not sold before the holidays, and had
ample opportunity to fully ripen so no russet fruit was ever sour. McCoy et al.
(1976) showed that at harvest, fruit with localized and extensive surface bronzing
(damage) and peel shrinkage had a lower juice volume, higher soluble solids, higher
acids, and higher concentrations of acetaldehyde and ethanol than normal fruit. Allen
(1979) also reached similar conclusions, indicating that weight per fruit at harvest was
negatively correlated with damage by citrus rust mite for ’Valencia’ and ’Pineapple’
oranges and for ’Duncan’ grapefruit. For all 3 varieties, soluble solids and percent of
acid were positively correlated with citrus rust mite damage (Allen 1979). Similar
results have also been reported on the pink citrus rust mite Aculops pelekassi (Kato
1977, Tono et al. 1978).
Calculation of economic loss from rust mite damage. Economic loss caused by
rust mite damage includes three major components: (1) fruit surface damage; (2)
reduced fruit growth; and (3) increased fruit drop. Models combining the three
aspects of economic loss have been developed by Allen et al. (1994a) for ’Valencia’
orange.
Behavior and Ecoloev
Behavior and Distribution
Citrus rust mites tend to aggregate within trees and on individual fruit as a
result of environmental factors, notably sunlight and temperature. Rust mites can
endure hot sun but tend to avoid direct sunlight. Shaded groves and the shaded side

17
of fruit do not usually exhibit mite densities as high as semishade areas. Hubbard
(1885) observed that although the rust mite cannot long endure the direct light and
heat of the sun, they also avoid dark shade. As a result of this behavior, a rust ring
might be formed on the fruit between the proportion of the orange most directly
exposed to the sun’s rays and that in the densest shadow. Hubbard (1885) also
observed that the proportion of the fruit facing directly to the sun frequently presented
a bright spot, and the opposite side an area of lighter bronze, with less sharply
defined boundaries. A laboratory observation made by Yothers & Mason (1930)
showed that rust mites tended to aggregate to the light during the day and scatter
during the night, but mites appeared to avoid direct sunlight. A similar phenomenon
has also been observed by later researchers (Albrigo & McCoy 1974, van Brussel
1975, Allen & McCoy 1979, Allen & Stamper 1979). Allen & Syvertsen (1979)
reported that a model of fruit temperature in relation to solar radiation indicated
strong temperature and water vapor concentration deficit gradients on fruit surface.
Therefore, mite distribution on the fruit surface might be a response to differences in
temperature and humidity on different parts of the fruit surface. It was also observed
that the degree of aggregation generally increases with mite density (Hall et al. 1991).
Aggregation generally complicates sampling, and a variety of sampling methods have
been used by researchers to estimate levels of citrus rust mites (Yothers & Miller
1934, Pratt 1957, Allen 1976, Bullock 1981, Knapp et al. 1982, Childers & Selhime
1983, Peña & Baranowski 1990, Hall et al. 1991, Rogers 1992, Rogers et al. 1993).
McCoy (1979) reported that there was a tendency for the rust mite to migrate

18
to newly formed stem growth and the under surface of leaves near the base of the
spring flush in late-march mainly by crawling, and that development on spring flush
during April is generally slow but more rapid than corresponding development on old
(previous year) flush. Dean (1959b) reported that citrus rust mites on grapefruit
leaves were more numerous on the east as well as the north side of the tree, being
most numerous in the northeast quadrant.
Population Dynamics vs. Season
The seasonal abundance of the citrus rust mite has been discussed by numerous
researchers. In Florida, rust mite is present on citrus trees throughout the year
(Yothers & Mason 1930). The lowest population occurs in January and February.
During March and April their numbers increase rapidly. During May and the first
part of June the rate of increase is much more rapid than at any other time of the
year. The period of maximum infestation usually occurs during late June or July or
even August, well after the beginning of rainy season. During the later part of the
rainy season, mite populations diminish almost to the point of extinction (Hubbard
1885, Yothers and Mason 1930, Pratt 1957, Simanton 1960). A second but much
smaller population peak usually occurs between November and early January (Yothers
and Mason, Pratt 1957, Knapp 1983). After this they very slowly and gradually
increase until the following June (Pratt 1957, Simanton 1960). The period of
maximum infestation occurs first on lemon and then on grapefruit and about one
month later on orange (Yothers & Mason, 1930).
Rust mite population is usually higher on fruit than on leaves, and citrus rust

19
mite prefers the lower leaf surface to the upper surface (Yothers & Mason 1930,
Thompson 1937, Swirski 1962).
Although the seasonal abundance of citrus rust mite appears to follow a
distinct patten of two population peaks, weather, natural enemies, and particularly
horticultural practices will cause atypical population fluctuations to the extent that
damage may occur any time of the year (McCoy et al. 1976, McCoy 1979). McCoy
et al. (1976) found typical mite population dynamics under unsprayed conditions;
however, peak densities varied in time and intensity under sprayed conditions.
Population Dynamics vs Climatic Factors
For many years it had been thought by citrus growers that heavy rains of
summer were directly responsible for the scarcity of rust mites during the rainy
season. They had thought that the heavy rains washed the mites from the foliage and
fruit. But Yothers & Mason (1930) reported that rust mites seemed to have the power
of sticking to the foliage in spite of the rains, although heavy driving rains did wash a
few mites from the foliage and fruit. This diminution in numbers was not appreciable
and had little or no bearing either on methods of control or on subsequent abundance
of the mites. This scarcity of rust mites was later attributed to the fungus disease,
Hirsutella thompsonii (Fisher et al. 1949, McCoy & Kanavel 1969).
Humid weather, as measured by the number of hours at the dew point
temperature, is favorable to the increase in rust mite population. Maximum
population levels are reached during the summer rainy season, and the winter period
of moderate rain, fog, and heavy dew. Dean (1959a) reported that rust mite

20
populations increased particularly during periods of high relative humidity while
periods of low relative humidity and very windy weather seemed unfavorable. Rust
mites increased generally following periods of greater precipitation, which appeared to
be associated with higher humidity, and Dean (1959a) further stated that relative
humidity appeared to be the most important weather factor influencing citrus rust mite
populations.
In Surinam, van Brussel (1975) reported that during rainy season, counts of
rust mites were low, and mite population increased at the beginning of the dry
seasons. Maximum counts were reached in 4-5 weeks, and then dropped to a low
level in a similar period. Low mite counts during the rainy seasons were not entirely
attributable to the entomophagous fungus H. thompsonii, despite the favorable moist
conditions for fungal growth. They were neither the result of washing-off by rain,
nor of drowning (the adult can survive 12 hours in water). They seemed to be the
result of larval mortality, which increased when larvae were wetted and a water film
was present on the food plant. A moist substrate seemed to interfere with molting,
and rain also interfered in oviposition since rust mites avoided egg-laying on wetted
parts of the food plants. The part of fruit exposed directly to sunlight were less
attractive to the rust mite than others, but these areas were also exposed to dew
condensation at night.
Yothers & Mason (1930) reported that although the freeze in February 1917
killed more than 99% of the mites in almost all Florida citrus groves due to low
temperature and heavy infestation, the only results of the reduction of mites by the

21
freeze in February was the postponement of the time of maximum infestation for a
about one month or six weeks. Yothers & Mason (1930) also reported that the
drought of the spring of 1922 effectively prevented mite population growth.
Mite-Pathogen Interaction
H. thompsonii Fisher (Fisher 1950a), is a specific fungal pathogen of Acari,
particularly eriophyid and tetranychid mites inhabiting citrus and other plants
throughout the world. It is recognized as the most important natural enemy attacking
citrus rust mite in Florida (Speare & Yothers 1924, Yothers & Mason 1930, Fisher et
al. 1949, Muma 1955b, 1958, McCoy & Kanavel 1969, McCoy et al 1976, Lipa
1971, McCoy 1981).
Spears and Yothers (1924), who studied the citrus rust mite in citrus orchards
in Florida, were the first to suggest that the marked decrease in mite numbers—a
phenomenon which occurred annually with the onset of the rainy season at the end of
June or early July - was probably due to a fungal disease. High mite populations per
grapefruit in the hundred thousands dropped to almost zero by the end of September.
Spears and Yothers (1924) observed hyphal bodies in abnormally dark-colored
sluggish mites. Furthermore they noticed mycelia on dead mites with hyphae
protruding from the cadavers. It was also noted that rust mites were more abundant
on trees sprayed with fungicides (copper sprays or compounds) than on unsprayed
trees (Winston et al. 1923), and the use of such fungicides evidently eliminated the
fungus disease which, under normal conditions, would have attacked the rust mites.
Yothers & Mason (1930), in reporting similar data, concluded that the reduction in

22
mite numbers could not have been the result of food scarcity, since on average only
half the untreated fruit were severely infested with rust mites. Fisher et al. (1949)
tentatively identified the fungus, which was regularly associated with dead mites as a
Hirsutella species, and later described as H. thompsonii (Fisher 1950a). Muma
(1955b) found that about 70% of the mites were infected with H. thompsonii, and that
the severity and duration of the fungal outbreak was proportional to mite density
(Muma 1958). Both Fisher et al. (1949) and Burditt et al. (1963) described color
changes of the citrus rust mite infected with H. thompsonii. McCoy and Kanavel
(1969) isolated the fungus on an artificial medium and confirmed its pathogenicity
against citrus rust mite. The biology and pathogenicity of H. thompsonii were further
studied by McCoy (1978a), Gerson et al. (1979), and Kenneth et al. (1979).
Both of the two nymphal stages and the adult can be infected by the pathogen
under field conditions (personal communication, C. W. McCoy), and the infectivity is
dependent on the presence of free water and high humidity (McCoy 1978a, Gerson et
al. 1979, Kenneth et al. 1979). In Florida, epizootics caused by interaction of
weather, mite and fungus occur regularly in summer, and diseased mites can be found
on fruit and foliage throughout the year (McCoy 1978a, McCoy 1981). Epizootics
lasting 2-3 weeks develop regularly in summer, and elimination of the mites results in
a high fungal residue that usually prevents further mite build-up during the fall and
winter (McCoy 1981).
H. thompsonii produces a conidium on conidiophores found on an external
mycelium outside the host on the plant substrate. Infection appears to be highest on a

23
substrate with free water; however, it will also occur at 90 to 100% relative humidity
(McCoy 1978). Once inside the host, the hyphae form a ramifying growth within the
hemocoel and after death erupt through the host cuticle onto the plant surface where
they reproduce asexually. It takes less than 4 hours for a spore to penetrate the mite
cuticle and about 2 days for the total infection process to be completed to sporulation
at 26-27°C (McCoy 1978, Gerson et al. 1979, Kenneth et al. 1979).
H. thompsonii has been developed as a mycoacaricide for the control of the
citrus rust mite by workers in the USA (McCoy and Selhime 1977, McCoy 1978a,
Mccoy and Couch 1978, McCoy et al. 1978, McCoy 1981, McCoy & Couch 1982,
van Winkelhoff & McCoy 1984), Surinam (Van Brussel 1975), and China (Yen
1974), but is not presently available commercially.
In Florida, application of fragmented mycelia of H. thompsonii resulted in
decreased mite numbers on the leaves and increased rate of mite infection at 1 week
post-treatment, and mite populations remained at low levels for 10-14 weeks (McCoy
et al. 1971, McCoy & Selhime 1977, McCoy 1978). These studies also showed that
the disease spread rapidly to untreated areas once the fungal epizootic reached a peak
in treated trees (McCoy 1978a). In Texas, different concentrations of Hirsutella
mycelia gave 40% infection of citrus rust mites after 6 days under laboratory
conditions (Villalon & Dean 1974).
In Surinam, van Brussel (1975) achieved control of low citrus rust mite
populations by applying a mycelial suspension of H. thompsonii at a dosage of 0.05 to
1 g/liter.

24
In Chekiang Province, China, the application of H. thompsonii for citrus rust
mite resulted in 90% mortality after 3 days (Yen 1974).
The reliability of this control, however, appears to be related to the effect of
weather on the survival of the mycelia during the 48 h after application. Applications
applied on cloudy days or in the late afternoon or early evening gave best results
(McCoy 1978a).
In addition to its potential as a mycoacaricide, H. thompsonii is a great
resource as a natural enemy of the citrus rust mite in groves where fruit is grown for
processing (McCoy et al. 1976a, McCoy et al. 1976b). McCoy (1978b) reported that
the use of oil as a selective fungicide, and the maintenance of higher citrus rust mite
densities in the summer significantly increased the natural control of citrus rust mite
by the parasitic fungus H. thompsonii without greatly affecting external fruit quality.
The seasonal incidence of disease in mite populations was significantly higher and
more effective in the unsprayed plots where citrus rust mite populations were
maintained at high densities (McCoy 1978b).
Similar effects by H. thompsonii to the blueberry bud mite (Acolitas vaccinii)
were reported (Baker & Neunzig 1968)
Management of Citrus Rust Mite
Chemical Control
Pesticides. Before 1957, sulfur and lime-sulfur were the only materials used
in Florida to control citrus rust mite (Hubbard 1885, Johnson 1961). Fisher (1957)
reported that zineb (zinc ethylene-bis-dithiocarbamate) very effectively controlled

25
russeting of citrus fruit. Johnson et al. (1957) showed that zineb and maneb
(manganese ethylene-bis-dithiocarbamate) controlled citrus rust mite. Currently
pesticides used to control citrus rust mite includes Petroleum oil, Kelthane, Ethion,
Agrimek, and Vendex (Childers & Selhime 1983, Knapp 1992).
Fungicides vs. H. thompsonii. Winston et al. (1923) first reported that citrus
rust mite was more abundant on copper sprayed citrus than on unsprayed citrus.
Yothers & Mason (1930) also reported that rust mites were more abundant following
copper sprays than where these sprays were omitted. Thompson (1939) reached the
same conclusion, especially if mites are present in small numbers at the time the
spray was applied. Griffiths & Fisher (1949, 1950) further demonstrated that copper
and zinc containing sprays were reducing the number of H. thompsonii, the
unsprayed controls had the lowest numbers of rust mites and the zinc and copper plots
had the highest numbers of rust mite. However, Lye et al. (1990) reported that
copper sprays, applied when the mite population started to increase, slightly reduced
mite populations in most of the sampling dates, but they did not examine the possible
adverse effect of copper on H. thompsonii.
Cultural Control
Hubbard (1885) observed that fruit were less liable to rust on low lands
compared to high lands and that groves planted upon moist, rich hammock or clay
soils, as a rule, produced fruit with less damage than those on high, sandy pine lands.
This result was commonly attributed to the abundance of moisture in low ground; but
it may be more directly due to the denser shade afforded by a more vigorous foliage

26
and reduced radiation from a darker soil. Townsend & Abbitt (1978) reported that
the east coast recorded the lowest rust mite activity and the ridge and west coast area
the highest. Bodenheimer (1951) observed that groves planted on wide spacings were
heavily attacked, especially young groves. It was generally believed that the citrus
rust mite is ordinarily less abundant on citrus trees growing in a cover crop than in
groves without a cover crop. One theory is that parasites, and especially the fungal
pathogen H. thompsonii flourish under humid conditions and that the relative humidity
in a grove in cover crop is higher than in one kept clean-cultivated. But Osbum &
Mathis (1944) observed no difference in rust mite infestation between trees growing
under these two conditions; however there were very small differences between the
temperatures and humidities recorded under the two treatments. Muma (1961)
reached similar conclusions. Cultural control methods have not been extensively used
for mite control.
Biological Control
Predators and parasitoids. The strawberry mite, Agistemus floridanus
Gonzalez, was found to feed and complete its life cycle on at least four economically
injurious pests of citrus, the citrus rust mite, Phyllocoptruta oleivora, the Texas citrus
mite, Eutetranychus banksi (McG.), the cloudy-winged whitefly, Dialeurodes citrifolii
(Morgan), and the six-spotted mite, Eotetranychus sexmaculatus (Riley)(Muma &
Selhime 1971). Maximum populations normally occur during the winter and spring
but can occur during the summer and fall. Muma & Selhime (1971) noted that the
strawberry mite does not appear to have a biological control potential on citrus in

27
Florida. Other predator species reportedly attacking the citrus rust mite include adult
mealywing (Coniopteryx vicina Hagen) (Muma 1955b, Muma 1967), adult lady beetle
Stcthorus nanus Lac. (Yothers & Mason 1930), black hunter thrips (Leptothrips mail
(Fitch) (Muma 1955a), the immature stage of a cecidomyid fly (Hubbard 1883,
Yothers & Mason 1930), syrphid flies and predaceous thrips (Aleurodothrips
fasciapennis) (Watson & Berger 1937). McCoy (1985) reported a new phytoseiid,
Euseius mesembrinus, which feeds on citrus rust mite. No internal parasite has ever
been found attacking the citrus rust mite (Yothers & Mason 1930). It is generally
believed that predators and parasitoids can not effectively control the citrus rust mite.
Pathogens. Except for the fungal pathogen H. thompsonii, no other pathogens
have been reported to attack the citrus rust mite. The parasitic fungus, H. thompsonii
Fisher, was the only significant natural enemy influencing citrus rust mite populations
(Spear & Yothers 1924, Yothers & Mason 1930, Fisher et al. 1949, Muma 1955,
McCoy & Kanavel 1969, van Brussel 1975, Gerson et al. 1979, Kenneth et al. 1979).
Integrated Control
Yothers (1918) reported that there was a very significant reduction in fruit
yield between sprayed and unsprayed plots from 1913 to 1915. But in a three year
study, Griffths (1951) found no significant yield differences in yield and internal
quality between sprayed and unsprayed groves, and the scales and citrus red mites
were less prevalent on the unsprayed grove. McCoy et al. (1976a, 1976b) reported
that the injury threshold for citrus rust mite was far above the current spray threshold,
medium oil spray was less detrimental than copper to the parasitic fungus of the citrus

28
rust mite and is preferable for greasy spot control in integrated systems. McCoy et
al. (1976a, 1976 b) further reported that the parasitic fungus, H. thompsonii, was
more effective in integrated systems where citrus rust mite populations were
maintained at high densities.
Survey Methodology
Various methods have been developed to estimate mite population density
(Yothers 1934, Turner 1975, Allen 1976, Hall et al. 1991, Rogers 1992, Rogers et
al. 1993). A hand lens is a very common instrument for estimating mite populations.
Those used usually have lOx or 20x magnification. With lOx magnification, only
immatures and adults can be seen; with 20x magnification, eggs, immatures, adults,
and visibly diseased mites are observable. An improvement made by Allen (1976) is
to mount a lOx or 20x magnifying lens over a piece of clear plastic upon which a cm2
grid has been etched. The grid is divided into 25 equal subdivisions, each having an
area of 4 mm2. All the mites under the grid or subdivisions are counted. This lens is
typically used for detailed studies. The most commonly used methods for quick
commercial scouting include the percent infested lens field (Yothers 1934, Knapp
1983) and the HB coding system (Rogers 1992, Rogers et al. 1993).
Study Objective and Methodology
Previous studies have made tremendous contributions to understanding the
citrus rust mite population system, and to the improved practices in rust mite control
(McCoy 1976a, 1976b, Allen 1980, 1981, Knapp 1983, Hall et al. 1991, Anonymous
1993, Rogers et al. 1993). As this review indicates, excellent quantitative studies

29
have been conducted on ’Valencia’ and ’Pineapple’ oranges and grapefruit (Allen
1976, 1977, 1978, 1979, 1980, 1981, Allen & Stamper 1979, Hall et al. 1991, Allen
et al. 1994). My study will be an extension of the quantitative studies by Allen, and
will be mainly concentrated on ’Hamlin’ orange, especially on fruit. The overall
objective is to develop a system for predicting CRM populations and evaluating
resulting damage or loss which can help growers make the best control decision with
a reduction in control costs. In order to achieve this objective, my approach was to
design a general framework for the proposed system, study the individual
components, and finally incorporate the individual components into an interacting and
cohesive entity. There are two major components in the system: (1) damage
dynamics and (2) rust mite population dynamics. The damage dynamics component
includes four aspects of rust mite damage: (a) relationship between mite population
density and fruit surface damage; (b) frequency distribution of mite damage on fruit in
a grove; (c) relationship between fruit surface damage and fruit drop; (d) relationship
between fruit surface damage and fruit growth. This information will enable us to
determine quantitatively the pest status of the citrus rust mite. In practical citrus
production, pesticide application decisions require reliable prediction of potential mite
population trends and resulting damage. The rust mite population dynamics model
would help to predict short-term mite population trends. The major biological factors
affecting mite population dynamics are probably the fungal pathogen H. thompsonii
and undamaged fruit surface. The major climatic factors are probably temperature,
humidity, and rainfall. These factors will be included in the mite population

30
dynamics component.
By combining damage dynamics and mite population dynamics, one will be
able to (1) estimate total volume and value loss from rust mite damage; (2) predict
mite population trend; and (3) predict potential mite damage and volume/value loss.
These results will help growers to make necessary mite control decisions.
The following chapters report major results of my studies. Each chapter starts
with a brief statement of the problem and a statement of a specific objective,
continues on materials and methods, and then results and discussion. The last chapter
is a summary of major results from my studies.

