Citation
Development and validation of a growth model for Florida-grown soybeans with disease stress

Material Information

Title:
Development and validation of a growth model for Florida-grown soybeans with disease stress
Creator:
Johnson, Steven Boyd, 1955-
Publication Date:
Language:
English
Physical Description:
xii, 152 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Dissertations, Academic -- Plant Pathology -- UF
Plant Pathology thesis Ph. D
Soybean -- Diseases and pests -- Mathematical models ( lcsh )
Soybean -- Growth -- Mathematical models ( lcsh )
City of Gainesville ( local )
Soybeans ( jstor )
Diseases ( jstor )
Pathogens ( jstor )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1982.
Bibliography:
Includes bibliographical references (leaves 143-150).
Additional Physical Form:
Also available online.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Steven Boyd Johnson.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
028557823 ( ALEPH )
09309165 ( OCLC )

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Full Text













DEVELOPMENT AND VALIDATION OF A GROWTH MODEL FOR
FLORIDA-GROWN SOYBEANS WITH DISEASE STRESS










BY

STEVEN BOYD JOHNSON





















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



UNIVERSITY OF FLORIDA

1982















ACKNOWLEDGMENTS



I wish to acknowledge the assistance of Dr. Richard D. Berger, major advisor for the studies and for the dissertation, who unselfishly contributed incalculable hours in these capacities. His dedication to science, his critical and independent thinking, and his approach to problems have earned my deepest respect. Special recognition for general assistance throughout the program of study and for critically reading and offering valuable suggestions on this dissertation is in order for the remainder of my supervisory committee: Drs. T. E. Freeman, H. H. Luke, and S. H. West. I would also like to recognize all the persons, too numerous to mention by name, that have in some way contributed to the completion of this dissertation. I also wish to acknowledge my wife, Jennifer, for she was the true sufferer through the long hours of the studies and preparation of the dissertation. The work was supported by funds from EPA grant no. CR-806277-020-0 and research funds from Dr. Berger.














TABLE OF CONTENTS



LIST OF TABLES ........................ o..o ............ ev

LIST OF FIGURES ............... o .......... o ........... vii

LIST OF ABBREVIATIONS ............. o ........... o ... o ... ix

ABSTRACT- ............................................ x

GENERAL INTRODUCTION ................................... 1

LITERATURE SURVEY ...................................... 4

I. DEVELOPMENT OF THE MODEL ......................... 8

A.) Introduction ..................................... 8

B.) Materials and Methods ............................ 9

1.) Field Plots, 1980 ............................. 12

2.) Field Plots, 1981 ............................. 12

C.) Results ......................................... 13

1.) Field Plots, 1980 ............................. 13

2.) Field Plots, 1981 ............................. 16

D.) Discussion ...................................... 28

1.) Field Plots, 1980 ............................. 28

2.) Field Plots, 1981 ............................. 35

Ii. DESCRIPTION OF THE MODEL ........................ 40

A.) Introduction .................................... 40

B.) Materials and Methods ........................... 41

C.) Results ......................................... 43

D.) Discussion ...................................... 58



iii










III. VALIDATION AND VERIFICATION OF THE MODEL ........ 67 A.) Introduction .................................... 67

B.) Materials and Methods ........................... 68

C.) Results ......................................... 82

D.) Discussion ... ......... e ...... ao.eo ....... oo.o..85

IV. APPLICATIONS FOR THE MODEL ...................... 94

A.) Introduction .................................... 94

B.) Uses For The Model .............................. 96

1.) Foliar Pathogens ... .... e .......... oo.**.* .... 96

2.) Above-ground Non-foliar Pathogens ............. 98

3.) Soil-borne Pathogens .......................... 103

4.) Foliage-feeding Insects ...................... 106

5.) Seed-feeding Insects ......................... 111

C.) Results ........................................ 115

D.) Discussion ............ ... .................... 117

SUMMARY*..* .......................................... 121

APPENDICES ........................................... 123

A: FUNGICIDES USED ................................ 123

B: EQUIPMENT USED ................................. 124

C: LEAF-AREA, DISEASE- AND INSECT-RATING SCALES...125 D: MATERIALS USED ................................. 142

LITERATURE CITED ..................................... 143

BIOGRAPHICAL SKETCH .................................. 151










iv















LIST OF TABLES



1. Soybean seed yields from plots, 1980 ............. 14

2. Dry-matter yields from individually harvested
soybean plants, 1980 ............................. 15

3. Pod and stem quality ratings from
individually harvested soybean plants, 1980 ...... 17 4. Soybean seed infection from plots, 1980 .......... 18

