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)
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xviii, 192 leaves : ill. ; 29 cm.
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English
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Yang, Yubin, 1962-
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bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

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

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University of Florida
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oclc - 33038031
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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).