CHAPTER 2
RELATIONSHIP BETWEEN MITE POPULATION
DENSITY AND FRUIT DAMAGE
Statement of the Problem and Study Objective
Predicting the dynamics of a crop-pest system is an important component of a
pest management program. In order to achieve this objective, we should at least
obtain the following information: 1) population dynamics (population prediction); 2)
damage dynamics (damage prediction); 3) yield loss (loss prediction). The citrus rust
mite, Phyllocoptruta oleivora (Acari: Eriophyidae), infests fruit, leaves, and young
twigs of all citrus species and varieties. It is a serious pest of citrus in Florida
(Knapp 1983), and most humid regions of the world (Davison & Lyon 1987). Its
economic importance is mainly due to damage to the fruit surface through extensive
feeding (McCoy & Albrigo 1975). Discolored fruit have less market value.
Furthermore, highly damaged fruit have a smaller growth rate and a higher drop rate,
if damage occurs early in the fruit growing season (Allen 1978, 1979, Yang et al.
1994). Mathematical models have already been established to relate fruit surface
damage to yield loss (Allen 1978, 1979, Yang et al. 1994). A study was conducted
to relate mite population density to rust mite damage on ’Valencia’ orange fruit (Allen
1976). The current study was undertaken to determine a quantitative relationship
31

32
between population dynamics of citrus rust mite and damage to ’Hamlin’ orange fruit,
which will be used as a damage prediction model of the mite IPM system.
Materials and Methods
Mite Damage
This study consists of six similar field studies, five of which were carried out
at a research citrus grove of the University of Florida Horticultural Sciences
Department, in Alachua County, FL., and the other at a commercial citrus grove in
Polk County, FL.
Studies 1-5 were located at the research grove consisted of an area of about 2
acres, with 8-yr-old ’Hamlin’ orange trees. Eight rows of trees ran from south to
north, with each row consisting of 14 trees. The sampling area consisted of the six
central rows of the study plot. The grove was well- maintained, and was irrigated by
a drip irrigation system as needed. A petroleum oil spray was applied on 14 July
1993 to control citrus rust mites, causing a 56% mite mortality by July 16.
Study 6 was located at the commercial citrus grove in Polk County. The study
plot consisted of an area of about 5 acres, with eight rows of trees running from south
to north, with each row consisting of about 35 trees, with 4-yr-old ’Hamlin’ orange
trees. The grove was also well-maintained. Irrigation was by overhead sprinklers.
A nutritional spray was applied on 12 June 1993, but the spray didn’t have much
effect on citrus rust mite populations. Sampling plans for the six studies were as
follows:

33
Study 1. This study was designed to elucidate the relationship between mite
density and fruit surface damage at the grove level. Twenty five trees were randomly
selected, six fruit from each tree were then selected and tagged, a total of 150 fruit.
Fruit were chosen so that they were approximately evenly spaced around the tree.
The study period was from 8 May to 11 December 1992.
Study 2.3.4. Studies 2, 3, 4 were designed to determine the possible effect of
fruit maturity on mite damage rate. They were conducted in the same grove as in
study 1 but on different fruit. In each of these three studies, fruit already with low
mite populations were specifically (not randomly) chosen and tagged. Mite population
density and fruit surface damage were estimated until mite populations declined to a
very low level. The duration and sample size for each of the studies were as follows:
17 June to 14 August 1992 (study 2: n = 30); 10 July to 11 September 1992 (study 3:
n=45); 4 September to 11 December 1992 (study 4: n=40).
Study 5. To obtain corroborating information on mite damage rate at the
grove level, a similar study was conducted from 24 May to 5 November 1993 in the
same grove as for the previous four studies. Thirty trees were randomly selected, six
fruit from each tree were then selected and tagged, for a total of 180 fruit. Fruit
were chosen so that they were evenly spaced around the tree.
Study 6. This study was designed to determine possible effects of tree age and
location on damage rate. It was conducted at the commercial citrus grove. The
sampling area was located at the center of the study plot. Twenty five trees were
randomly selected from each of the central 6 rows at every sampling, with one

fruitfrom each tree, for a total of 150 fruit. The study was conducted from 28 May
to 17 Nov. 1993.
34
In all the six studies, the sampling interval was 1-3 times a week. Rust mite
population density was determined with the help of a 20x hand lens mounted over a
piece of clear plastic upon which a one cm2 grid had been etched. The grid was
divided into 25 equal subdivisions, each having an area of 4 mm2. Only mites within
the middle 4 squares were counted, for a total area of 4*4 (i.e. 16 mm2) per count.
In the study at the research citrus grove, four counts were made for each fruit (i.e. a
total of 4*4*4=64 mm2 fruit surface area), with one count from each quadrant of the
fruit. In the study at the commercial citrus grove, eight counts were made for each
fruit (i.e. a total of 8*4*4 = 128 mm2 fruit surface area), with two counts from each
quadrant. Mite density was converted to mites/cm2 for data analysis. Fruit surface
damage was estimated visually at each sampling date. The method for damage
estimation was to visually examine the four quadrants of a damaged fruit, and then
estimate the percent damaged surface area. A comparative study by Allen (personal
communication) indicated that average variation in damage estimation for the same
person and among different people was about 5-10%. Allen’s comparative study also
showed that this variation decreased with experience and with the increase in sample
size. Damage estimation usually is more accurate in the cases of both low and high
surface damage, and less accurate in the case of intermediate surface damage. This is
because of the nonlinear response of human eyes to object surface.

35
Fruit Growth
As part of the attempt to determine the possible effects of fruit maturity on
mite damage rate, measurement of fruit growth was conducted at the research grove
from 8 May 1992 to 17 February 1993. Fruit surface area growth was considered as
an indicator of fruit maturity. At the beginning of fruit growing season in early
spring, six fruit from each of the 25 tagged trees in study 1 were randomly selected
and tagged, a total of 150 fruit. Fruit were chosen so that they were about evenly
spaced around the tree. Fruit equatorial circumference was measured with a flexible
measuring tape. Measurements were taken every one to two weeks. These fruit were
kept from mite damage by applying abamectin (Agrimek, MSD Agvet, Merk & Co.,
Inc.) when mite populations on the fruit were high. Fruit with high mite populations
were dipped into a 1:5000 Agrimek solution twice during the study period: once on
16 July 1992, and again on 7 August 1992. A summary of all the experimental
designs can be found in Table 2-1.
Data Analysis
Damage (Damage Rate). To avoid excessive use of symbols, the same symbol
in different equations might have different meanings and values. Mite population
density was converted to mites/cm2. Since eggs were unlikely to do any damage to
the fruit, mite-days were calculated based on the nymphal and adult mite density.
The formula for calculating mite days is: Mite days = (Mean mite density between
two consecutive samplings) * (Sampling interval). Working on ’Valencia’ oranges,

36
Table 2-1. Summary of experimental designs.
Study
Location
Duration No. fruit
Sampling
1
Alachua
May 08-Dec 11, 1992
150
Random T*
2
Alachua
Jun 17-Aug 14, 1992
30
Selectedb
3
Alachua
Jul 10-Sep 11, 1992
45
Selected
4
Alachua
Sep 04-Dec 11, 1992
40
Selected
5
Alachua
May 24-Nov 05, 1993
180
Random T
6
Polk
May 08-Nov 17, 1993
150
Random'
Fruit Growth Alachua
08 May 1992-17 Feb 1993 150
Random T
a Fruit were randomly selected and tagged at the beginning of the study, and
subsequent sampling were conducted on the same tagged fruit.
b Fruit were specifically selected so that they all had moderately low mite populations
which would increase in a short period of time and cause fruit damage at about the
same time.
' Fruit were randomly selected at every sampling date.

37
Allen (1976) started with the assumption that the rate of damage was proportional to
mite density, i.e.
^ = am(t) 2-1
dt
where y is cumulative % damage; m(t) is mite density, and a is instantaneous
damage rate per mite per day. If a is constant, equation 2-1 implies that ÉL is a
dt
linear function of mite density. Equation 2-1 is equivalent to
t
y=af m{t)dt
0 2-2
or
y = ax(t)
where *(?) = cumulative mite days (area under the mite population graph) at time t •
Data in Allen (1976) suggested that a is probably not constant (a function of time). I
adopted a pragmatic approach here of fitting the data to a power curve of the form
y = exp(a);ci’ 2-3
where y = cumulative percent damage; x = cumulative mite days; a and b —
constants. Equation 2-3 fitted the data well. By taking the derivative of equation 2-3
we obtain the instantaneous damage rate per mite day
— = exp (a)bxb~x
dx
2-4

38
where is equivalent to the "a" of equation 2-2 (i.e. the slope of mite days vs.
dx
damage graph). Here the damage per mite day ("a" of equation 2-2) is a nonlinear
function of mite days.
Fruit growth. Fruit was assumed to be spherical, and fruit surface area was
calculated based on measurements of fruit circumferences. We used a logistic growth
equation for fruit surface area (y ) in relation to time (t)
y = £ 2-5
* 1 + exp (a-bt)
Where y = cm2; t = time of the year (Julian days). The growth rate can be
obtained by taking the derivative of equation 2-5
dyg _ c*fc*exp(a-fo) 2-6
dt (1 + exp (a-bt))2
Data-fitting to equations were performed with TableCurve (Jandel Scientific
1992). The predetermined significance level for testing r2 (coefficient of
determination) (Cornell & Berger 1987) for each equation was />=0.05.
Results
Cumulative Damage vs. Cumulative Mite Days
The relationships between damage and mite days, from six sets of data, are
illustrated in Figs. 2-la to 2-6a, the parameters for the data-fitted curves are
presented in Table 2-2. All data sets (Figs. 2-la to 2-6a) demonstrated similar trends,

39
i.e. with the increase of mite days, damage showed an accelerating increase. This
trend was clearly demonstrated by an almost linear increase in damage rate per mite
day in relation to mite days (Figs. 2-la to 2-6a). The result from study 4 also
showed a slightly accelerating increase in damage with mite days(Fig. 2-4a), but this
accelerating effect is very small as compared with the other studies. This is probably
due to low mite population density.
Cumulative Mite Days vs. Time
When mite days were plotted against time, they exhibited a sigmoid growth in
all six sets of data (Figs. 2-lb to 2-6b). Since mite days equals the area under the
mite population curve, the shape of the population curve determines the shape of
cumulative mite days. Mite population dynamics curves are more or less
symmetrically bell-shaped in all six sets of data (Figs. 2-lc to 2-6c), resulting in
sigmoid cumulative mite day curves (Figs. 2-lb to 2-6b). If there were two
population peaks, we would expect a double-sigmoid curve of cumulative mite days.
If mite population were constant for a rather long time, we would expect a linear
increase in cumulative mite days with regard to time.
Damage Rate vs. Fruit Maturity
The data-fitted function for fruit area growth is
= 146.3346 2_7
y* ~ l+exp(4.389115-0.023039Í)
(R2 = 0.9930; F<0.05). The sigmoid trend of mite damage rate with time did not
closely correlate with fruit surface area growth which exhibited a more or less convex

40
growth during the study period (i.e. from 8 May 1992 to 17 February 1993) (Fig. 2-
7). This was clearly demonstrated by the results from studies 2, 3 and 4 (Figs. 2-2b
to 2-4b): The three sets of data obtained at different time of the year demonstrated
similar sigmoid trend in damage rate, which seemed to be more correlated with the
mite population peak than with fruit growth (Figs. 2-2b, c to 2-4b, c). In a study by
Allen (1976), the author suspected a possible relationship between the time-varying
damage rate and fruit maturity, both of which were sigmoid functions of time. The
current study indicated that damage rate was not necessarily related to fruit maturity,
but was an accelerating function of mite days. Although the damage rate was not
closely correlated with fruit maturity, time (i.e. fruit maturity) did affect the damage
rate, and therefore the damage. This effect was clearly demonstrated through the
results of studies 2, 3, and 4 (Figs. 2-2a to 2-4a): With increasing fruit maturity, it
took fewer and fewer mite days to cause the same amount of fruit surface damage.
For example, to cause a 10% fruit surface damage, it took about 3100, 2600, and
1500 mite days in June-August (study 2: Fig. 2-2a), July-September (study 3: Fig. 2-
3a), and September-November (study 4: Fig. 2-4a), respectively. In conclusion, the
original damage rate, equation 2-1, is probably a more complicated function involving
time-varying parameters and nonlinear mite density effects.
Damage vs. Tree Age and Location
Results from the research citrus grove (8-yr-old) and from the commercial
citrus grove (4-yr-old) showed similar trends in population dynamics (Fig. 2-5c vs. 2-
6c). The relationships between damage and mite days from the two studies were very

41
similar in 1993 (Fig. 2-5a vs. 2-6a). For example, 3000 mite days resulted in about
22% fruit surface damage in both groves (Fig. 2-5a vs. 2-6a). This was also
reflected in the similarity of the damage rate per mite day from the two studies (Fig.
2-5a vs. 2-6a). The results suggest that the general trend between mite days and
damage (equation 2-3) may hold true for trees with different ages and in different
areas, for the same citrus variety. This property of mite damage may greatly simplify
building damage models for rust mite management programs.
Discussion
Why Does Damage per Mite Day Increase with Mite Days? Results from this study
clearly demonstrated that damage rate increases with increasing mite days.
Observations on ’Valencia’ orange by Allen (1976) also indicated similar trend,
though the author related the damage rate increase to time instead of cumulative mite
days. There are several possible reasons for this phenomenon. One is that mites
inject digestive enzymes into cells while feeding, these enzymes might have an
accumulated accelerating effect in causing the death of epidermal cells. Another
reason is that death of a cell might expedite the death of adjacent damaged cells.
Another reason is human limitation in seeing the damage. The mites are so small that
they feed on individual cells causing punctures that are much smaller than the cells
themselves (McCoy & Albrigo 1975, Allen et al. 1992). Thus damage accumulates
one cell at a time. As the accumulation of dead cells becomes visible to the eye, it
might give rise to an artificial nonlinearity, i.e. fewer and fewer mite punctures are
needed to cause visible fruit surface damage, resulting in a superficial phenomenon of

42
increasing damage per mite day with season and mite days. Alternatively, there may
actually be nonlinear and threshold effects of mite density. The observed increase in
damage per mite day is probably a combined result of these factors. Fortunately,
whatever the explanation or mechanism(s), the derived empirical equations can still be
used in predicting mite-caused fruit surface damage.
Zero Damage Mite Density
It has been suggested (McCoy & Albrigo 1975, Allen et al. 1992) that cells
may recover from mite punctures, and if so, more than one puncture within a limited
time period may be needed to cause the death of a cell. This may be true since fruit
can support low mite populations without showing visible surface damage. We define
effective cumulative mite days (ECMD) as the total cumulative mite days minus the
cumulative mite days which have already recovered from mite feeding, and zero
damage density (ZDD) as the mite density at which the number of newly-punctured
cells equals to the number of cells recovered from mite feeding. The relationship
between Effective Cumulative Mite Days and Zero Damage Density can be described
by
t
ECMDit) = I (mit) -ZDD)dt 2-8
ro
where m(t) — mite density at time t • The zero damage density may be a function of
fruit maturity and damage. The effective cumulative mite days may give better
prediction of mite damage than cumulative mite days, especially when mite
populations are low for a long time. This subject is currently being studied.

43
What Is the Recommendation?
From the above analysis, it is clear that mite damage is affected by many
factors. The relationship between cumulative damage and cumulative mite days is
probably a combined result of these factors. It may take many years of research
before we can eventually elucidate the possible effects of different factors. Since
model parameter estimates for the six studies did not vary much (Table 2-2), I suggest
using an averaged model as a temporary damage prediction model, which can be
modified when more information is available. Since sampled fruit in studies 2, 3 and
4 were not randomly selected (see Materials and Methods), and may not represent the
fruit on a grove level, only results from studies 1, 5 and 6 were averaged. The
parameters for this damage prediction model is shown in Table 2-2. The prediction
model is
y = exp(-13.901008) **2 086012 2'9
This formula can be used in predicting fruit surface damage based on mite population
survey data or predicted mite populations.

44
Table 2-2. Parameter estimates for power curve, equation 2-3.
Study
Parameter
(a)
Parameter
(b)
R2
1
-11.120513
1.784393
0.9958*
2
-16.011120
2.273361
0.9895*
3
-17.912093
2.567227
0.9860*
4
- 5.539264
1.066059
0.9621*
5
-15.654411
2.269957
0.9958*
6
-14.928099
2.203687
0.9973*
1,5,6
-13.901008*
2.086012*
combined
2.435209b
0.263303b
4 Mean.
b SD.

Cumulative mite days
Adult-Immature mites / cmA2 Fruit surface damage (%)
45
Cumulative mite days
05
CD
E
ra
â– o
<15
o
CO
t
o
w
Fig. 2-1. Relationships between mite population and fruit damage (Study 1.
Alachua County, Florida, 1992). (a) Fruit surface damage/damage rate
vs. cumulative mite days; (b) Cumulative mite days/damage rate vs.
time; (c) Mite population dynamics/cumulative fruit surface damage vs.
time.

Adult-Immature mites / cmA2 Cumulative mite days
46
Vp
>
03
"D
d
E
®
03
l_
0
CT>
03
E
03
Q
Cumulative mite days
v?
>,
03
"O
d
'I
0
03
u.
0
O)
03
E
03
Q
Relationships between mite population and fruit damage (Study 2.
Alachua County, Florida, 1992). (a) Fruit surface damage/damage rate
vs. cumulative mite days; (b) Cumulative mite days/damage rate vs.
time; (c) Mite population dynamics/cumulative fruit surface damage vs.
time.
Fig. 2-2.
Fruit surface damage (%)

47
Fig. 2-3. Relationships between mite population and fruit damage (Study 3.
Alachua County, Florida, 1992). (a) Fruit surface damage/damage rate
vs. cumulative mite days; (b) Cumulative mite days/damage rate vs.
time; (c) Mite population dynamics/cumulative fruit surface damage vs.
time.

Cumulative mite days
Adult-Immature mites / cmA2 Fruit surface damage (%)
48
120 160 200 240 280 320 360
O)
03
E
03
"D
Q)
O
03
*fc
D
C/Í
Relationships between mite population and fruit damage (Study 4.
Alachua County, Florida, 1992). (a) Fruit surface damage/damage rate
vs. cumulative mite days; (b) Cumulative mite days/damage rate vs.
time; (c) Mite population dynamics/cumulative fruit surface damage vs.
time.
Fig. 2-4.