5. Soybean seed infection from individually
harvested plants, 1980 ........................... 19

6. Soybean seed yields from plots, 1981 ............. 20

7. Dry-matter yields from individually
harvested soybean plants, 1981 ................... 22

8. Dry-matter yields from individually harvested
soybean plants (analyzed with
block three removed), 1981 ....................... 23

9. Pod and stem quality ratings from individually
harvested soybean plants, 1981 ................... 25

10. Soybean seed infection from plots, 1981 .......... 26

11. Soybean seed infection from individually
harvested plants, 1981 ........................... 27

12. Soybean seed yields from
separate experiment, 1981 ........................ 29

13. Soybean pod and stem quality
ratings from separate experiment, 1981 ........... 30

14. Soybean seed infection from
separate experiment, 1981 ........................ 31

15. Harvested above-ground plant dry matter
proportioned into seeds, stems, and pods for
two soybean cultivars, 1981 ...................... 83



V









16. Published values, model predictions, and
1980 and 1981 raw data for the same parameters ... 84

17. Harvested, above-ground soybean-plant dry-matter
proportioned into seeds, stems, and pods
for two seasons .................................. 86

18. Final plant dry-matter ratios for two
soybean cultivars, 1981 .......................... 89















































Vi















LIST OF FIGURES



1. The dry-matter accumulation for soybean
leaves of known area over time ................... 45

2. The dry-matter accumulation for soybean
stems over time .................................. 47

3. The dry-matter accumulation for soybean
seeds over time ................ ................. 49

4. The dry-matter accumulation for soybean
pods over time ............. 0.0 ................... 51

5. The dry-matter accumulation for soybean
petioles over time ............................... 53

6. The dry-matter accumulation for soybean
leaves over time ................................. 55

7. The dry-matter accumulation for entire
soybean plants over time ......................... 57

8. Flow chart of the soybean growth model
(N = number of days; 0 = rate of change) ......... 61

9. The dry-matter accumulation for soybean leaves,
converted from leaf area (Fig. 1),
from individually harvested
plants over time, 1980 ........................... 63

10. The dry-matter accumulation for soybean leaves,
converted from leaf area (Fig. 1),
from individually harvested
plants over time, 1981 ........................... 65

11. Model-predicted versus actual dry-matter
accumulation for seeds, 1980 ..................... 70

12. Model-predicted versus actual dry-matter
accumulation for stems, 1980 ..................... 72

13. Model-predicted versus actual dry-matter
accumulation for pods, 1980 ...................... 74



Vii










14. Model-predicted versus actual dry-matter
accumulation for seeds, 1981...................... 76

15. Model-predicted versus actual dry-matter
accumulation for stems, 1981....................... 78

16. Model-predicted versus actual dry-matter
accumulation for pods, 1981 ....... .. .. .......... 80

17. Incorporation of a foliar-disease submodel
into the soybean growth model (Fig. 8) .......... 100

18. Incorporation of an above-ground, non-foliar
disease submodel into the soybean growth
model (Fig. 8) ............................. 105

19. Incorporation of a soil-borne disease
submodel into the soybean growth


20. Incorporation of a foliage-feeding insect
submodel into the soybean growth
model (Fig. 8)........ ................. . .. ......110

21. Incorporation of a seed-feeding insect
submodel into the soybean growth
model (Fig. 8)..................................... 114






























viii
















LIST OF ABBREVIATIONS



in base e (natural) logarithm

log base 10 logarithm m slope of linear regression equations

R coefficient of determination

r correlation coefficient

Yo initial disease

Ymax maximum disease level

* multiplication

** exponentation

exp base of natural logarithm k epidemic rate for Gompertz transformation

b (-ln{Yo}) in Gompertz transformation

t time

P probability level

LSD least significant difference LAI leaf area index g gram

ha hectare

1 liter










ix















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


DEVELOPMENT AND VALIDATION OF A GROWTH MODEL FOR
FLORIDA-GROWN SOYBEANS WITH DISEASE STRESS By

Steven Boyd Johnson

December, 1982

Chairman: Dr. Richard D. Berger Major Department: Plant Pathology


Holistic field experiments with soybean were conducted over two growing seasons, in which fungicides were applied to achieve various disease intensities. The experiments were monitored at weekly intervals from planting through harvest. Each week, the disease

intensity of five different foliar diseases, the insect damage, and the area of each individual leaf were measured from representative plants. The above-ground portion of the plants, which had been measured through the growing season, were harvested for dry-matter yields. The experiments continued after harvest when the pathogen presence in the seed from the individually monitored plants and in the seed from the plots was determined.



x










A narrow range of disease intensities resulted from the application of the fungicides and, consequently, yield differences were nonsignificant. However, quality of the soybean pods and stems from the individually monitored plants were significantly improved with the application of a fungicide.

A regression-derived soybean growth model was developed from the holistic field experiments. The

model was driven by the dry-matter accumulation of soybean leaves over time. Separate equations which described the dry-matter accumulation of soybean stems, pods, petioles, and seeds were developed and related to the leaf dry-matter accumulation equation by ratios, updated with each time step.

Model validation was performed with measurements taken from holistic field experiments conducted over two growing seasons. The measurements were independent of the measurements used to develop the model. Disease intensities were too low over both growing seasons for a true yield difference to be realized from the fungicide applications.

Model verification was performed with published values. Dry-matter ratios and slopes of dry-matter accumulation for soybean organs, as described by the model, were comparable with published values.





Xi










Theoretical submodels were developed for foliar

pathogens, above-ground non-foliar pathogens,

foliage-feeding insects, and seed-feeding insects. Possible applications for the model are to develop disease intensity yield loss relationships and threshold levels of disease-induced loss.














































xii















I. GENERAL INTRODUCTION



The soybean (Glycine max (L.) Merrill), an annual plant, is included in the kingdom Planta, phylum Tracheophyta, class Angiospermae, order Rosales, family Leguminosae, and is one of the oldest cultivated crops. The geographic adaptability, high oil content, and high nutritive value of the pressed seed mash have placed the soybean into prominence in United States agriculture. Since 1954, the United States has been one of the world's largest producer of soybeans.

Throughout the geographical distribution of the

soybean, diseases reduce yield quality and quantity.

The most prevalent fungal diseases of soybean in Florida are purple stain (Cercospora kikuchii Matsumoto & Tomoyasu), frogeye leaf spot (Cercospora sojina Hara.), downy mildew (Peronospora manshurica (Naoum.) Syd. ex Gaum.), target spot (Corynespora cassiicola (Berk. and Curt.) Wei.), Rhizoctonia blight (Rhizoctonia solani

Kuehn), anthracnose (Colletotrichum truncatum (Schw.) Andrus and W. D. Moore), and pod and stem blight

(Phomopsis sojae Leh. {Diaporthe sojae Leh.}) {10, 18, 75}. Diseases which cause yield reduction and plant defoliation in other soybean growing regions are not



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present (rust QhakUsora pachyrhizi Sydow)) or not prevalent in some portions of Florida (brown spot

(Septoria glycines Remmi.1). The devastation of soybean in areas of the world by diseases, some presently in Florida, necessitates the establishment of disease

intensity-yield loss relationships.

The relationship between foliar diseases and yield of soybeans has not been characterized. One approach to determine the disease intensity-yield loss relationship would be to measure the host growth without stress (diseases, insects, drought, poor nutrition) and concurrently subject other host plants to various levels of stress and measure the resulting change in yield.