Cumulative mite days
Adult-Immature mites / cmA2 ^ruit surface damage (%)
49
>
cd
"D
0)
£
a
CD
1—
0)
05
cd
E
CD
a
Cumulative mite days
>
CD
"O
d
E
CD
■4—»
CD
CD
O)
CD
E
CD
Q
Julian day (1=1 Jan. 1993)
Fig. 2-5. Relationships between mite population and fruit damage (Study 5.
Alachua County, Florida, 1993). (a) Fruit surface damage/damage rate
vs. cumulative mite days; (b) Cumulative mite days/damage rate vs.
time; (c) Mite population dynamics/cumulative fruit surface damage vs.
time.

Cumulative mite days
Adult-Immature mites / cm»2 Fruit surface damage (%)
50
Cumulative mite days
CD
O)
ro
E
CO
â– O
o
CO
D
(/)
Relationships between mite population and fruit damage (Study 6. Polk
County, Florida, 1993). (a) Fruit surface damage/damage rate vs.
cumulative mite days; (b) Cumulative mite days/damage rate vs. time;
(c) Mite population dynamics/cumulative fruit surface damage vs. time.
Fig. 2-6.

Fruit surface area (cmA2)
51
Julian day (1=1 Jan. 1992)
Fig. 2-7.
Relationships between fruit surface area growth and time (Alachua
County, Florida, 1992).

CHAPTER 3
RELATIONSHIP BETWEEN MITE DAMAGE AND
FRUIT GROWTH AND DROP
Statement of the Problem and Study Objective
Reports on the economic importance of citrus rust mite refer not only to fruit
surface discoloration, but also to fruit drop and size reduction, with an associated loss
of fruit quality and yield. Hubbard (1885) noted that "...if severely attacked by the
rust mite before it has completed its growth, the orange does not attain its full size.
Very rusty fruit is always small." Yothers (1918) observed that "russet" grade
(damaged) oranges and grapefruit were 12.5% (volume) smaller than undamaged fruit
before shipment. Those studies did not indicate whether damaged and undamaged
fruit of the same initial size actually grow at different rates. Small size could
presumably be correlated with rust mite damage because of location effects on the tree
or because of higher mite densities on fruit that were initially small compared with
other fruit. Allen (1979a) made the first attempt to establish a cause-effect
relationship between rust mite damage and small fruit size at harvest, and showed that
damaged ’Duncan’ grapefruit grew slower and their final diameter was smaller than
for undamaged fruit. Another effect of rust mite damage is increased fruit drop.
Ismail (1971) showed that, after picking, fresh fruit were found to lose water faster
and develop an abscision zone more readily if they had rust mite damage. Studies by
52

53
Allen (1978, 1979b) indicated that fruit drop rates were increased by rust mite
damage on ’Valencia’ and ’Pineapple’ oranges and also on ’Duncan’ grapefruit.
The objective of this study was to measure the effects of rust mite damage on
’Hamlin’ orange fruit growth and drop, and to construct loss models for this variety
for use in rust mite management programs.
Materials and Methods
This study was conducted at a commercial citrus grove in Hendry County, FL,
from 8 June to 17 December 1991 with 5-yr-old ’Hamlin’ orange trees on Swingle
rootstock. Fruit were damaged by rust mites a week before the experiment was
started, and no subsequent damage occurred. Fruit were chosen to include a range of
rust mite damage from 0 to 100% of the fruit surface. Fruit with different amounts
of rust mite damage were tagged evenly around each tree to eliminate potential
location effects. Every 2-3 wk, transverse fruit diameters were measured with a
caliper, fruit surface damage was estimated visually, and fruit drop was recorded. A
total of 593 fruit were tagged on 55 trees (10-20 fruit per tree) for both growth and
drop studies. An additional 228 fruit (on another 10 trees) were tagged for the drop
study only. A follow-up study of correlation of fruit size with mite damage was
conducted in a ’Hamlin’ orange grove of the University of Florida Horticultural
Sciences Department in Alachua County in January 1992. Nine trees were chosen,
and diameters and damage of all the fruit on each tree were recorded. Mean diameter
and mean damage of all the fruit on each tree were obtained.

54
Data Analysis
Fruit drop and mite damage. Fruit were grouped into five equal intervals of
percentage surface damage: 0-19, 20-39,..., 80-100%. Mean damage and cumulative
rate of fruit drop were calculated for each category based on all the fruit tagged
initially. Cumulative percentage fruit drop (FDrop) was fitted to a two-variable
logistic function of damage (*) and time (t) with the SAS-NLIN procedure (SAS
Institute 1985). The form of the logistic function is
F = _ 3-1
rop 1 + exp(a-(b +cx)t)
A positive value of parameter c would indicate increasing fruit drop with increasing
mite damage (*). This function assumes that cumulative percentage fruit drop (F )
is logistic and that the rate (b + cx) within the logistic is a linear function of damage
(x).
Fruit growth and mite damage. To reduce the possible effects of initial
diameter differences on fruit growth, we used percentage diameter increase instead of
diameter as the growth indicator. Percent diameter increase (F ,) for each fruit
was obtained using the following formula:
Growth
Diameter at sampling date - Initial diameter (8 June) *
Initial diameter (8 June)
Fruit were grouped into five equal intervals of percentage surface damage: 0-
19, 20-39,..., 80-100%. Mean damage and mean percentage diameter increase were

55
calculated for each category. Percent diameter increase (f ) from individual fruit
was fitted to a two-variable logistic function of damage (x) and time (t) with SAS-
NLIN procedure (SAS Institute 1985). The form of the logistic function is
k + px
3-2
F,
Growth
1 + exp(a -(b + cx)r)
A negative value of parameter p would indicate smaller final % fruit growth
(FGrowth) incre^ng mite damage (x). A negative value of parameter c would
indicate a decreasing percent fruit growth (FCrowth) with increasing mite damage (x).
This function assumes that percentage fruit growth (FGrowth) is logistic and that both
the final percentage fruit growth (k + px) and the rate (¿ + cx) within the logistic are
linear functions of damage (x). The predetermined significance level for testing R2
(Cornell & Berger 1987) was P — 0.05. The predicted result was compared with
observed. Prediction error was calculated using the formula
3-3
Prediction error = Predicted value - Observed value
Mean squared error of prediction (MSEP) was calculated using the formula (Wallach
& Goffinet 1989, Thomley & Johnson 1990)
3-4
where m — number of observations; n = number of model parameters; y =
predicted value; y = observed value.

56
Results
Fruit Drop and Mite Damage
Fruit drop rate increased with increasing mite damage, and most drop occurred
late in the fruit growing season (Fig. 3-1). The cumulative drop by 17 December for
damage categories 0-19, 20-39, 40-59, 60-79, and 80-100% was 6.4, 9.3, 9.4, 12.6,
and 21.0%, respectively. These results were similar to those obtained by Allen
(1979b) on ’Valencia’ and ’Pineapple’ oranges and ’Duncan’ grapefruit. Our results
also indicated an accelerating fruit drop with increasing mite damage and time (Fig.
3-1). This effect is illustrated more clearly by fitting equation 3-1 to the data (Fig. 3-
2). The data-fitted model is
f = 122 3-5
^ 1 + exp (7.230067-(0.010659 + 0.00007473 x)f)
where FDrop = cumulative percent fruit drop, t = Julian day (1 = 1 January), x =
percentage fruit surface damage, R2 = 0.8197 (P < 0.05). Notice here that
parameter c of equation 3-1 is positive, indicating increasing fruit drop with
increasing mite damage as expected. The maximum prediction error was less than 6
(cumulative percent fruit drop) (Fig. 3-3). The mean squared error of prediction was
5.17.
Fruit growth and mite damage. Fruit with almost the same initial transverse
diameter and different amounts of rust mite damage grew at slightly different rates
and diverged slightly with time (Fig. 3-4). Diameter growth (percentage increase)
was always highest for the lowest damage category, and fruit diameters (by 17

57
December) for damage categories 20-39, 40-59, 60-79, and 80-100% grew 2.6, 2.5,
2.4, and 1.7% less, respectively, than that of the lowest category (Fig. 3-4). The
overall data suggested a slight negative relationship between final fruit size and mite
damage (Fig. 3-4). This effect is demonstrated in the data-fitted percentage diameter
increase model (Fig. 3-5). Fitting to the data, we obtained the following
parameterized form of equation 3-2
p = 33.73 - 0.0108* 3 6
Gr where FGrowth — percentage increase in fruit diameter, t = Julian day (1 = 1
January), x = percentage fruit surface damage, R2 = 0.8405 (P < 0.05). Notice
here that parameter p and c of equation 3-2 are both negative, indicating a negative
effect of mite damage on fruit growth. The maximum prediction error was less than
3 (percent diameter increase) (Fig. 3-6). The mean squared error of prediction was
1.62.
Discussion
A study by Allen (1979a) on the effect of mite damage on ’Duncan’ grapefruit
growth showed a greater size reduction than in our ’Hamlin’ orange study. In the
grapefruit study, size reduction resulted from growth divergence of the damage
categories during June, July, and August (the primary period of fruit expansion).
Timing of damage in relation to the fruit growth cycle is important. In our study,
most of the fruit growth terminated approximately 3 mo after damage had occurred
(’Hamlin’ is an early maturing variety), and differences in mean diameter among

58
damage categories were not as pronounced as in the case of ’Duncan’ grapefruit
(Allen 1979a). One reason for this is that the remaining diameter growth following
the damage for the ’Hamlin’ oranges in this study was approximately 30% as
compared with 50-80% remaining growth for the ’Duncan’ grapefruit (Allen 1979a).
Late-season (January 1992) observations on ’Hamlin’ oranges at the University of
Florida Horticultural Science Department grove showed a strong negative correlation
of fruit size with mite damage (Fig. 3-7). This is probably due to fruit shrinkage
from water loss. It is known that water loss from fruit is exacerbated (approximately
a 3-fold increase) by rust mite damage both on and off the tree (Ismail 1971, McCoy
et al. 1976, Allen 1978, 1979a) and is probably worse on small rootstock systems
than on large ones (Allen 1979a). Thus, water stress may be the mechanism
responsible for increased fruit drop with mite damage.
Because rust mite damage is associated with increased water loss, future
research might examine the possibility of reducing yield loss by minimizing water
stress on damaged fruit. That is, can we reduce pesticide usage and maintain yield by
substituting water management for rust mite management? Further studies should also
look for differences between early and late-season mite damage on fruit growth and
drop and on the effects of leaf damage on yield. The fruit growth and drop models
developed in this study will be used to estimate yield loss (percentage volume) from
rust mite damage. The difference between the yield loss and cost of mite control will
determine whether control action at a certain time is economically justified in a given
grove.

Observed cumulative drop (/°)
59
Fig.3-1. Observed cumulative fruit drop (percentage) for ’Hamlin’ orange fruit
with different amounts of rust mite damage (Hendry County,
FL.,1991).

60
x = Damage (%)
f'vfe-
V*-
( etCetv^
dt0p ^
d^VlsO^S'""
*$$>'"**
'if \99W
Y V-*- ’
. ,0^Sfl
LÚ0^ 3

Observed (% cum. drop)
61
Fig. 3-3.
Prediction error for the percent fruit drop of ’Hamlin’ orange fruit with
different of amounts rust mite damage (Hendry County, FL, 1991).

% diameter
62
Fig. 3-4.
Observed transverse diameter increase (percentage) of ’Hamlin’ orange
fruit with different of amounts rust mite damage (Hendry County, FL,
1991).

u\ V
u\V
A3p\9®lá
^*zz**~
(fc&
(%) 86eoiea = x
£9

Observed (% diam. increase)
64
Fig. 3-6.
Prediction error for the percent diameter increase of ’Hamlin’ orange
fruit with different of amounts rust mite damage (Hendry County, FL,
1991).

Mean fruit diameter (mm)
65
Fig. 3-7.
Mean fruit surface damage plotted against mean fruit diameter by tree
for nine ’Hamlin’ orange trees (Gainesville, FL, January 1992).

CHAPTER 4
FREQUENCY DISTRIBUTION OF MITE DAMAGE ON FRUIT
Statement of the Problem and Study Objective
Extensive feeding by the citrus rust mite, Phyllocoptruta oleivora (Ashmead)
(Acari: Eriophyidae) causes fruit surface discoloration (i.e. russet) (Albrigo & McCoy
1974, McCoy & Albrigo 1976), and it has been reported that heavy surface russet
reduces growth and increases drop of the damaged fruit (Allen 1978, 1979, Yang et
al. 1994). Mite damage is not equally distributed over all the fruit in a grove (Hall et
al. 1991), and furthermore, only high percentage surface damage shows obvious
effect on fruit growth and drop (Allen 1978, 1979). It is therefore important to know
the fraction of fruit in a grove that falls into the higher percentage russet categories.
More specifically, given the mean percentage fruit surface russet, one wants to know
the fractions of fruit that fall into various russet categories (i.e. the frequency
distribution). This would then permit us to calculate average losses over the
distribution from (1) reduced fruit grade, (2) reduced growth, and (3) increased drop
(Allen 1978, Allen et al. 1994a). Allen & Stamper (1979) reported that the relative
frequency distribution of mite damage on ’Valencia’ and ’Pineapple’ orange, and on
’Duncan’ grapefruit can be described with a modified beta distribution, with the mean
as its only parameter. In this study I seek to develop a simpler, closed-form density
and cumulative distribution function which avoids the somewhat awkward beta
66

67
function in integral form. The purpose was two fold: 1) to determine the frequency
distribution of percentage russet on ’Hamlin’ orange fruit, and 2) to express the
distribution in terms of the mean percentage russet with a simple mathematical
formula which will eventually be used in constructing loss models in rust mite
management programs.
Materials and Methods
This study was conducted at a commercial citrus grove in Polk County, FL,
from 24 August to 13 October 1993 with 4-yr-old ’Hamlin’ orange trees. The study
plot consisted of an area of about 5 acres, with eight rows of trees running from north
to south, with each row consisting of about 35 trees. The sampling area was located
at the center of the study plot. Ten trees were tagged at each of the central 6 rows
before any visible mite damage occurred. Ten fruit were randomly selected from
each of the four quadrants (south, east, north, and west) of a tagged tree, with a total
of forty fruit per tree. Fruit surface damage was estimated visually. Sampling was
made every one to two weeks. The total number of fruit for each sampling was
40*10*6 (i.e. 2400). The study plot was under regular management during the study
except that pesticides were not applied.
Data Analysis.
Fruit were grouped into a zero class and 5 % intervals of percentage surface
damage, i.e. 0, 1-5, 6-10, ..., 96-100%. Mean damage for each group was
calculated by averaging the damage of all the fruit included in the group. In the study
by Allen & Stamper (1979), group frequency was fitted directly to equations. In
attempts for simpler solutions, it was found that the logistic distribution function gave

68
excellent fit to the cumulative frequency distribution. The logistic distribution
function is
1
" — . («0,
1 + exp(-- -)
b
4-1
The mean of the logistic distribution is a; the variance of the logistic distribution is
TT *
— *bz (Patel et al. 1976). The purpose is to use mean damage to determine the
3
relative frequency of different damage classes. Since damage class (*) can only be
from 0 to 100%, therefore, only the part of the logistic distribution which lies
between o and 100 is used. The mean of this data-fitted truncated logistic
distribution is the mean damage, which is different from the mean (a) of the actual
logistic distribution, as is the variance. Parameters a and b of our fitted distribution
were found to change with mean fruit surface damage (p.). We therefore assumed
that parameters a and b were functions of mean fruit surface damage (p), i.e. and In order to determine the functional forms for fl(p) and ¿(p), we first
fitted each of the six sets of observed data to the logistic distribution function
(equation 4-1) separately, and then fitted the estimated a and b values to functions of
the mean damage (p). The following function was found to give a good fit to
parameter a in relation to mean fruit surface damage (p)

69
a(n) = a0 + a x\l + where aQ, av a2 =parameters. The following function was found to give good fit to
parameter
¿(p)=60+¿1exp(-¿>2p) 4-3
where ¿ bv b2 =parameters. The above data-fitting process was accomplished with
TableCurve (Jandel Scientific 1992). The final form of the cumulative frequency
distribution is the following two-variable logistic function of mean fruit surface
damage (jx) and damage class (*)
1
1 + exp(-
b( ii)
4-4
where ¿j(^) and b(\i) are functions of jx as defined in equations 4-2 and 4-3. I
replaced a(^) and b(\x) in equation 4-4 with equations 4-2 and 4-3, and then used the
SAS-NLIN procedure (SAS Institute 1985) for simultaneous estimation of all six
parameters (aQ, av a2, b0, bv b2) based on the original six sets of data. The final
frequency distributions were based on these SAS-NLIN estimates.
The corresponding density function can be obtained by taking the partial
derivative of the cumulative frequency distribution (equation 4-4) with respect to
damage class (*), giving

70
dF (x) h*tX^ h ^
Fm - 4*00 - b b
4-5
dx
(1 + exp(-^))2
b
Although the density function (equation 4-5) describes a continuous distribution from
negative infinity to positive infinity, our damage classes are limited only to the range
of [0, 100] %â–  To make the density function (equation 4-5) integrate to one between
0 and 100%, we should divide equation 6-5 by the total area {a) between these
limits. This area can be found directly from equation 4-4, so that
A = FFreq(100)-FFrJ0) =
1
1
Freq''
. . 100-a. . , 0-a.
1 +exp( -—-—) l+exp(-——)
b b
4-6
Dividing equation 4-5 by A, we obtain
1 . x-a.
1 7;exp(__r)
r , . 1 b b
fFrcqW = -*
A (1 + exp(-^))2
4-7
for our logistic density function where the dependence on ^ has been dropped for
simplicity. Mean squared error of prediction (MSEP) was calculated using the
formula (Wallach & Goffinet 1989, Thomley & Johnson 1990)
MSEP = £
¿-i
(Si-y)2
m-n
4-8
where m = number of observations; n = number of model parameters; y =
predicted value; y. = observed value.

71
Results
Quadrant Distribution of Damaged Fruit on Trees.
Damaged fruit were not equally distributed among the four quadrants of the
tree (Fig. 4-1). In the early stage of mite damage when the mean fruit surface
damage was low, fruit on the east quadrant of the tree had the highest mean surface
damage, followed by the north quadrant. But in the late stage of mite damage when
the mean fruit surface damage was increased, fruit on the north quadrant of the tree
had the highest mean surface damage, followed by the east quadrant. The west
quadrant always had the lowest mean surface damage. By the time of the last
observation (i.e. October 13, 1993), mean damage for the north, east, south, and west
quadrants were 42, 39, 30 and 24%, respectively. Since fruit surface damage is
directly related to total mite population supported by the fruit, the north side of the
tree should have the highest mite population, followed by the east, south and west.
Rust mites prefer moderate temperatures, and avoid direct sun-lit fruit surface when
air temperature is high (Hubbard 1885, Yothers & Mason 1930, Albrigo & McCoy
1974, Allen & Mccoy 1979). The uneven distribution of mite damage is probably a
result of mite response to the differences in temperature and sunlight distributions
among the quadrants. Allen & McCoy (1979) studied the temperature and rust mite
distribution in the north top, north bottom, south top, and south bottom quadrant of a
tree. Their results indicated that the north bottom quadrant had the most favorable
temperatures and usually the most rust mites; the south bottom was also favorable and
had high mite densities. They also found that the south top quadrant was least
favorable, often having temperatures in the lethal range, and had the lowest rust mite

72
population, but no observations were made on the east and west quadrant (Allen &
McCoy 1979). Rust mite scouting programs could probably make use of these
difference in mite distribution.
Distribution of Damaged Fruit.
Distribution of damaged fruit over the damage classes changed tremendously,
depending on the overall mean damage. When the mean damage was low, most of
the fruit had no rust mite damage, and the cumulative distribution demonstrated a
convex rise to a saturation plateau at one (Fig. 4-2). With the increase of mean fruit
surface damage, the proportion of fruit without damage decreased, and the proportion
of fruit with higher damage correspondingly increased. As a result, the cumulative
distribution changed from convex to sigmoid (Fig. 4-2). Each of the six sets of
cumulative distribution data was fitted to the logistic equation (equation 1), and the
results are summarized in Table 4-1. Parameters a and b were then fitted to
equations 4-2 and 4-3, respectively, as functions of mean percent damage (^). The
parameter estimates using the above two-step procedure and using SAS-NLIN
procedure (with equations 4-2 and 4-3 inserted into equation 4-4) are summarized in
Table 4-2. The relationships between parameters a(n) and ¿(|¿) and mean fruit
surface damage are shown in Fig. 4-3. The cumulative frequency distribution can be
obtained by replacing parameters a{u) and b(\x) in equation 4-4 with equations 4-2
and 4-3; the predicted results are shown in Fig. 4-4. The mean squared error of
prediction was 18.04.

73
The probability density function can be obtained by replacing parameters a(ji)
and ¿(y) in equation 4-7 with equations 4-2 and 4-3. The predicted probability
density distribution is shown in Fig. 4-5. With increasing
mean damage, the probability density curve changes from an exponential decay to a
symmetrical unimodal curve, with the peak shifting toward higher damage classes
(Fig. 4-5).
Discussion
Properties of the Cumulative Frequency Distribution Function.
The logistic distribution function (equation 4-1) has been used to model insect
phenology (Dennis et al. 1986, Kemp et al. 1986, Dennis & Kemp 1988) as a
stochastic process. Here we used the truncated logistic for describing the frequency
distribution of rust mite damage on citrus fruit. As manifested in the equations 4-2
and 4-3, the mean and variance of the full (untruncated) logistic distribution are
functions of the mean of the truncated distribution (the data). Parameter
exhibits a sharp increase when the mean fruit surface damage is low, and a slower
linear increase with further increase in mean damage (equation 4-2, Fig. 4-3).
Parameter ¿(^) also exhibited a sharp increase, but then approaches a constant value
with further increasing damage (equation 4-3, Fig. 4-3). This indicates that as the
peak of the density function shifts towards higher damage, there is little change in the
variance after the data mean exceeds about 20%. This is similar to shifting a normal
density curve to a higher mean without changing the variance.

74
Application of the Cumulative Frequency Distribution Function.
The cumulative frequency distribution function (equation 4-4) will enable us to
easily determine the proportion of fruit which falls into a specific damage class if the
mean fruit surface damage is known. For example, the proportion of fruit which falls
between damage class xx and x2 is FFreq(xv p) - Ff (xv p) • In commercial citrus
production, it is often necessary to determine the proportion of fruit which can go to
fresh fruit market. If fruit with more than x percentage of the surface russetted is
damaged enough to be rejected from the fresh fruit market, then the proportion of
fruit which can go to the fresh fruit market (the ’pack-out’) would simply be
1
1 + exp(-
x-a(p)v
b{ p)
4-9
In Fig. 4-4, we can observe the proportion of ’pack-out’, Ff for any damage
class cut-off (x) as a function of the mean damage (p).
Another intended application of the established equation is to determine yield
loss from rust mite damage. Rust mite damage reduces growth and increases drop of
damaged fruit (Allen 1978, 1979, Allen et al. 1994, Yang et al. 1994), but these
effects are not uniformly distributed over damage classes, with more obvious effects
on the more heavily damaged fruit. It is therefore necessary to integrate these effects
over the whole damage class, based on the frequency distribution of fruit to obtain
average effects as functions of damage. Mathematical models describing the
relationships between fruit growth and drop and fruit surface damage have been

75
developed (Allen 1978, 1979, Yang et al. 1994). Allen et al. (1994) have established
differential equations to estimate volume loss from reduced fruit growth and drop, by
combining the frequency distribution with growth and drop models. These models are
to be further improved and fine-tuned so that they can be used in predicting mite
damage losses. The established models in this paper should also prove useful in pest
management studies.

Table 4-1. Relationship between mean fruit surface damage and estimates for
parameters a and b in equation 4-1.
76
Date
Mean damage
(%)
Parameter
(a)
Parameter
(b)
R2
8-24-93
0.6
-19.45044
7.0134054
0.9730*
8-31-93
2.4
-9.677496
7.5374539
0.9703*
9-07-93
6.2
-5.032474
10.943753
0.9966*
9-14-93
12.2
5.224359
11.241025
0.9960*
9-27-93
25.0
21.19182
10.984929
0.9957*
10-13-93
34.0
29.79047
10.984405
0.9882*
* Significant at p =0.05.

77
Table 4-2. Parameter estimates for equations 4-2 and 4-3 by two different methods.
Method
Equation
Parameter
b0
Parameter
ai
bi
Parameter
a2
b2
R2
TableCurve
4-2
-11.185925
1.2398129
-16.209061
0.9899*
4-3
11.207186
-5.365157
0.273146
0.7875
SAS-NLIN
4-4*
-9.7211588
1.1878809
- 3.077703
0.9993*
11.3049751
-8.623718
0.228797
1 Inserting equations 4-2 and 4-3 into equation 4-4 before data-fitting.
Significant at p =0.05.

Mean damage (%)
78
Fig. 4-1.
Observed distribution of damaged fruit on trees (Polk County, Florida,
1993).

Observed cumulative frequency
79
Fig. 4-2. Observed relative cumulative frequency of mite damage on fruit (Polk
County, Florida, 1993).

Parameter a
80
Fig. 4-3.
Relationship between parameter a (b) in the logistic equation (equation
4-1) and mean fruit surface damage.
Parameter b

Predicted cumulative frequency
81
Fig. 4-4.
Predicted relative cumulative frequency of mite damage on fruit (Polk
County, Florida, 1993).

f(x) =
82
100
Fig. 4-5.
S2MT freqUenCy 0f mi,e dam^ » fruit
(Polk County,

CHAPTER 5
MITE POPULATION DYNAMICS ON
FRUIT AND LEAVES
Statement of the Problem and Study Objective
A mite population often undergoes a dramatic change during the year. They
may increase more than 100 fold in just a few months, and then it crashes to almost
zero in a few weeks. Therefore, prediction has been a major difficulty in designing
mite management programs. Previous studies indicate that high relative humidity
favors rapid mite population increase (Muma 1955, Dean 1959, Reed et al. 1964),
though contrary reports exist (van Brussel 1975). Many researchers have attributed
the rapid mite population decline to the action of a fungal pathogen Hirsutella
thompsonii (Yothers & Mason 1930, Fisher et al. 1949, Muma 1955, McCoy &
Kanavel 1969, McCoy et al. 1976, McCoy 1981), and extensive efforts have been
made to fully make use of this fungal pathogen in mite control (McCoy et al. 1971,
McCoy et al. 1976, McCoy & Selhime 1977, McCoy 1981, McCoy & Couch 1982).
Due to a lack of understanding of the fruit-mite-pathogen interactions, the success of
using the fungal pathogen (commercial products and natural control) has been very
limited. This study was undertaken to observe the population dynamics of citrus rust
mite at close time intervals under field conditions, to identify those factors which are
most important in determining the fruit-mite-pathogen interactions. The results from
83

84
this study and previous studies will eventually be used to quantify the fruit-mite-
pathogen interactions.
Materials and Methods
This study consists of five similar field studies, which were carried out at
three different sites in Florida: two at the Budwood Foundation Grove of the
Southwest Florida Research and Education Center, Collier County; two at a research
grove of the University of Florida Horticultural Sciences Department, Alachua
County; and one at a commercial citrus grove, Polk County. The study site at Polk
County is about 125 miles south of the study site in Alachua County. The study site
at Collier County is about 125 miles south of the study site in Polk County.
Budwood Foundation Grove. 1991
Two studies were conducted from 26 May to 22 August 1991. One study was
conducted in a ’Hamlin’ plot consisting of 2 rows of 4-yr-old ’Hamlin’ orange trees,
with each row consisting of 76 trees. The other study was conducted in a ’Valencia’
plot consisting of 2 rows of 4-yr-old ’Valencia’ orange trees, with each row consisting
of 76 trees. Thirty trees were selected from each study plot, four to six fruit were
tagged on each tree, with a total of 142 fruit for the ’Hamlin’ plot and 145 for the
’Valencia’ plot. Weather data were recorded at a weather station about half a mile
away from the grove during the study period. The grove was well-maintained, with a
microjet irrigation system, and without pesticide applications.
Research Grove. 1992, 1993
The study plot at the research grove consisted of an area of about 2 acres, with
8-yr-old ’Hamlin’ orange trees, with eight rows of trees running from south to north,

85
with each row consisting of 14 trees. The sampling area was located at the center of
the study plot. The grove was under regular management, with a microjet irrigation
system. A petroleum oil spray was applied on 14 July 1993 to control citrus rust
mites, causing a 56% mite mortality by July 16. One study was conducted from 8
May to 11 December 1992 for the fruit and from 8 May to 24 December 1992 for the
leaves. The other from 24 May to 5 November 1993 for the fruit, and from 7
January to 12 November 1993 for the leaves. In the study in 1992, twenty five trees
were randomly selected, six fruit from each tree were then selected and tagged, a
total of 150 fruit; in the study in 1993, thirty trees were randomly selected, six fruit
from each tree were then selected and tagged, a total of 180 fruit. Fruit were chosen
so that they were about evenly spaced around the tree. Rainfall data were recorded
from a rain gauge about 500 meters away from the study plot. Temperature and
humidity data were obtained from the Green Acre Weather Station about 10 miles
away from the study plot.
Commercial Grove. 1993
The study was designed to determine possible effects of tree age and location
on mite population dynamics. The study plot consisted of an area of about 5 acres,
with eight rows of trees running from south to north, with each row consisting of
about 35 4-yr-old ’Hamlin’ orange trees. The sampling area was located at the center
of the study plot. Twenty five trees were randomly selected from each of the central
6 rows at every sampling, with one fruit from each tree, a total of 150 fruit. The
study was conducted from 28 May to 17 Nov. 1993 for fruit and from 28 May to 17
Dec. 1993 for leaves. The grove was also under regular management, with an

86
overhead sprinkler irrigation system. A nutritional spray was applied on 4 June 1993,
but the spray didn’t have much effect on citrus rust mite populations. Weather data
were obtained from a weather station about 2 miles away from the study plot.
In all five studies, sampling was made 1-3 times a week, and rust mite
population density was determined with the help of a 20x hand lens mounted over a
piece of clear plastic upon which a one cm2 grid had been etched. The grid was
divided into 25 equal subdivisions, each having an area of 4 mm2. Only mites within
the middle 4 squares were counted, with a total area of 4*4 (i.e. 16 mm2) for each
count. In the studies at the Budwood Foundation Grove and at the research citrus
grove, four counts were made for each fruit (i.e. a total of 4*4*4=64 mm2 fruit
surface area), with one count from each quadrant of the fruit; and four counts were
made for each leaf, with two on the upper leaf and two on the lower leaf surface. In
the study at the commercial citrus grove, eight counts were made for each fruit (i.e. a
total of 8*4*4=128 mm2 fruit surface area), with two counts from each quadrant; and
four counts were made for each leaf, with two on the upper and two on the lower leaf
surface. Mite cadavers showing mycelia growth were considered as caused by the
fungal pathogen (Hirsutella thompsonii), and the number of such mite cadavers was
used as an indicator of the pathogen population. Mite density was converted to
mites/cm2. Fruit surface damage was estimated visually at each sampling.
A summary of all the experimental designs for fruit and leaves can be found in
Table 5-1.

87
Table 5-1. Summary of experimental designs.
County
Variety
Duration
Year
Sample size
Sampling
Collier
Valencia
May 26-Aug 22
1991
145*
Random T
Collier
Hamlin
May 26-Aug 22
1991
142*
Random T
Alachua
Hamlin
May 08-Dec 11
1992
150*
Random T
Alachua
Hamlin
May 24-Nov 05
1993
180*
Random T
Polk
Hamlin
May 28-Nov 17
1993
150*
Random11
Collier
Valencia
May 26-Aug 22
1991
240b
Random
Collier
Hamlin
May 26-Aug 22
1991
240b
Random
Alachua
Hamlin
May 08-Dec 24
1992
200b
Random
Alachua
Hamlin
Jan 07-Nov 12
1993
200b
Random
Polk
Hamlin
May 28-Dec 17
1993
200b
Random
* Number of fruit sampled.
b Number of leaves sampled.
c Fruit were randomly selected and tagged at the beginning of the study, and
subsequent sampling were conducted on the same tagged fruit.
d Fruit/leaves were randomly selected at every sampling date.

88
Results
Budwood Foundation Grove. 1991
Population dynamics of citrus rust mite on ’Hamlin’ and ’Valencia’ fruit were
similar (Figs. 5-la, 5-2a). Both populations began to build up in late-May, reached a
rather high level in early June, and more or less maintained at the same level between
early June and early July, and then declined to a very low level by early August.
CRM population peak on ’Hamlin’ fruit was higher than on ’Valencia’ fruit (Fig. 5-la
vs. 5-2a). CRM populations in both ’Hamlin’ and ’Valencia’ plots did not reach a
high level, as a result, the damage caused by CRM was very light: a mean damage of
about 3% in the ’Hamlin’ plot (Fig. 5-lb), and about 1% in the ’Valencia’ plot (Fig.
5-2b). The parasitic fungal pathogen (Hirsutella thompsonii) was probably the most
important factor which had prevented the CRM populations from reaching high levels.
Fungal pathogen populations, indicated by mite cadavers showing mycelia growth, in
both study plots, were found closely correlated with mite dynamics (Figs. 5-la, 5-2a).
The warm and humid weather conditions (Fig. 5-6) had certainly contributed to the
effectiveness of the fungal pathogen in keeping mite populations at very low levels.
Mite populations on leaves in both plots showed similar patterns to that of
fruit, but populations on leaves were much lower than on fruit (about one tenth of that
on fruit), and there were more mites on the upper than on the lower leaf surface
(Figs. 5-lc, 5-2c). Fungal infested mite cadavers were also found on both upper and
lower leaf surface, but they were relatively few.

89
Research Grove. 1992
CRM population on fruit began to build up in late May and early June, and
reached the highest peak in mid-July, and then declined to a very low level (Fig. 3a).
The highest mite density was about 150 mites / cmA2, about five times as high as
observed in the Budwood Foundation Grove in 1991 (Figs. 5-la to 5-2a vs. 5-3a).
Although pathogen population was closely correlated with CRM population (Fig. 5-
3a), it was too late to prevent CRM from reaching a very high level, resulting in
heavy fruit surface damage (about 30%)(Fig. 5-3b). CRM population on leaves also
exhibited similar dynamic patterns, but was lower than on fruit, the highest population
was about 120 mites /cm*2. There were more mites on the upper than on the lower
leaf surface.
Research Grove. 1993
CRM population demonstrated a dynamic pattern similar to that observed in
1992 (Fig. 5-3a vs. 5-4a). The population peak occurred later and was lower than
that of 1992. Although the fungal pathogen was also closely correlated with CRM
population, it was too late to prevent mite population from reaching high level,
resulting in heavy fruit surface damage (about 24%) (Fig. 5-4b). Although mite
populations on leaves showed similar trend to that of fruit, they were much lower,
and more mites were found on the lower than on the upper leaf surface (Fig. 5-4c).
Commercial Grove, 1993
CRM population dynamics was similar to that observed at the research grove
in 1993 (Fig. 5-4a vs. 5-5a), but the population peak occurred about one month later

90
and was higher than that at the research grove (Fig. 5-4a vs. 5-5a). The fungal
pathogen population started late and was low, too late and too low to prevent high
mite density, incurring heavy fruit surface damage (34%) (Fig. 5-5b). CRM
population on leaves followed similar pattern; here more mites were found on upper
leaf surface when mite population was low, but more mites were found on lower leaf
surface when the mite population was high.
Discussion
Mite Population and the Fungal Pathogen
The fungal pathogen has been found to be a very important factor responsible
for rapid mite population decline (Yothers & Mason 1930, Muma 1955, McCoy &
Kanavel 1969, McCoy et al. 1976, McCoy 1981). Muma (1955) observed that
highest rust mite population on leaves occurred in early July, and that large rust mite
populations that developed in late spring and early summer were greatly reduced
following rains, and this was attributed to the effect of H. thompsonii. In the current
study at the Budwood Foundation Grove, the fungal pathogen was so effective in
preventing mite populations from reaching high levels that very little damage
occurred, but the fungal pathogen was too late in season to prevent heavy mite
damage in the research and commercial groves. Warm temperature and high
humidity are essential for epizootic development (Fuxa 1987, Onstad & Carruthers
1990). The warm temperature and high humidity (as indicated by the leaf wetness
duration) at the Budwood Foundation Grove (Fig. 5-6) may have favored the
development of pathogen epizootics (Figs. 5-la, 5-2a), while a lack of high humidity

91
at both the research and commercial groves may have hindered and delayed the
development of pathogen epizootics (Figs. 5-7 to 5-9). This clearly indicates that
fungal epizootics may occur at relatively low mite population densities when favorable
conditions exist for epizootic development. There may exist a mutual complementary
effect between weather and mite population density in the development of fungal
epizootics. Epizootics may occur and persist at a relatively low mite population if the
weather is most ideal for pathogen development (as in the case of the Budwood
Foundation Grove: Figs. 5-la to 5-2a); on the other hand, a relatively high mite
population is needed in order for epizootics to occur and persist if the weather is not
ideal for pathogen development as in the cases of the research and commercial groves
(Figs. 5-3a to 5-5a). In all the five cases the highest pathogen populations were less
than one-tenth of the highest susceptible mite populations (immature and adult stages).
One possible reason is that a large portion of pathogen-infected dead mites may have
been removed from the fruit surface by wind, rain or contact.
Mite Population and Food Availability
Yothers & Mason (1930) reported that the reduction in mite numbers could not
have been the result of food scarcity, since on average only half the untreated fruit
were severely infested with citrus rust mite. In our field observations we also found
that even when mite populations were at their highest levels, mite density on most
fruit was not very high. But food scarcity may still become a major factor in causing
mite population crash. There are two major reasons: (1) diminishing suitable fruit
surface and (2) population self-regulating mechanisms. Citrus rust mite prefers area

92
of the fruit where there is enough sunlight, but it avoids direct sunlit area, and shaded
part of fruit surface (Yothers & Mason 1930, van Brussel 1975, Allen & McCoy
1979). With the progress of the season, the relation of fruit to sunlight direction will
change due to the seasonal movement of the Earth around the Sun, on the other hand,
the increasing weight of fruit will bring the fruit down and the emergence of new
flushes will shade the fruit, this will further change the relation of fruit to sunlight
direction. But the overall effect should be a reduction in the proportion of the fruit
surface which is suitable for rapid mite development due to shading. Although the
shading effect changes gradually through the season, the rapid increase of fruit
surface damage quickly diminishes the suitable fruit surface, because the most suitable
fruit part is first damaged. Since rust mites have very limited migration, each fruit
can be considered as a more or less independent food source. With its high
reproductive rate, a high mite population can build up in a very short time. High
mite density along with heavy damage makes the fruit unsuitable for continuing mite
population growth. In the field, it is a very common phenomenon to observe a rapid
population crash on a heavily infested fruit, probably due to mite migration or
increased mortality, or male-skewed sex ratio, or reduced reproduction.
Except for the fungal pathogen, mechanisms associated with food scarcity and
crowdedness might be responsible for this crash: (1) increased self-destructive
migration; (2) increased male-biased sex ratio; (3) reduced fecundity; and (4)
increased mortality. Laboratory observations showed that many adult mites dropped
from heavily infested fruit, while very few mites were found to drop from fruit with

93
low mite population. This is an indication of massive migration of mites away from
heavily infested and damaged fruit. Since mites mainly rely on wind for their
migration, only a small proportion can reach suitable food source by chance, the
majority of them perish during migration. A study of mite sex ratio in relation to
mite density and fruit surface damage (unpublished data) indicated that high male to
female sex ratio was related to high mite density and heavy rust mite damage,
although this might be attributed to female-biased migration, male-biased sex ratio can
not be excluded. Probably several mechanisms are involved in an observed mite
population crash.
Mite Population vs. Tree Age and Location
Mite populations on both fruit and leaves in the 8-yr-old research grove peaked
about one month earlier than the 4-yr-old commercial grove (Figs. 5-4a, c vs. 5-5a,
c). The pathogen population was higher in the 8-yr-old research grove than the 4-yr-
old commercial grove (Figs. 5-4a vs. 5-5a). Even with these differences, both
populations showed very similar dynamic patterns. This result indicated that tree age
and grove location may not affect the general trend of mite population dynamics, the
only difference was in the timing and extent of population peaks, and the activity of
fungal pathogen. The activity of Hirsutella thompsonii was probably determined by
local weather conditions, and initial mite and pathogen population densities.
Therefore, general population prediction models might be easily adjusted for use for a
specific grove and location.

94
Mite Population and Weather
In all the five studies, mite population peaks occurred in the rainy season (i.e.
from mid-June to late August). Rain did not seem to have much adverse effect on
mite population increase. Yothers & Mason (1930) noted that although the heavy
driving rains did wash a few mites from the foliage and fruit, this diminution in
numbers was not appreciable and had little effect on subsequent abundance of the
mites and they further noted that rust mites crawled to the lower leaf surface to
protect themselves to a certain extent from the rains. But van Brussel (1975) reported
that low mite counts during the rainy seasons were not entirely attributable to the
entomophagous fungus, Hirsutella thompsonii, despite the favorable moist conditions
for fungal growth. They were neither the result of washing off by rain, nor of
drowning (the adult can survive 12 hours in water), and they seemed to be the result
of larval mortality, which increased when larvae were wetted and a water film was
present on the food plant, and probably increased mortality, or male-skewed sex ratio,
or reduced reproductive rate (van Brussel 1975). In the current study, mite
populations reached highest peaks during the rainy season, therefore, increased larval
mortality could not be a major factor in rapid mite population decline. Even though
larval mortality may increase because of the rainy weather, and may affect the extent
of mite population peaks, it did not affect the general mite population trend.
Hobza & Jeppson (1974) reported that under constant temperatures (20, 25,
and 30°C), higher relative humidity favored citrus rust mite population growth on
excised lemon fruit. Observations by other researchers (Muma 1955, Dean 1959,

95
Reed et al. 1964) suggested that high relative humidity favored mite population
development. Since rainfall is closely associated with relative humidity, the rainy
season is also a season of high relative humidity, which should favor both mite
population and pathogen population growth. An increasing pathogen population will
eventually bring down the increasing mite population. This is obviously the case in
the Budwood Foundation Grove in which pathogen population activity was very early
and effective due to frequent rains and high relative humidity (Fig. 5-6).
Hobza & Jeppson (1974) reported that the theoretical optimal temperature for
mite population growth was 24.5°C, and limiting temperatures were 17.6 and 31.4°C.
Allen et al. (1994) reached a similar conclusion, except that the lower temperature
was about 11°C. Although these results were from laboratory studies under constant
temperatures and humidities on excised fruit, we may still use this information for
analyzing mite population development under natural conditions. The annual cycle of
average daily temperature in central Florida has a summer maximum of 28.5°C and a
winter minimum of about 16.5°C. Therefore, mite population can develop all the
year round. Mite population peaks occurred in the warm and humid summer. Lower
populations in winter and spring were probably due to slow development associated
low temperature, and high mortality associated with low temperature and low
humidity. Although high mite population peaks occurred in summer when mean daily
temperatures were high, mite population peaks were not closely correlated with the
yearly temperature cycle. This indicates that although temperature may affect mite
population growth, the sharp mite population peak was not a direct result of

96
temperature effects, because temperatures during the summer seasons vary very little
while mite population underwent tremendous change.
Mite Population on Upper vs. Lower Leaf Surface
Results on mite population dynamics on upper and lower leaf surface from this
study were not consistent. Results from the Budwood Foundation grove in 1991
(Figs. 5-lc, 5-2c) and from the research grove in 1992 (Fig. 5-3c) clearly showed
higher mite populations on the upper than on the lower leaf surface, but results from
the commercial grove (Fig. 5-4c) and from the research grove (Fig. 5-5c) in 1993
showed higher mite population on the lower than on the upper leaf surface most of the
time. Reason(s) for the observed differences is not clear. Literature also presents
similar reports (Yothers & Mason 1930, Swirski 1962, van Brussel 1975, McCoy
1980). Swirski (1962) and McCoy (1980) showed that there were more citrus rust
mites on the lower than on the upper leaf surfaces, van Brussel (1975) found that on
mature orange and grapefruit trees there were twice as many mites on the upper as on
the lower leaf surface, and further demonstrated that mite population on the upper or
lower surface is markedly influenced by the age of the host plant.
Although mite populations on the upper and lower leaf surface did not exhibit
a consistent trend, the dynamics were very similar, and closely correlated with mite
population dynamics on fruit. This indicates that mite population dynamics on fruit
can represent the general mite population trend on both sides of leaves, and mite
sampling on fruit is sufficient for mite control and prediction purposes.

97
Quantification of Effects of Biotic and Abiotic Factors on Mite Population Dynamics
This report is only a qualitative description on the possible effects of different
biological and climatical factors on mite population dynamics. Data from this study
and also from previous studies will be used to establish a mathematical model which
quantifies these interactions. The basic approach will be a three step process. The
first step is to build a mathematical model; the second step is to estimate model
parameters based on data from this study and previous studies; the third step is to
further adjust model parameters, so that the model can be used for local mite
population prediction. A decision making system for the citrus rust mite is currently
under development, which includes mite population prediction, mite damage
prediction (Allen 1976; Yang et al. 1994), and yield loss prediction (Allen 1980,
1981, Allen et al. 1994). The decision making system will be used by extension
specialists and citrus growers for rust mite management.

Mites / cmA2 Mites / cmA2 Mites / cmA2
98
120
180
240
300
10
0
360
C\|
<
E
o
c
0)
o>
o
â– C
ro
CL
O)
CD
E
CD
"O
0)
o
CD
*fc
=5
(/)
'5
LL
120 180 240 300 360
Julian day (1=1 Jan. 1991)
Fig. 5-1. Mite population dynamics, (a) Population dynamics of citrus rust mite
and its fungal pathogen on fruit; (b) Dynamics of citrus rust mite
population and fruit surface damage on fruit; (c) Population dynamics
of citrus rust mite on leaves. (’Valencia’ orange, Collier County,
Florida, 1991).

Mites / cmA2 Mites / cmA2 Mites / cmA2
99
120
10
180
240
300
- 5
360
CM
<
E
o
c
CD
05
O
.C
ra
Q.
0)
O)
ro
E
ra
"O
o
aj
t
Z5
co
'5
i—
LL
120
180
240
300
360
120 180 240 300 360
Julian day (1=1 Jan. 1991)
Fig. 5-2. Mite population dynamics, (a) Population dynamics of citrus rust mite
and its fungal pathogen on fruit; (b) Dynamics of citrus rust mite
population and fruit surface damage on fruit; (c) Population dynamics
of citrus rust mite on leaves. (’Hamlin’ orange, Collier County,
Florida, 1991).

Mites / cmA2 Mites / cmA2 Mites/cmA2
100
120 180 240 300 360
<
E
o
c
0
O)
o
£
ra
Q_
50
25
120
180
240
300
360
0
O)
ro
E
ra
x>
0
o
ro
t
3
0 60 120 180 240 300 360
Julian day (1=1 Jan. 1992)
Fig. 5-3. Mite population dynamics, (a) Population dynamics of citrus rust mite
and its fungal pathogen on fruit; (b) Dynamics of citrus rust mite
population and fruit surface damage on fruit; (c) Population dynamics
of citrus rust mite on leaves. (’Hamlin’ orange, Alachua County,
Florida, 1992).

Mites / cmA2 Mites / cmA2 Mites / cmA2
101
120 180 240 300 360
CM
<
E
o
c
05
O
n
ra
CL
©
05
CD
E
CD
"O
©
o
CD
t
D
0 60 120 180 240 300 360
Julian day (1=1 Jan. 1993)
Fig. 5-4. Mite population dynamics, (a) Population dynamics of citrus rust mite
and its fungal pathogen on fruit; (b) Dynamics of citrus rust mite
population and fruit surface damage on fruit; (c) Population dynamics
of citrus rust mite on leaves. (’Hamlin’ orange, Alachua County,
Florida, 1993).

Mites / cmA2 Mites / cmA2
102
120 180 240 300 360
CN
<
E
o
c
O)
O
-C
03
0.
03
03
E
03
"O
03
O
03
t
3
C/J
Fig. 5-5. Mite population dynamics, (a) Population dynamics of citrus rust mite
and its fungal pathogen on fruit; (b) Dynamics of citrus rust mite
population and fruit surface damage on fruit; (c) Population dynamics
of citrus rust mite on leaves. (’Hamlin’ orange, Polk County, Florida,
1993).

Leaf wetness duration (hr)
103
o
o
l—
D
â– c
CO
0
CL
E
0
Julian day (1 = 1Jan. 1991)
Fig. 5-6. Weather data, (a) Daily mean temperature; (b) Daily leaf wetness
duration (hrs); (c) Daily rainfall (cm) (Immokalee, Collier County,
1991).

Tempearture ( °C)
104
Fig. 5-7.
Weather data, (a) Daily mean temperature; (b) Daily rainfall (cm)
(Gainesville, Alachua County, 1992).

Tempearture ( °C)
105
Fig.
5-8. Weather data, (a) Daily mean temperature; (b) Daily rainfall (cm)
(Gainesville, Alachua County, 1993).

Leaf wetness duration (hr)
106
o
o
a)
i—
3
â– c.
co
cu
o.
E
0)
^ 1 1 1
a
120 180 240 300 360
J
b
120 180 240 300 360
Fig. 5-9. Weather data, (a) Daily mean temperature; (b) Daily leaf wetness
duration (hrs); (c) Daily rainfall (cm) (Lake Alfred, Polk County,
1993).

CHAPTER 6
MITE POPULATION PREDICTION:
AN AGE-STRUCTURED MODEL OF THE
FRUIT-MITE-PATHOGEN SYSTEM
Statement of the Problem and Study Objective
As indicated from the results in Chapter 5, citrus rust mite (CRM) populations
undergo tremendous changes during the season, reaching high peaks in just a few
weeks, and causing severe damage. The peak population also declines quickly,
probably as a result of the combined effects of weather, the fungal pathogen
Hirsutella thompsonii, and food availability. It is therefore necessary to develop a
mite population prediction system, so that we can predict mite population and damage
trends, and take timely actions. The objective of this study was to build a
mathematical model which could make short-term (within 1-6 months) predictions of
mite population trends and resulting damage.
Materials and Methods
The Fruit-Mite-Pathogen System
The citrus rust mite feeds on the fruit surface. Two aspects of fruit could
affect observed mite population dynamics: (1) fruit surface area increase during the
growing season will dilute mite population density; (2) extensive feeding may cause
fruit surface deterioration causing a decline in food availability for the citrus rust
107

108
mite. This deterioration in food source may in turn limit further mite population
growth. A fruit surface area growth model was developed in Chapter 2 (equation 2-
7). A model relating percent fruit surface damage to cumulative mite days during
mite population growing season was also developed in Chapter 2 (equation 2-9).
There are four developmental stages for the citrus rust mite: egg,
protonymph, deutonymph, and adult. Mite development times and reproductive
capability are probably the most important parameters affecting potential mite
population growth. These mite population parameters are mainly a function of
climatic factors, especially temperature. Information relating mite development to
temperature was obtained from Allen et al. (1994b) (Table 6-1). Mite survival is
mainly related to temperature, humidity, and activity of the fungal pathogen,
Hirsutella thompsonii.
The fungal pathogen, H. thompsonii, is probably the most important biological
factor regulating mite population dynamics. It attacks the adult stage of the citrus rust
mite (personal communication, C.W. McCoy), causing regular epizootics under the
natural conditions of Florida (McCoy 1981). It produces conidia on conidiophores
found on an external mycelium outside the host on the plant substrate. Once inside
the host, the hyphae form a ramifying growth within the hemocoeel and after death
erupt through the host cuticle onto the plant surface where they reproduce asexually.
It takes less than 4 hours for a spore to penetrate the mite cuticle and about 2 days for
the total infection process to be completed to sporulation at 25-30°C (McCoy 1979,
Gerson et al. 1979, Kenneth et al. 1979). The pathogen development can be divided

109
into two distinct stages: (1) latent stage or incubation period, referring to the period
from initial infection to the beginning of sporulation. Full sporulation at 27°C takes
place within 12 hours after death of the host (Gerson et al. 1979); (2) infectious stage,
referring to the period from sporulation to the complete loss of the infectivity of the
mite cadaver. For convenience, each Hirsutella-infected mite (dead or alive) is
considered a pathogen unit. The life time of this pathogen unit is from the time of
initial infection to the time when it completely loses its infectivity. In the latent
stage, when the pathogen develops inside the live body of the mite, temperature is
probably the most important factor affecting the duration of this stage. Pathogen-
infected live adult mites were assumed to produce no eggs. In the infectious stage,
the mite cadaver can sustain the fungus for a few days after which the fungus itself
dies, whether or not conidia have been produced. The survival rate is mainly a
function of humidity, solar radiation, and temperature. Infectivity is dependent on the
presence of free water and high humidity (McCoy 1978). In this study only
temperature, leaf wetness duration, and rainfall were considered (see Chapter 5 for
weather data: Figs. 5-6 to 5-9). Although only adult mites are found showing
mycelia growth (C.W. McCoy, personal communication), it seems likely that the
nymphal stages can also be attacked. In the model simulation, both adult and
nymphal stages are assumed to have equal susceptibility to the fungal pathogen
infection.

110
Model Development
There are probably many ways to model the fruit-mite-pathogen system. The
method developed by Chi & Liu (1985) was used in this study, but with considerable
modification. Chi & Liu (1985) used a multiple column matrix to express the age-
stage-structure of animal populations with metamorphosis. The process of animal
population growth can be simulated through a set of difference equations. There are
five basic matrices which need to be built for the simulation: (1) age-stage-structure
matrix (N); (2) age-stage-specific growth rate matrix (G); (3) age-stage-specific
development rate matrix (D); (4) age-stage-specific mortality matrix (M); and (5) age-
stage-specific fecundity matrix (F) (Chi & Liu 1985). The definitions for the five
matrices are given in Figs. 6-1 and 6-2.
The age-stage-structure matrix. The basic concept of Chi & Liu’s (1985)
multiple column matrix model is demonstrated in Fig. 6-1. In this method, the
population structure is given in matrix N with k rows and m columns, where k is the
number of age classes, and m is the number of stages. In the case of citrus rust mite,
six columns were used (Fig. 6-1), with each column representing one stage. The first
column represents CRM egg stage, and the second, third, and forth columns represent
the protonymph, deutonymph, and adult stages, respectively. The continuous age
variable for a stage is divided into discrete age classes of the same duration. Then,
n gives the number of individuals in age ¿ and stage j . After one age interval,
individuals in age j and stage j grow to age j+i but still be in the same stage j , or
develop to stage j +1. The fifth column represents the latent pathogen stage, which

Ill
Matrix N
Egg N, N2 Adult P, P,
nn nn nu nu nl5 nl6
n2l n22 n23 n7A n25 n26
\n,l ni2 n3 ni4 ni5 ni6)
I
(E/iu Hna E/ia Lni4 Ena Zni6)
(Yn \
En2;.
iE/i,,
v 6jJ
Age structure
Stage structure
Fig. 6-1. The age-stage-structure matrix (N) of the citrus rust mite and its fungal
pathogen. n = number of individuals in age / and stage j ; Egg =
egg stage; N, = protonymph stage; N2 = deutonymph stage; Adult =
adult stage; P, = latent pathogen stage; P, = infectious pathogen stage.

112
Matrix G Matrix D
f8n
812
8x2
814
8x5
8x6
'¿XX
¿X2
¿X2
¿X4
¿X5
¿X6
821
822
822
¿>24
825
826
¿21
¿22
¿22
¿24
¿25
¿25
8¡i
8,2
8b
8,4
8i5
8,6j
A
¿a
¿3
¿H
¿Í5
¿,6t
Matrix M Matrix F
'mxx
mX2
mX2
mX4
mX5
mX6
'0
0
0
f14
0
0N
m2X
m22
m22
m24
m25
m26
0
0
0
f14
0
0
m,2
mB
mi4
mi5
m ,
¡6)
0
0
0
fi4
0
0
y
Fig. 6-2. The age-stage-specific growth rate matrix (G), developmental rate
matrix (D), mortality matrix (M), and fecundity matrix (F). g =
probability that an individual from age i and stage j will grow to age
¡ +1 of the same stage after one age interval (day); ¿ = probability
that an individual from age ¿ and stage j will develop to the first age
class of stage j+\ after one age interval (day); m= probability that
an individual in age ¿ and stage j will die after one age interval (day);
f = number of offspring that will be produced by every individual in
age i and stage j during one age interval (day).

113
is developed from the protonymph, deutonymph, and adult stages, as a result
ofinfection by the infectious fungal pathogen. The number of age classes for a stage
can be determined by the development time of the stage and the length of the age
class interval. The number of age classes for different stages may be different due to
different development times. In this case, the highest age class number among all
stages was used for the age-stage-structure matrix. Elements which are out of the
range of stage distribution were set to zero in the calculation of the following
sections.
Age-stage-specific growth rate, developmental rate, mortality rate and
fecundity. In the Lewis-Leslie matrix, only age-specific survival rates and fecundity
are considered (Lewis 1942, Leslie 1945, 1948), Chi & Liu’s (1985) multiple column
matrix method takes the stage differentiation into consideration. Therefore, there are
four factors which relate to all individuals, namely: age-stage-specific growth rate,
developmental rate, mortality rate, and fecundity. These four factors can be set into
four matrices of the same dimension (Fig. 6-2). In matrix G (Fig. 6-2), the element
g.. (the age-stage-specific growth rate) is the probability that an individual in age j
and stage j will grow to age j +1 but still be in stage j after one age interval. In
matrix D (Fig. 6-2), ¿ (the age-stage-specific developmental rate) is the probability
that an individual in age j and stage j will develop to stage j +1 after one age
interval. Because adult mites and the infectious pathogen will not develop to further
stages, i.e. they will develop to death, j for them is the probability that individual in

114
age i and stage j will die after one age interval. In matrix M (Fig. 6-2), m.. is the
probability that an individual in age j and stage j will die after one age interval.
For the adult mite and the infectious pathogen stages, m should be the mortality rate
excluding ¿f.. In matrix F (Fig. 6-2), f.. (the age-stage-specific fecundity) is the
number of offspring that will be produced by every individual of n~ within one age
interval. In this case, only rust mite adults have a f ^o, and the other f have the
value zero.
Mite and pathogen population growth. A time step of one day (i.e. at = 1)
was used in the simulation process. When the age-stage-structure of mite and
pathogen population at time t is known, the age-stage-structure for time / +1 can be
obtained through the operation of the following difference equations:
Citrus rust mite:
*«4
«11 (r+l)=£ n|4(f)4(0 lst element for egg(new eggs)
i=l
'«/
n1;(r+l)=J^ 1st elements for nymphs/adults
i = l
ntJ(t+1) =n(l_l)j(t)g(i_1)j(t) other elements

115
Fungal pathogen:
‘aj 4
y(r)(l -e yNt‘Pl) 1st element for latent pathogen
¿=1 1-2
*a6
n16(i+l)=J^ n¿(fidgit) 1st element for infec. pathogen
i=l
«i>.(r+l)=n(i..lv(í)g(i-i)/ where
n.j, f.., d g = matrix elements (see Figs. 6-1 and 6-2);
a = tolerance level (see equation 6-5);
i = number of age groups for stage j (see equation 6-7);
e"fN6pi = time step survival rate after pathogen attack (proportion day1);
Y = time step pathogen transmission rate ((pathogen unit)'1 day'1);
p = proportion of infectious pathogen attacking mite stage j (2<.j¿4) ;
At = time step = 1 (day).
This simulation procedure implicitly assumes that simulation time step equals the
length of age class interval. The first element for CRM egg stage at time t+1,
Hn(r+1), equals the total number of new eggs produced by all age classes of adults
within one time step. The first element for the protonymph stage at time t+1,

116
h12(í+1), equals the total number of individuals which develop from all age classes of
egg stage after one time step. The first element for the deutonymph stage at time
i+1, n13(f+l)> equals the total number of individuals which develop from all age
classes of protonymph stage after one time step. The first element for the adult stage
at time r+1, nu(r+l), equals the total number of individuals which develops from all
age classes of deutonymph stage after one time step. The first element for the latent
pathogen stage at time ¿+1, n15(r+l), equals the total number of protonymphs,
deutonymphs and adults which are attacked by the fungal pathogen within one time
step. The first element for the infectious pathogen stage at time r+i, n16(f+l), equals
the total number of individuals which develop from all age classes of the latent
pathogen stage after one time step. Any element rather than the first for all the CRM
and the fungal pathogen stages at time t+1, /r(i+l)0>l) > equals the number of
individuals which develop from the previous age class of the same stage after one
time step.
Mite and pathogen population density adjustment due to fruit growth. Since
fruit surface area increase will dilute mite and pathogen populations on fruit from
time t to time /+i, it therefore necessary to adjust mite and pathogen population
density after every time step simulation. A fruit area growth function was developed

in Chapter 2 (equation 2-7), which is
117
146.3346
6-1
* l+exp(4.389115-0.0230390
where = fruit surface area (cm2); t — Julian day (1 = 1 Jan.). A fruit surface
area growth factor from time t to time j+i is defined as
Time step growth factor =
6-2
where time step At = 1. A growth factor of > 1 indicates that the fruit is growing;
a growth factor of = 1 indicates that the fruit is not growing. Dividing the age-stage-
structure matrix by the growth factor results in the adjusted age-stage-structure matrix
6-3
where
n..(t+1) on the left side = adjusted age-stage-structure matrix element;
n (i+1) on the right side = age-stage-structure matrix element before
adjustment.
Model Parameter Specification
Determination of the number of age classes. The continuous age variable for a
stage is divided into discrete age classes of the same duration. The number of age
classes for a stage is determined by its developmental time and simulation time step

118
(which should equal the age class interval). If the range of development time for a
stage is known, the number of age classes for the stage can be calculated using the
following formula
xr , r , Maximum development time
Number of age classes =
Simulation time step
The maximum development time is the time by which all individuals of a cohort of a
stage have developed to next stage. Functions relating the cumulative emergence of
different CRM stages in relation to temperature have been developed by Allen et al.
(1994b) (Table 6-1), which are logistic functions of the form
F(t) =
1
l+exp(--^-^)
b
6-4
where f(f) = the proportion of individuals of a cohort of a stage which have
developed to next stage by time t, and the dependence on temperature (7) has been
dropped for simplicity (Table 6-1). Since equation 6-4 is continuous between 0 and
+oo, there is no absolute maximum development time. This is caused by the property
of the logistic function, not by the characteristics of the citrus rust mite. It is
therefore necessary to determine an arbitrary maximum development time for each
stage in order to run the simulation. Assuming a is a very small value (a = 0.0001
in the current paper), I used the time by which 1-a (i.e. F(t) — 0.9999) proportion of
individuals of stage j have finished their development as the arbitrary maximum

119
development time (taJ) for the stage. The maximum development time (* ) can be
calculated using the cumulative emergence equation
and therefore,
-*=F(.taj) =
1
t,-a
l+exp(-——)
6-5
t.=a-bLn—^— 6-6
1-a
Dividing the maximum development time (f ) by the time step (ar) yields the
number of age classes for stage j
i = 6-7
Ar
Since may not be an integer, its integer part plus one was used as the number of
Ar
age classes (j ). All the individuals in the last age class (j ) will not develop to
further age classes, they either die or develop to the first age group of the next stage.
For simplicity, initial density at the beginning of simulation for each stage was
assumed to be in the first age group only, with other age groups having zero values.
Elements for the mortality matrix M. Estimating the element values for the
mortality matrix M is probably the most difficult task, because it is usually difficult to
obtain the necessary information. A 20% stage mortality was assumed for immature

120
mite stages based on laboratory data from Allen et al. (1994b) under constant
temperature conditions. Since the latent pathogen stays in the live mite body, a 20%
stage mortality for the latent pathogen stage was also assumed. Adult mites and the
infectious pathogen will eventually develop into death, so no extra mortality was
assumed. In this model, I assumed that the mortality factors act equally for all age
classes of a stage. If the mean developmental duration (x), the stage mortality
(m ) and the time step (At) are known, the step size mortality (m..) can be
stage ij
calculated using the following equation
6-8
(1 - m/'4' - 1 -
or
6-9
If the time step equals 1 (day), equation 6-9 becomes
6-10
Effects of climatic factors (e.g. temperature and humidity) on both mite and pathogen
mortality have not been quantified. The pathogen effect on mite mortality will be
discussed in the next section.
Elements for the growth rate matrix G and developmental rate matrix D. An
easy way to calculate the element values for matrices G and D is to build a
cumulative emergence function. The cumulative emergence functions have already
been established for all the stages of the citrus rust mite (Allen et al. 1994b). Gerson

121
et al. (1979) reported that it took about 2-3 days from the fungal pathogen infection of
mites to sporulation. This period is similar to the protonymph development time,
therefore the latent pathogen was assumed to have the same cumulative emergence
function as the protonymphs, and the survival of the infectious pathogen was assumed
to follow an exponential decay process similar to that of the adult rust mites. The
functional forms and corresponding coefficients for the mite and pathogen
development are summarized in Table 6-1.
If there is no mortality, elements d{j and g.. can be calculated with the
following equation (Yang & Huang 1991, Berry & Stinner 1992)
l-F/i-l)
g =1-d.
6y u
6-11
where F(i) = cumulative emergence function for stage j (Table 6-1).
If mortality occurs, the following adjustment for ¿ and g.. is needed
da = d¡M ~ mi?
Sij = s,/1 - miP
6-12
where
m.. = time step mortality for individuals in age \ and stage j ;
d.., g.. on the left side = adjusted values;
d.., g.. on the right side = values without mortality (i.e. equation 6-11).

Equation 6-12 assumes that mortality occurs before development and growth.
If mortality from the fungal pathogen is included, the following further
122
adjustment for and g.. is needed for the susceptible mite stages (nymphs and
adults)
6-13
where
d.. and g.. on the left side = adjusted values
d.. and gon the right side = values without pathogen (i.e. 6-12)
e ’yA^ = proportion survival after pathogen attack (Nicholson & Bailey 1935)
N6j = infectious pathogen population density (pathogen units cm'2)
Y = realized pathogen transmission rate ((pathogen unit)'1 day'1)
The pathogen transmission rate (y) is mainly a function of humidity and temperature
(Filajdic & Sutton 1992, Mathieu & Kushalappa 1993, Tamm & Fluckiger 1993,
Carisse et al. 1993). Daily leaf wetness duration (\y hours) was used to represent
humidity. Previous studies indicated that temperature extremes reduce pathogen
transmission rate, while high relative humidity increases pathogen transmission rate,
and temperature effect on pathogen transmission rate was slightly negatively-skewed
(Filajdic & Sutton 1992, Mathieu & Kushalappa 1993, Tamm & Fluckiger 1993,
Carisse et al. 1993). For simplicity, a modified normal density distribution function

123
was used to describe the effect of temperature on pathogen transmission rate. The
modified normal density function is
PT
exp(-
2*li
6-14
where
p = proportion of realized pathogen transmission rate;
T = temperature (°C);
T' = temperature at which the highest transmission rate occurs (i.e. Pr = l);
Tb = indicator of temperature range for effective pathogen transmission.
Parameters 7^ and Jb were set at 26°C and 5.5°C, respectively, based on studies by
Gerson et al. (1979) and Kenneth et al. (1979). Equation 6-14 assumes a symmetrical
temperature effect on pathogen transmission rate toward temperature extremes.
Previous studies suggested a sigmoid increase in pathogen transmission rate
with increasing leaf wetness duration (Filajdic & Sutton 1992, Mathieu & Kushalappa
1993, Tamm & Fluckiger 1993, Carisse et al. 1993). A logistic distribution function
was used to describe the effect of leaf wetness duration on pathogen transmission rate.
The logistic distribution function is
P =
, , W-a.
l+exp(- )
6-15
where

124
p ~ proportion of realized pathogen transmission rate;
W
W = daily leaf wetness duration (hours);
a = the leaf wetness duration which causes half of the maximum pathogen
transmission rate (i.e. p = 0.5 at a)',
Ft
b = indicator of the steepness of the logistic curve.
If the maximum pathogen transmission rate is y , then the realized pathogen
transmission rate (y), in relation to leaf wetness duration (w) and temperature (7),
is
Y =
Ymax*PW*PT =
1
1 , W-a.
l+exp(- )
. (T-T/
*exp(- r—)
6-I6
Since H. thompsonii is a facultative pathogen and it can survive without rust
mite host (Gerson et al. 1979), a minimum density of 0.005 pathogen unit was always
assumed throughout the simulation.
Elements for the fecundity matrix F. Females of any age were assumed to
have equal reproductive capacity. Therefore, eggs produced by each female per time
step (f^) is
Total eggs (R^)
Female life time (t)
♦Time step (At)
*At
6-17
Allen et al. (1994b) related the total number of eggs produced each female (RTou¡¡) to

125
temperature (7), which is
Rj.^ = 11.590936 - 3.622485*7 + 0.291811 *72 - 0.005733*73 6-18
In the study by Allen et al. (1994b), a female to male sex ratio of 0.5 was assumed.
In this simulation, the same sex ratio was used, so
/. =!^í* Ar*0.5 6-19
V T
The reproductive rate represented by equation 6-19 may not be fully realized
when mite population is high due to intraspecific competition for food and/or space, it
is therefore necessary to introduce a density-dependent factor into equation 6-19. The
following density-limiting factor was used
1
1
N, .-a
1 + exp(- )
6-20
where N = total mite population density; parameters a and b in equation 6-19
represent species-specific density-limiting properties. Parameter a is related to
carrying capacity, higher values of a would indicate higher carrying capacities.
Parameter b is related to the intensity of the density-limiting factor, higher values of
b would indicate a slower approach of the density-limiting effect to its maximum.
This density-limiting factor assumes a sigmoid effect, having a value of close to 1 at
low mite population density, and a value of close to zero at high mite population
density, The reproductive rate with the density-limiting factor is

126
4 - i
N'.-a
l+exp(-———)
6
)*í?Z£^*Aí*0.5
6-21
High mite populations often cause extensive fruit surface damage, this
inevitably reduces food quality for the citrus rust mite, and further more, mites avoid
directly-sunlit and shaded areas, this behavioral response of mites to light (probably
also temperature) further limits their food availability. It is therefore necessary to
introduce a food limiting factor into the reproductive function (equation 6-21). The
proportion of undamaged fruit surface was used as the limiting factor. If d is the
proportion of damaged fruit surface area, then 1 -£) is the proportion of undamaged
fruit surface area, then equation 6-21 becomes
Aj = (l-flWi -
i
N, .-a
l+exp(- )
)*-
'’Total
*Af*0.5
6-22
t
A model was developed in Chapter 2 relating cumulative percent fruit surface damage
to cumulative mite days (equation 2-9). The model is
y=exp(-13.901008)x2 086012 6‘23
where x = cumulative mite days. Cumulative mite days (*) can be calculated using
the following equation
*«)-£
*0
*2-4(í)+*2-4 ('+A')_
t
2
6-24

127
where tQ = beginning time of observation or simulation; iV2 4(r) = sum density of
the protonymph, deutonymph and adult stages at time t â–  N2 4(f+Ar) = sum density
of the protonymph, deutonymph and adult stages at time t+At- The beginning time
(rQ) should start when mite populations are very low for accurate prediction, because
equation 6-23 was obtained using field data starting with very low mite populations.
Therefore the proportion of damaged fruit surface is £> = .
100
van Brussel (1975) reported that adult mites did not lay eggs when the fruit
surface was covered with water during and after rain. I introduced a rain factor
(p ) into equation 6-21
fa “ -
1
N, .-a
l+exp(- )
)*i?Z£^*Ar*0.5
6-25
Since not enough information is available on the effect of rain on egg production, a
value of 1 for p was assumed if rainfall for a specific date is less than 1 cm; and a
value of 0.5 for p was assumed if rainfall for a specific date is more than 1 cm.
rain
Matrix Element Calculation - Varying Temperature
If temperature changes with time (day), then the developmental durations of all
the mite and pathogen stages will change, this will inevitably lead to a change in the
number of age classes after every time step simulation. The following method was

128
used to adjust the number of age classes. If Tt and j are temperatures at time t
and r+i, andia(f) and are the corresponding number of age classes, and if all
the individuals in the same age class are assumed to be evenly distributed with regard
to age, then one time step at time *+i should equal JüííL time steps at time t • The
number of individuals for an age class at time r+i should equal the number of
individuals which fall within the corresponding time interval at time t â–  This
'«(f* i) i
method uses expansion or compression of the age vector: expansion when *a(t) is
la(t*l)
less than one; compression when .. *g(fL is larger than one. For example, if 10 and
20 are the number of age classes at time t and t+\ respectively, since 10/20 = 1/2 is
less than one, we need to expand the individuals in the 10 age classes at time t to the
corresponding 20 age classes at time r+i before carrying out simulation at time r+l.
After this adjustment, we can still use the general model to simulate the population
dynamics under changing temperatures. The simulation program was written in
Matlab (Math Works Inc. 1992).

129
Model Parameter Estimation
Some of the model parameters cannot be easily determined. For example,
parameters related to pathogen transmission rate (equation 6-16), and density-
dependent mite egg production (equation 6-20). It is understandable that interactions
among model parameters may exist, and different parameter combinations may
produce similar model behavior. Since the main interest is in mite population
prediction, these interactions will not be fully explored in the current paper, so long
as the model behaves properly.
The general approach for parameter estimation was to adjust certain model
parameters so that the model behavior was closer to the real data qualitatively and
quantitatively. A parameter combination which gives the best result to all tested field
data was then chosen for use in the model. The major climatic factors included in the
simulation were temperature, humidity and rainfall (see Chapter 5 for weather data);
the major biological factors were fruit age, surface damage, and pathogen population
density. Three sets of data from field studies on ’Hamlin’ orange fruit (Polk County
grove 1993, Alachua County 1992, 1993, see Chapter 5) were used for this parameter
estimation process. The initial observed mite population densities were used as the
initial mite population densities in the model. The actual daily temperature, leaf
wetness duration, and rainfall recordings were the environmental factors which drove
the model. Since there was no recording of the leaf wetness duration for the two
studies at the University of Florida Horticultural Sciences Department citrus grove, a
daily mean of 10.5 hours of leaf wetness duration was assumed through the

130
simulation. Parameters to be estimated are those in equations 6-16 and 6-20.
Mean squared error of prediction (MSEP) was calculated using the formula
(Wallach & Goffmet 1989, Thomley & Johnson 1990)
MSEP = ¿ 6-26
¡=i m~n
where m = number of observations; n = number of model parameters; y. =
predicted value; y. = observed value.
Results
Parameter Estimates
Estimated values for parameters in equations 6-16 and 6-20 are presented in
Table 6-2. The effects of leaf wetness duration and temperature on pathogen
transmission rate is shown in Fig. 6-3. The effect of the density-limiting factor on
mite reproduction is shown in Fig. 6-4. The maximum pathogen transmission rate
(y ) was es6matec* at 0-1 (pathogen unit)'1 day'1. The leaf wetness duration which
results in half of the maximum pathogen transmission rate was estimated at 11 hours
per day (i.e. p = 0.5 at a = 11 hours) (Table 6-2). A larger value of a would
indicate the pathogen requirement for longer wetting hours; a smaller value of a
would indicate the pathogen requirement for shorter wetting hours. Parameter b in
equation 6-16 was estimated at 0.8 hours, which is an indicator of the standard
deviation of the logistic distribution curve. A larger value of b would indicate a

131
slower approach to the maximum transmission rate; a smaller value of b would
indicate a faster approach to the maximum transmission rate; These two parameters
are characteristics of the fungal pathogen. The temperature which results in the
highest pathogen transmission (7 ) was estimated at 26°C (Table 6-2); the parameter
T was estimated at 5.5°C, a larger value of r would indicate high pathogen
b b
transmission rate over wider temperature range; a smaller value of 7 would indicate
high pathogen transmission rate over narrower temperature range. The mite
population density which reduces mite reproductive rate by half was estimated at a —
150 mites cm'2. The standard deviation indicator (b) was estimated at 15 mites cm'2.
A larger value of b would indicate a slow reduction in mite reproductive rate; a
smaller value of b would indicate a faster reduction in mite reproductive rate. The
estimated parameter combination (Table 6-2) may be only one of the possible
parameter combinations which can produce similar results.
Observed vs. Simulated Mite/Pathogen/Damage Dynamics
Polk County 1993. The observed and simulated mite and pathogen population
dynamics for the study at the Polk County citrus grove were close (Fig. 6-5a vs. 6-
6a), so were the fruit damage and cumulative mite days (Figs. 6-5b,c vs. 6-6b,c).
The observed mite population peak time was about 260 Julian days (Fig. 6-5a); the
simulated mite population peak time was also about 260 Julian days (Fig. 6-6a). The
observed pathogen population peak time was about 270 Julian days (Fig. 6-5a); the
simulated pathogen population peak time was about 290 Julian days (Fig. 6-6a). The

132
observed fruit surface damage was about 35% (Fig. 6-5b); the simulated fruit surface
damage was about 28% (Fig. 6-6b).
Alachua County 1993. The observed mite population peak time was about
230 Julian days (Fig. 6-7a); the predicted mite population peak time was also about
230 Julian days (Fig. 6-8a). The observed pathogen population peak time was about
260 Julian days (Fig. 6-7a); the predicted pathogen population peak time was also
about 250 Julian days (Fig. 6-8a). The observed fruit surface damage was about 25%
(Fig. 6-7b); the simulated fruit surface damage was about 35% (Fig. 6-8b).
Alachua County 1992. The observed mite population peak time was about
220 Julian days (Fig. 6-9a); the predicted mite population peak time was about 230
Julian days (Fig. 6-10a). The observed pathogen population peak time was about 240
Julian days (Fig. 6-9a); the predicted pathogen population peak time was about 250
Julian days (Fig. 6-10a). The observed fruit surface damage was about 30% (Fig. 6-
9b); the simulated fruit surface damage was about 35% (Fig. 6-10b).
Collier County 1991. The results from the study at Collier County were not
included in parameter estimation process, because no parameter combination could be
found which gives close prediction for data sets from Polk County and Alachua
County. The estimated parameter combination (from Polk County and Alachua
County) was used to simulate mite and pathogen dynamics at the Immokalee Budwood
Foundation grove in Collier County, the predicted results were much higher than
observed (Fig. 6-11 vs. 6-12). The fungal pathogen actually was very high and
effectively kept the mite population at a very low level in the Immokalee Budwood

133
Foundation grove in 1991 (Fig. 6-11), while the model failed to generate results
similar to the observed data (Fig. 6-12). There may have been other factors
unaccounted in the model which could have resulted in a low mite population.
The mean squared errors of prediction for mite populations in Alachua County
1992, 1993 and Polk County 1993 are 658.6, 306.6, and 1114.0, respectively. The
reason for the high squared errors of prediction is because mite populations are very
high. Another reason is that the simulated mite population peaks did not coincide
completely with the observed mite population peaks. Because of the dramatic change
in mite population densities, even a slight shift (for example, a few days) in mite
population peaks will result in huge errors (Figs. 6-5a vs. 6-6a, 6-7a vs. 6-8a, 6-9a
vs. 6-10a). The mean squared error of prediction for the mite population in Collier
County was not calculated because the model obviously failed to produce results
similar to the observed data (Fig. 6-1 la vs. 6-12a).
Discussion
Need for a Maximization Tool
The above model parameter estimates were obtained by visual comparison
between simulated and observed population curves. For accurate estimation, it is
necessary to develop a maximization tool (system) which can select the best
combination of parameter estimates for given sets of data. A software package for
system identification could be applied to search for best fit parameters but this was
not available in this study.

134
Need for Pathogen Biology
As compared to the citrus rust mite, information on the biology of the fungal
pathogen is very limited (McCoy 1979, Gerson et al. 1979, Kenneth et al. 1979).
During the simulation process, the development of latent pathogen was assumed to be
the same as the protonymph stage. We also assumed that the infectious pathogen
development into death was the same as adult mite development into death.
Although these assumptions were partly based on laboratory observations (McCoy
1979, Gerson et al. 1979), the actual pathogen development and death might be quite
different. With detailed study on pathogen biology, we might be able to greatly
improve model behavior, especially with information on pathogen transmission rate
and survival under natural conditions.
Modeling Pesticide-Induced Mortality.
In our fruit-mite-pathogen system, mortality of all mite and pathogen stages
have been kept constant for simplicity. A future development would incorporate a
pesticide-induced mortality model into our system. Pesticide application may cause
differential mortality to mite and pathogen populations. Jones et al. (1977) developed
a process-oriented model to simulate dynamic insect mortality through time after
pesticide application. This process-oriented model has been used by Hardman (1989)
for simulating pesticide-induced mortality for the European red mite, Panonychus ulmi
(Kock). This pesticide-induced mortality model should be easily incorporated into our
system.

135
Parameter Calibration and Model Application
The established model is in a preliminary form. Much work on model
parameter adjustment and calibration is needed before it can make accurate
predictions. Complete recordings on mite, pathogen and weather data are rare. With
local mite and weather data for adjusting model parameters, especially parameters
related to pathogen transmission rate, model prediction will be greatly improved.

136
Table 6-1. Parameter estimates for equations describing the relationship between cumulative
emergence (F(t,7)) and temperature (7).
Stage
3o
ai
do
bi
R2
Egg*
-59.82963
1.21298
809.52603
-0.218371
20.213928
0.7078
1st nymph*
-15.81029
0.34221
229.93210
0.115959
3.928845
0.9111
2nd nymph*
-14.65189
0.28090
229.34018
0.177027
2.389133
0.8670
Adultb
-4.51372
256.91348
0.00000
-0.089292
22.473226
0.9707
Lat. Path.*
-15.81029
0.34221
229.93210
0.115959
3.928845
0.9111
Inf. Path."
-4.51372
256.91348
0.00000
-0.089292
22.473226
0.9707
1 The cumulative emergence function is F(t,T) =
1
, , t-a(Th
1 + exp(---
b(T)
a(T) = b The cumulative emergence function is F(t,T) =
1
1 + exp(-^^)
¿(7)
a(T) = a0 + ^ , and b(T) = b0 +
where
where

137
Table 6-2. Parameter estimates for pathogen transmission rate and density-
dependence
Equation
Parameter
Definition
Value
Units
6-16
Y TTlfll
max. trans. rate
0.1
(pathogen unity'day1
a
mean
11
hours
b
indicator for SD*
0.8
hours
mean
26
°C
Tb
indicator for SD*
5.5
°C
6-20
a
mean
150
mites cm'2
b
indicator for SD*
15
mites cm'2
1 SD = Standard deviation.

138
Fig. 6-3.
rate.
Effect of leaf wetness duration and temperature on pathogen transmission

Proportion of eggs laid
139
Fig. 6-4. Density-dependent egg-laying curve for the citrus rust mite.

140
CN
<
E
o
c
O)
O
CD
CL
Fig. 6-5. Observed fruit-mite-pathogen system dynamics, (a) mite and pathogen
population; (b) fruit surface damage; (c) cumulative mite days (Polk
County, Florida, 1993).

Mites(Pathogens)/cm/v2
141
Gamamax = 0.1 Pa=26 Pb=5.5 PaO = 11 Pb0=0.8
120 180 240 300 360
Julian day (1=1 Jan.)
Fig. 6-6. Predicted fruit-mite-pathogen system dynamics, (a) mite (thick solid
line) and pathogen (thin solid line) population; (b) fruit surface damage;
(c) cumulative mite days (Polk County, Florida, 1993).

Fruit surface damage
142
120 180 240 300 360
0 60 120 180 240 300 360
Julian day (1=1 Jan. 1993)
Fig. 6-7.
Observed fruit-mite-pathogen system dynamics, (a) mite and pathogen
population; (b) fruit surface damage; (c) cumulative mite days (Alachua
County, Florida, 1993).
Pathogen / cmA2

M¡tes(Pathogens)/cm A2
143
Gamamax=0.1 Pa = 26 Pb=5.5 PaO = 11 Pb0=0.8
120 180 240 300 360
Julian day (1=1 Jan.)
Fig. 6-8. Predicted fruit-mite-pathogen system dynamics, (a) mite (thick solid
line) and pathogen (thin solid line) population; (b) fruit surface damage;
(c) cumulative mite days (Alachua County, Florida, 1993).

Fruit surface damage (%)
144
120 180 240 300 360
Fig. 6-9.
Observed fruit-mite-pathogen system dynamics, (a) mite and pathogen
population; (b) fruit surface damage; (c) cumulative mite days (Alachua
County, Florida, 1992).
Pathogen / cmA2

M¡tes(Pathogens)/cm A2
145
Gamamax=0.1 Pa=26 Pb=5.5 PaO = 11 Pb0 = 0.8
120 180 240 300 360
Julian day (1=1 Jan.)
Fig. 6-10. Predicted fruit-mite-pathogen system dynamics, (a) mite (thick solid
line) and pathogen (thin solid line) population; (b) fruit surface damage;
(c) cumulative mite days (Alachua County, Florida, 1992).

Fruit surface damage Mjtes, cm*2
146
120 180 240 300 360
120 180 240 300 360
Fig. 6-11.
Observed fruit-mite-pathogen system dynamics, (a) mite and pathogen
population; (b) fruit surface damage; (c) cumulative mite days (Collier
County, Florida, 1991).
Pathogen / cmA2

M¡tes(Pathogens)/cm *2
147
Gamamax = 0.1 Pa = 26 Pb=5.5 PaO = 11 Pb0 = 0.8
Julian day (1=1 Jan.)
Fig. 6-12. Predicted fruit-mite-pathogen system dynamics, (a) mite (thick solid
line) and pathogen (thin solid line) population; (b) fruit surface damage;
(c) cumulative mite days (Collier County, Florida, 1991).

CHAPTER 7
CALCULATION OF VOLUME LOSS
FROM RUST MITE DAMAGE TO FRUIT
Statement of the Problem and Study Objective
Economic loss from citrus rust mite damage to fruit results from three aspects
of mite damage: (1) reduced fruit grade due to surface damage; (2) reduced fruit
growth; and (3) increased fruit drop. Fruit can either go for fresh fruit market or
processed fruit market depending on the extent of rust mite damage. Fresh fruit have
a higher market value than processed fruit (Anonymous 1992). Total crop yield will
be reduced from fruit growth reduction and drop increase. Therefore total value loss
include value loss due to reduced fruit grade and value loss due to total yield loss.
Crop yield can be expressed in weight or volume. In this paper volume was used to
describe fruit crop yield. Previous chapters deal with specific aspects of rust mite
damage. This chapter is intended to integrate all the three aspects of rust mite
damage (Allen 1981, Allen et al. 1994). The objective was to develop a model to
estimate total volume loss from rust mite damage. By combining this with a mite
population model developed in chapter 6, one would be able to predict the mite
population trend and at the same time total volume loss from potential rust mite
damage. Since fruit crop yield differs among groves, and crop value varies with
148

149
season and year, only a formula will be given to calculate total value loss from rust
mite damage.
Materials and Methods
The calculation process includes the following six steps: (1) mite population
prediction; (2) fruit surface damage prediction; (3) frequency distribution of mite
damage to fruit; (4) volume/value loss from reduced fruit growth and increased fruit
drop; (5) value loss from reduced fruit grade; and (6) total value loss from mite
damage. If one only wants to estimate volume or value loss for a given mean fruit
surface damage, the first two steps are not necessary.
Mite Population Prediction
If our interest is in predicting potential value loss, then we first need to predict
future mite population trend, this can be accomplished with the simulation model
developed in Chapter 6. The inputs to the model would be: prediction period, initial
mite population density, and weather data (i.e. daily mean temperature, daily leaf
wetness duration, and daily rainfall).
Fruit Surface Damage Prediction
Based on the predicted mite population dynamics, one can calculate cumulative
mite days (x) as a function of time, and then predict fruit surface damage fiy) (%)
using the following model established in Chapter 2 (equation 2-3)
y=exp(a)xb 7-1
This cumulative percent fruit surface damage is a predicted mean. Damage rate per

150
mite day (^) can be obtained by taking the derivative of equation 7-1, which is
dx
dx
— =exp (a)bxb~l
7-2
where a — -13.901008; b = 2.086012 (Table 2-2). This damage rate function will
be used in predicting volume loss due to rust mite damage.
Frequency Distribution of Mite Damage to Fruit
With the mean damage (equation 7-1), one can calculate the cumulative
frequency distribution of mite damage on fruit based on the following functions
developed in Chapter 4 (equations 4-2, 4-3, 4-4, Table 4-2)
7-3
a(p) = aQ + fljp + a2exp(-p)
7-4
b(\i)=bQ+blexp(-b2\i)
7-5
where
FFre(x,\i) = proportion of fruit which has less than x proportion surface
damage in a grove with a mean damage of jx;
iQ = -0.8899397; ^ = 0.10717377; ^ = -5.3115167 (Table 4-2);
bQ = 0.0897463; = 0.20459698; b2 = 0.4304787 (Table 4-2).

151
By replacing ¿j(p) and b(\i) in equation 7-3 with equations 7-4 and 7-5, we have the
cumulative frequency distribution function. The probability density function can be
obtained by taking the derivative of equation 7-3 and then dividing by the area (a =
FFreq(100,\i) - FFreq(0,\i)) under the rate curve so that the density integrates to one
between [0, 100]%. This density function is
A
*
x-a
~b
)
(1 + exp(-^))2
o
7-6
where a(^) and b(\i) are given by equations 7-4 and 7-5. This density function will
be used in calculating volume loss from increased fruit drop and reduced fruit growth.
Volume and Value Loss from Increased Fruit Drop and Reduced Fruit Growth
Fruit growth and drop vs. damage. In Chapter 3, it was established that
cumulative percent fruit drop is a function of mite surface damage (x) and Julian day
(t) (equation 3-5). Proportional fruit drop (FD (x,t)) is used here in this chapter,
which is
^Dropi*’ Ü
1
1 +exp(a-£>(x)r)
7-7
where a = 7.230067; b = 0.010659+0.00007473*• The corresponding drop rate
function (f ) is
J Drop

152
dFDrop^O . , n _ ¿>(x)exp(g-fr(x)r) 7o
Drop (1 +Qxp(a~b(x)t))2
In Chapter 3, it was established that cumulative % diameter fruit growth is a
function of mite surface damage (x) and Julian day (t) (equation 3-6). Proportional
fruit growth (FGrowth(x,t)) is used here in this chapter, which is
FGrowth^ ~ 1+exp(a-&(*),) * Too 79
where
Kx) = 33.73 - 0.0108*;
¿2=7.9943611
b(x) = 0.039723 - 0.00000916*;
The corresponding rate function is
dFGrowth^ . ( v k(x) * b(x) * exp (a-b(x)t) ^ 1 7.10
(1 +exp(<3-¿>(*)r))2 100
If fruit are spherical, then volume growth is (see Appendix A for details)
7-n
where = Fruit diameter at time rQ when damage occurs. This diameter should
be the same for any damage class (*) at time ¿ . The volume growth rate function
would be the derivative of equation 7-11, which is

153
Growth
Growth
7-12
Total proportional volume loss. Calculating yield (volume) reduction from
size loss and fruit drop is mainly a matter of averaging drop or size reduction over
the frequency distribution to produce grove-level means. The variables
VQ, N0, V', and N represent volume per fruit and the number of fruit in an
undamaged grove and volume per fruit and the number of fruit in a grove having
mean damage p., respectively. Then the rate equations of number and volume for an
undamaged grove are
~ = -N0*(drop rate) = -NJDrop(0,t)
7-13
-y- = Volume growth rate = fGrowth¿0,t)
at
7-14
Equation 7-13 means that the rate of total fruit number change in a grove having zero
damage is the product of fruit number and fruit drop rate. Equation 7-14 describes
the per fruit volume growth rate in a grove having zero damage (i.e. ^ = 0).
The rate equations for number and volume per fruit for a grove with mean damage
>0 are

154
dN.
100
— = -N *
dt •*
(average drop rate) = -N^ f fDrop(xJ)fFrtq(x,i)dx 7-15
dV.
100
-*■ = Average volume growth rate = f fCrowthii.x, t)fFreq(x, t)dx 7‘16
Equation 7-15 describes the rate of total fruit number change in a grove having ^
damage by averaging fruit drop over all damage classes of [0, 100]%. Equation 7-16
describes per fruit volume growth rate in a grove having ^ damage by averaging fruit
volume growth rate over all damage classes of [0, 100]%.
The total fruit crop volume in a grove having zero damage is the product of
total fruit number (nq) and volume per fruit (VQ), which is NQVQ- The total fruit
crop volume in a grove having a mean damage of ^ is the product of total fruit
number (jv^) and volume per fruit (V^), which is N V • The total proportional
volume loss (TPVL) at mean damage ^ can then be calculated as
Total Proportional Volume Loss = TPVL = 1 -
N V
N V
iyo 'o
7-17
Proportional volume and value loss for fresh and processed fruit. Assuming
that fruit with xpackouI percent damage or less can go to the fresh fruit market (x^^
= 5% was assumed), and fruit with more than xpackout percent damage will go to the

processed fruit market, then the drop and volume rate equations for the fresh fruit
would be
155
dN.
xpackoMX
= -N^{average drop rate) = -N^ f fDrop(x,t)fFreq(x,t)dx 7'18
dV.
poctcmt
Ir*'m,ume srow,h rate* l f-*#'*"#'** 749
In order to calculate volume loss for the fresh fruit, we need to know the
packout number (N0packout) and packout volume (VQpackout) of fruit in a grove without
damage. Since the proportion of fruit with xpackout percent damage will change with
mean damage (jx) in a grove, we should calculate the packout number (N0pa£h>ut) and
packout volume (V0pacbjlit) °f fruit in a grove without damage based on the
corresponding frequency of fruit in a grove with mean damage ^. The rate functions
are
dNn . , ’ad¡T 7-20
^— = ~N0*(drop rate)*(packout frequency) = NJDrop(0,t) J fFreq(x,t)dx
dV,
podcout
0, packout
~dT
= (Growth rate) * {packout frequency) = fGrowthV(0,t) f fFreq{x,t)dx
7-21

156
The proportional volume loss for fresh fruit (PVLFF) would be
N V
Proportional Volume Loss for Fresh Fruit = PVLFF = 1 - —
N V
O.packout O.packout
7-22
The proportional volume loss for processed fruit (PVLPF) would be
7-23
PVLPF = Total Volume Loss - Fresh Fruit Volume Loss = TPVL - PVLFF
If market price for fresh fruit per box is pp, and market price for processed fruit per
box is pp, then value loss per box for the fresh fruit section is PVLFF*PF, and value
loss per box for the processed fruit section is PVLPF*Pp-
Adjustment for on-tree mean damage (^). Because of a higher drop rate for
highly damaged fruit, on-tree mean damage will decline slowly from the initial
damage if no new damage occurs, and will be slightly lower than calculated from
equation 7-1 if new damage occurs. Therefore it is necessary to adjust the mean
damage (^) during simulation. The following equation has been developed by Allen
et al. (1994a) for this adjustment when no new damage occurs
100 100
~ = Ia i fDrop(XJ)f~ f ^Drop^Frc^^ ^
01 0 0
If new damage occurs, the updated mean damage (^) equals the adjusted mean plus

157
new damage. The damage rate is
100 100
Yt = ^ ijDrop(X^VFreq(x,t)dx ~ f xf^Jx^Fr^dx 7-25
where ^ = damage rate per mite day, which is equation 7-2; m(t) = mite density
dx
per cm2 at time t â– 
Value Loss from Reduced Fruit Grade
If the cut-off level between fresh and processed fruit is x ^ percent surface
damage, let us examine total crop value in two different groves: one having no
damage, the other having a mean damage of ^. In the first case (i.e. no damage), all
the fruit in the grove can go to the fresh fruit market, then the value per box is p .
In the second case (i.e. damage p,), the proportion of fruit which can go to the fresh
fruit market is FFreq(xpackout, p) (equation 7-3), the rest, 1-FFttq{xpadame p), will go to
the fresh fruit market. So, the value per box is
p (x . n)+P *(l-F (x . u'fi. Value loss per box due to reduced fruit
F Frcq^ packoux’ rJ 1 p Va 1 Freq^ packoui’ r
grade (VLRG) is the difference between the value per box without damage and the
value per box with damage , which is
VLRG = (1- FFrt¿x^u)).(.PF-Pp) 7-26

158
Total Value Loss from Reduced Fruit Grade. Reduced Fruit Growth, and Increased
Fruit Drop
The total value loss per box is a sum of the value loss from reduced fruit
grade and volume reduction. Total volume reduction can be divided into fresh fruit
section (PVLFF, equation 7-22) and processed fruit section (PVLPF, equation 7-23).
Therefore, total value loss per box is
Total value loss per box = VLRG + PVLFF*Pp + PVLPF*Pp 7-27
If the expected total boxes of citrus fruit crop per acre is TotalBoxes, then total value
loss per acre is
7-28
Total value loss per acre = Totalboxes*(VLRG + PVLFF*Pf + PVLPF*Pp)
Control decision can be made based on this estimated value loss and control cost.
A program which can carry out the above calculations has been developed in
Matlab (MathWorks Inc. 1992). Several scenarios of rust mite damage are examined
below, and the resulting volume loss is calculated.
Results
Volume Loss without New Damage
If we assume that mite damage had already occurred at 200 Julian days (July
19th) (1 = 1 Jan.), and if we further assume that the mean damage was 25%, and no
new damage occurred, then the total volume loss was about 2.01% by 350 Julian days
(Fig. 7-la), the volume loss for the processed fruit was about 1.87% (Fig. 7-lb), and

159
the volume loss for the fresh fruit was about 0.14% (Fig. 7-lc). As a result of higher
drop of highly damaged fruit, mean fruit surface damage decreased from 25 % to
about 24.5% (Fig. 7-2c). If mean fruit surface damage was increased to 50%, the
total volume loss was 5.73% (Fig. 7-3a), and 5.69% for processed fruit (Fig. 7-3b),
and 0.04% for fresh fruit (Fig. 7-3c), and there was about 1% decrease in mean fruit
surface damage (Fig. 7-4c). From the result we can clearly see that, with the
increase of mean damage from 25% to 50%, volume loss for fresh fruit decreases
from 0.14% (Fig. 7-lc) to 0.04% (Fig. 7-3c). This is because the proportion of fruit
with xpackou! percent damage decreases with increasing mean damage. The results also
indicate an accelerating increase in volume loss (Figs. 7-1, 7-3), this is caused by an
accelerating increase in fruit drop with the progress of the season (see Chapter 3 for
details).
The number and volume change of fruit for groves without damage and with
damage are also presented (Fig. 7-2a vs. 7-2b, Fig. 7-4a vs. 7-4b). The volume
growth curve (Figs. 7-2a, b, 7-4a, b) is an indicator of fruit growth, fruit growth
levels off with the progress of the season. The decreasing fruit number curve (Figs.
2a, b, 4a, b) indicates loss of fruit due to drop.
Volume Loss with New Damage
The above estimation of volume loss was based on the assumption that damage
occurs at a certain time and no new damage follows. It is often necessary to simulate
damage dynamics and the resulting volume loss with increasing mite populations. If
we assume that there is no damage at the time of simulation, and new damage occurs

160
during simulation, we can simulate mite population dynamics first, and then damage
loss based on predicted mite population. Data (see Chapters 5, 6) from the study at
Polk County in 1993 were used for this simulation. The simulated mite and pathogen
populations are shown in Fig. 7-5a, simulated fruit surface damage and mite days are
shown in Figs. 7-5b, c, respectively. The predicted total volume loss is about 0.87%
by 322 Julian days (Fig. 6a), about 0.82% for processed, and 0.05% for fresh fruit.
Discussion
Volume Loss for Fresh Fruit vs. Processed Fruit
If a 5 % cutoff level is set for fresh and processed fruit, volume loss for the
fresh fruit from reduced fruit growth and increased drop is insignificant (Figs. 7-lc,
3c), the volume loss is mainly for the processed fruit. An increase in cutoff level
would increase the volume loss for the fresh fruit. An increase in mean damage with
constant cutoff level would decrease volume loss for the fresh fruit (Fig. 7-lc vs. 3c).
Mite Control Decision
As indicated above, volume loss is an accelerating function of time. Mite
damage time and fruit harvest time will greatly affect the eventual volume loss. The
total value loss would be further determined by crop values. If mite control cost is
known, one will be able to determine whether and when mite control is necessary
based on value gain and control cost (Allen 1981). Allen (1981) estimated volume
and economic loss mainly based on data from ’Valencia’ orange. The predicted
volume loss (Allen 1981, Fig. 1) is higher than our results on ’Hamlin’ orange. This
is probably due to higher drop rate and greater fruit growth reduction observed in

161
Allen’s studies (Allen 1978, 1979a, 1979b). Also the time period used here (day 200-
350) is relatively short. The results on ’Hamlin’ orange in the current paper and
Allen’s (1981) results on ’Valencia’ orange both indicate an accelerating increase in
volume loss, this general trend might also be true of other citrus varieties.
In the current paper, volume loss was examined for a rather short period (i.e.
from day 200 to day 350). This is because the damage-related studies ended by 350
Julian days, prediction beyond data-supported time limit might be misleading. Another
reason for the short period prediction is that ’Hamlin’ orange is an early season crop,
usually harvested in October and November. If for some reason(s), the fruit crop is
exposed in the field for longer period, volume loss would be much higher than
predicted here, because volume loss slightly accelerates through time (Figs. 7-la and
7-3a). This is especially the case with ’Valencia’ orange, which is a late season fruit.
’Valencia’ fruit crop may be exposed in the field until next May (Allen 1980, 1981).
This extended exposure may result in heavy loss (Allen 1980, 1981). In Florida, over
90% of the round oranges are used in processed products (Townsend & Abbitt 1978,
Anonymous 1992). Even though percent volume loss is only a few percentage points,
total volume loss for the processed fruit may run very high. Therefore mite control
may still be necessary for the processed fruit groves. Since early season damage
reduces fruit growth, and fruit drop accelerates with time, therefore early season
damage prevention has double benefits: (1) fruit growth will not be affected; (2)
heavy fruit drop might be largely prevented because not enough time will be left for
the accelerating fruit drop process to occur before harvesting. This is clearly

162
demonstrated by the simulated volume loss for the study at Polk County in 1993
(Figs. 6-6 and 7-5). The simulated mite population peak occurred at about 270 Julian
days Gate September)(Fig. 6-6a). Even with an almost 30% final damage (Fig. 6-6b),
the resulting total volume loss was less than 1% by 322 Julian days (Fig. 7-5a). This
is because less than two months were left between the time of full damage (early
October) and 322 Julian days (late November) (Fig. 6-6b).
Looking Into the Future
The overall objective of this study was to develop a system for mite and
damage prediction, and for loss assessment. Although the established system seems
to produce very promising results, the model should be further calibrated and adjusted
with more field data before it can be put into practical use. A research version of this
established system (written in Matlab programming language) (MathWorks Inc. 1992)
is currently available. A simplified and more user-friendly version of this program is
being considered. Data on other citrus varieties could be easily incorporated into the
program. Citrus extension specialists and industry pest management personnel, could
use the simplified version in their mite management practices.

Volume loss (processed) Total volume loss
163
mu=25% at t=200
0.02
0.015
0.01
0.005
0
200 250 300 350
1.5

0

CO
_o
0
E 0.5
o
>
0
200 250 300 350
Julian day (1 =1 Jan.)
Fig. 7-1. Volume loss from rust mite damage, (a) total volume loss; (b) volume
loss for processed fruit; (c) volume loss for fresh fruit (mu=25% at
t=200).

Number/Volume Number/Volume
164
Julian day (1=1 Jan.)
Fig. 7-2. Effect of mite damage on fruit growth and drop, (a) volume change
(dashed line) and number change (dashdot line) (mu=0); (b) volume
change (dashed line) and number change (dashdot line) (mu=25 at
t=200); (c) mean damage change due to drop (mu=25% at t=200).

Volume loss (processed) Total volume loss
165
mu=50% at t=200
0.06
0.04
0.02
0
200 250 300 350
4
o 2
E
= 1
o
>
0
200 250 300 350
Julian day (1=1 Jan.)
Fig. 7-3. Volume loss from rust mite damage, (a) total volume loss; (b) volume
loss for processed fruit; (c) volume loss for fresh fruit (mu=50% at
t=200).

Number/Volume Number/Volume
166
Julian day (1=1 Jan.)
Effect of mite damage on fruit growth and drop, (a) volume change
(dashed line) and number change (dashdot line) (mu=0); (b) volume
change (dashed line) and number change (dashdot line) (mu=50 at
t=200); (c) mean damage change due to drop (mu=50% at t=200).
Fig. 7-4.

Volume loss (processed) Total volume loss
167
0.01
0.008
0.006
0.004
0.002
0
150 200 250 300 350
0.01
0.008
0.006
0.004
0.002
0
150 200 250 300 350
6
-C
ui
O
~4
(/}
00
_o
0
E 2
o
>
0
150 200 250 300 350
Julian day (1 =1 Jan.)
Fig. 7-5. Predicted volume loss from rust mite damage, (a) total volume loss;
(b) volume loss for processed fruit; (c) volume loss for fresh fruit
(mu=0% at t= 160) (Polk County, Florida, 1993).

CHAPTER 8
SUMMARY AND DISCUSSION
Previous chapters presented results of studies for determining the effects of
citrus rust mite damage to ’Hamlin’ orange fruit, population dynamics of the citrus
rust mite, and for predicting mite population trends and volume loss from rust mite
damage. This chapter summarizes important results from these studies, then discusses
the practical applications of these results in rust mite management, and finally
identifies those areas which need further studies.
Important Results
Fruit Damage vs. Mite Population Density
Six studies were conducted in two separate groves to quantify the relationship
between fruit surface damage and mite density. The general trend in fruit surface
damage was an accelerating increase in relation to cumulative mite days. Cumulative
mite days showed a sigmoid trend in relation to time due to a unimodal mite
population peak. Damage rate also demonstrated a sigmoid trend in relation to time.
The sigmoid time-varying damage rate was mainly a result of sigmoid increase in
cumulative mite days resulting from the single-peaked, more or less symmetrically
bell-shaped mite population growth. Increasing fruit maturity increases fruit
susceptibility to mite feeding, as indicated by a decline in cumulative mite days
required to result in the same amount of fruit surface damage. Tree age and grove
168

169
location did not seem to have obvious effect on the general trend in damage and
damage rate. Two new concepts "Effective Cumulative Mite Days" and "Zero
Damage Mite Density" were introduced and their potential application discussed. A
power function was used to describe the relationship between cumulative damage and
cumulative mite days. Damage rate functions were also derived.
Fruit Growth and Drop vs. Mite Damage
Effects of early season damage by the citrus rust mite, Phyllocoptruta oleivora
(Ashmead), on ’Hamlin’ orange fruit growth and drop were studied from 8 June
through 17 December 1991, in Hendry County, FL. ’Hamlin’ fruit drop increased
with increasing fruit surface damage by the citrus rust mite. The data also indicated a
slightly accelerated fruit drop with increasing mite damage and time. The overall
data suggested a slight negative relationship between fruit size and mite damage.
Cumulative percentage drop and percentage diameter increase were fitted to two-
variable logistic functions of damage and time.
Frequency Distribution of Mite Damage to Fruit
Frequency distribution of citrus rust mite (Phyllocoptruta oleivora) damage on
’Hamlin’ orange fruit was studied from 24 August to 13 October 1993, in Polk
County, FL. In a 4-yr-old ’Hamlin’ orange grove with north-south row orientation,
fruit on the north quadrant of the tree had the highest mean surface damage, followed
by the east, south and west quadrant. With the increase of mean fruit surface
damage, the cumulative frequency distribution changed from convex to sigmoid; the
relative frequency distribution changed from an exponential decay curve to a

170
symmetrical unimodal curve, with the peak shifting toward higher damage class as
mean fruit surface damage was increased. The cumulative frequency distribution was
fitted to a two-variable logistic function of mean fruit surface damage and damage
class. The probability density function was also obtained.
Mite and Pathogen Population Dynamics
Five similar studies on population dynamics of citrus rust mite (Phyllocoptruta
oleivora) were conducted in three separate groves on ’Hamlin’ and ’Valencia’ orange
trees during 1991-1993. Although there were differences in the extent and timing of
population peaks between years and among groves, the general population trend was
similar. Mite populations were usually very low before May, began to build up from
early May to early June, quickly reached the highest levels in the rainy season (June,
July, and August), and then quickly crashed. Mite populations on leaves were
correlated with mite populations on fruit, but were much lower than on fruit. The
studies in 1991 and 1992 showed higher mite population on the upper than on the
lower leaf surfaces, but the studies in 1993 showed higher mite population on the
lower leaf surface most of the time. Rainfall did not seem to have direct effect on
mite population crash. The high relative humidity resulting from rains favored the
epizootic development of the fungal pathogen Hirsutella thompsonii, and was one of
the major factors responsible for rapid mite population crash. Other factors include
rapid diminution of suitable fruit surface due to heavy rust mite damage, and
probably, population self-regulation mechanisms (such as increased mortality, self¬
destructive migration, reduced reproductive rate, and male-biased sex ratio). The

171
study also indicated that Hirsutella thompsonii alone may prevent heavy rust mite
damage on fruit in southern Florida where high relative humidity exists during the
summer rainy season.
Fruit-Mite-Pathogen System Simulation
An age-structured model of the fruit-mite pathogen system was established to
study the interactions between citrus rust mite, the fruit and the fungal pathogen. The
model consists of a set of difference equations. Data from studies on population
dynamics of the citrus rust mite were used to estimate parameters related to pathogen
transmission rate and density-dependent mite reproduction. Using the same set of
parameter combination, the simulated mite populations were in close agreement with
the observed mite populations both in the timing of mite population peak and the
highest mite population density. The timing of simulated pathogen population peaks
was also in close agreement with the timing of observed pathogen population peaks.
With further parameter adjustments, the population model should improve its short¬
term mite population predictions (1-6 months).
Calculation of Volume Loss from Mite Damage
Rust mite damage to fruit reduces fruit grade and growth, and increases fruit
drop. A model consisting of a set of differential equations was established to
calculate the total proportional volume loss due to rust mite damage. The model also
allows us to determine the proportional volume loss for the fresh fruit as well as the
proportional volume loss for the processed fruit. The economic loss model was also
coupled with mite population model. The combined model has the following

172
prediction capabilities: (1) mite population trend; (2) pathogen population prediction;
(3) fruit size growth prediction; (4) fruit surface damage prediction; (5) total
proportional volume loss prediction; (6) proportional volume loss prediction for fresh
fruit depending on packout level; (7) proportional volume loss prediction for the
processed fruit depending on packout level. Model predictions need to be tested
through further field studies.
Practical Applications
Prediction of Fruit Surface Damage
In commercial citrus production, it is often necessary to keep rust mite damage
below certain level. In chapter 2, a function has been established to relate fruit
damage to cumulative mite days (equation 2-3 and Table 6-2 and equation 7-1), which
is y = exp(a).rb (where a = -13.901008 and b = 2.086012)- We can use this
equation to calculate the maximum cumulative mite days for any damage level
control. Cumulative mite days is determined by mite population density. Growers
usually scout the citrus rust mite every one to two weeks. Their scouting results are
usually either in percent infested lens fields or in some other form of relative mite
density. These results can be converted to mite population density cm2 required for
damage calculation (Knapp & Fasulo 1983, Rogers 1992, Rogers et al. 1993).
Prediction of Mite Population Trend
The established mite population model can make mite population predictions
over a few months without huge error, as indicated by results from chapter 6.
Prediction error usually accumulates with time. If we set our maximum prediction

173
time at only one month, prediction error should be rather small. By the end of the
one month prediction period, field surveyed mite population data should be used as
the model initial mite density, and model simulation continues. This step-by-step
prediction should have a rather high accuracy. Mite control decisions may be based
on the predicted mite population trend. Growers usually scout the citrus rust mite
every one to two weeks. If this prediction model is implemented, scouting is needed
only once every month, although more frequent sampling will increase accuracy.
Because of the model capability to project future mite population trend, growers can
make early preparation if a mite population outbreak is to occur soon. Reduction in
scouting times and early preparation for mite control will save growers tremendous
time and labor.
Control Strategies for Fresh Fruit Groves and Processed Fruit Groves
Results from this study clearly demonstrated that heavy rust mite damage
causes significant volume loss to a ’Hamlin’ orange fruit crop. Therefore, citrus rust
mite is not only a problem for the fresh fruit groves, it is also a potential problem for
the processed fruit groves. In the following, I assume that a grove for fresh fruit can
tolerate a maximum damage level of 5% without any value reduction. Mite control
decisions for the fresh fruit grove will be based on this 5 % cutoff level. Mite
control decisions for the processed fruit grove will be based on total volume loss.
Based on the formula relating fruit damage to cumulative mite days (equation
2-9), a 5% damage level equals 1695 cumulative mite days. I call this the critical
cumulative mite days. There are many ways to achieve this damage control level.

174
One approach is to apply the first miticide spray just before cumulative mite days
reaches the critical level which causes 5% damage. The second spray, and the
following spray, should be applied at a mite population level which causes no new
damage. This low mite population level is currently not known.
A second approach is to apply the first miticide spray well before the critical
cumulative mite days. For example a cumulative mite days which causes 2% fruit
surface damage. The second spray may be applied at the cumulative mite days which
causes a 4% cumulative fruit surface damage, for example. This means the second
spray for the second approach can be applied at a higher mite population density,
because 2% new damage is allowed between the first and second spray. Since fruit
susceptibility to mite feeding increases with fruit maturity, equal amount of
cumulative mite days causes higher overall damage late in the fruit growing season.
The second approach actually shifts the cumulative mite days to a later time, higher
damage should result from this approach. Therefore, the first approach is probably
the best choice. Because there are probably many factors involved in causing mite
damage, this conclusion should be further tested.
In the first approach, no new damage is allowed between the first and second
sprays, and the following sprays. In the second approach, a 2% new damage is
allowed between the first and second approach. An immediate question is how to
calculate the new damage. Since the damage formula established in chapter 3
(equation 2-9), was built based on data for continuous mite population growth, i.e.
without miticide interruptions. Miticide applications introduce discontinuity in mite

175
population growth, the formula may not be used for damage estimation except for the
period before the first miticide application. There are two ways the established
damage formula may be used: (1) apply the formula with cumulative mite days
regardless of the discontinuity; and (2) apply the formula with new cumulative mite
days starting from the previous spray. These are the two extreme predictions. It has
been suggested that cells may recover from mite punctures (McCoy & Albrigo 1975,
Allen et al. 1992). Some of the punctured cells may recover between sprays, i.e.
damage may recover somewhat with time. Actual damage may be between the two
extreme possibilities and may be closer to the lower extreme due to cell recovering.
For the processed fruit grove, the major concern is volume loss rather than
fruit surface damage. There is no absolute cutoff damage level. Since total volume
loss accelerates with time, the general approach is to prevent early season damage.
As indicated in chapter 7 (Fig. 7-5), even high mite damage may not cause obvious
volume loss if the time between damage and harvesting is short. The established
volume loss model along with the mite population model is able to predict volume
loss if damage, damage time and harvesting time are known.
The scouting methods currently used by citrus growers apply to both the fresh
and processed fruit groves so long as the counts can be converted to mite density per
cm2.
Further studies
Model Calibration and Implementation
Although mite population and volume loss models are built based on field data,

176
they should be tested and calibrated for practical implementation. The model is
currently written in the Matlab language (MathWorks Inc. 1992). An extension
version should be developed so that it is more user friendly.
Effect of Mite Population Discontinuity on Damage Rate
In the current paper, the damage function was established based on data for
continuous mite population growth. Interruptions by pesticide applications might
change the damage dynamics. Number and timing of sprays to control mites has not
been considered in this research and needs to be further studied.
Standardized Survey Method
A standardized survey method is currently not recommended to citrus growers.
For example, two people may talk about percent infested lens field, but their actual
lens view area may be different. A detailed study is necessary to relate results from
different survey methods to actual mite population density per cm2. This would
greatly improve the efficiency of information exchange among growers, and speed up
the process of technology transfer from research to extension to producers.

177
APPENDIX
RELATION BETWEEN VOLUME AND PERCENT DIAMETER GROWTH
If we assume D(t) = fruit diameter at time t; D(0) = fruit diameter at time
zero; then cumulative % diameter growth is F (xt)=--*^ > so
Growth^ > £(0)
D(xj) = D(t¿)( 1 + FGrowü)' ^ieref°re fruit volume at time t is
The fruit volume growth rate is
fGrowthV ~ ^Kro) *(1 Growth)1 * *fGrowth

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BIOGRAPHICAL SKETCH
Yubin Yang was bom on July 21, 1962, to Mr. and Mrs. Shanjian Yang of
Hunan Province, People’s Republic of China. He graduated from DongYueGuan
High School in 1979. In August, 1983, he received the Bachelor of Science degree in
forest pest management from Nanjing Forestry University. He then entered
Guangdong Entomological Institute as a graduate student, where he worked on
integrated management of citrus pests. He graduated in the summer of 1986 with a
Master of Arts degree in entomology. He continued to work on citrus pest
management in the same Institute until January 1991, when he began his doctoral
studies at the University of Florida with an emphasis in population dynamics and
citrus integrated pest management.
192

I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of Philosophy.
/fon\C. Allen, Chair
I Associate Professor of Entomology
^a«a Nematology
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of Philosophy.
Jrofessor of Entomology and
Nematology
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of Philosophy.
l C-brA/i
Harvey L. Ciomroy
Professor of^Entomology andj
Nematology
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of Philosophy.

I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of Philosophy.
1A.
ámes E. Lloyd
Professor of Entomology and
Nematology
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of Philosophy.
Philip A. Stansly
Associate Professor of Entor
and Nematology
This dissertation was submitted to the Graduate Faculty of the College of
Agriculture and to the Graduate School and was accepted as partial fulfillment of the
requirements for the degree of Doctor of Philosophy.
August 1994
tty
Dean, College of Agriculture
Dean, Graduate School

LD
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. y^cZ5
UNIVERSITY OF FLORIDA
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