Both the host growth and stress components can be described mathematically. The host growth model, with

and without the stress factors, would need validation and verification to prove its applicability for decision processes in soybean crop management. In the case of this project, the controlled stress factors were diseases. In the growth model, leaf area could be

mathematically removed to simulate stress. The influence of disease on yield can be examined by removing leaf area from fungicide-treated plants equivalent to the disease levels on non-treated plants.

The approach of modeling will help field projects become more efficient, or at least can help direct






3



investigations toward aspects of the pathosystem which need clarification.

Any model is the simplified representation of a system. The soybean growth model developed with disease stress, described here, does not cover all aspects of plant growth, but that was not its intended purpose. The purpose of this new model was to be a beginning framework for a disease intensity yield loss model. Further model refinements could incorporate pathogen response to environmental conditions and growth of systemic, non-foliar pathogens.

Data were analyzed on an Amdahl 470 V6 and an IBM 3033N at the facilities of the Northeast Regional Data Center of the State University System of Florida, and on an APPLE II Plus microcomputer (48 K memory); all computers were located on the University of Florida campus, Gainesville, Florida.















II. LITERATURE SURVEY



Morse (62), in reviewing the ancient history of the soybean, claimed that the first written record of the soybean was 2838 B. C. It was not until around 1900

that commercial soybean acreage became established in the United States. At that time, the soybean acreage was grown mainly for forage. As late as 1934, only 25% of the soybean acreage in the United States was harvested for seed. By 1941, more soybean acreage was harvested for seed than for forage. Today, the soybean acreage grown for forage in the United States is minimal.

A model is a simplified representation of a system. A system is a collection of components and their interrelationships. A model, therefore, represents a collection of components, or more often a component and its inputs and outputs. A model which covers all

aspects of crop growth defeats its purpose. Such a model would be too large to solve detailed problems which arise under field conditions. The simpler the model is, while retaining accuracy, the more effective the model becomes. Simple models are easier to evaluate critically, and easier to apply to wide ranges of



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conditions. A model can be used to predict the system response to various changes in inputs, without going to the actual system. The usefulness of models for

research programs, whether for identification of problems or solving problems, cannot be overstated.

Modeling of systems dates back as far as records were kept, and yet is as current as today. Development of maps, models of land or water masses, continuing through the development of laws of physics, modeling the effect of gravity, etc., to today's high-speed digital-computer simulations of biochemical processes, are examples of models. Likewise, soybeans are one of the world's oldest cultivated crops, yet today are under intensive investigation to increase yields. Soybeans, like modeling, can be viewed as rich in tradition and yet extremely modern.

Soybeans as a crop and modeling as a science started to converge with the interest of agricultural scientists in yield maximization. Early modelers of

soybean growth were concerned with production of soybeans as a forage source, and the effect of defoliation (cattle grazing) on leaf, stem, and seed yield (26). The maximization of the entire soybean plant was investigated in this work, because the soybean was grown as a forage source. Interest shifted from modeling the injury from grazing to modeling the injury






6



from hail (25, 85). More recently, insect damage (9, 34, 80, 81) and disease damage (43) have been modeled. McAlister and Krober (46) approached the situation differently; they measured the yield changes and the changes in the biochemical components of the soybean plant parts in response to artificial defoliation. The recent soybean modeling work has focused on seed yield maximization, as soybean production is now almost exclusively a seed crop. Soybean workers have investigated several diseases and their relation to yield loss (17, 36, 40, 41, 86). At present, the models are, at best, restricted to a particular location for a particular season. A flexible model for soybean growth which would give loss estimates from diseases does not exist. None of the models for soybean disease loss have been incorporated into growth models.

Paralleling the interest in defoliation yield loss relationships for soybeans were those of other crops. Chester (13) published an article on the nature of artificial defoliation experiments to provide a basis for disease-loss estimates. Chester drew from studies

involving wheat, corn, oats, barley, and onion. Disease-loss, hail-loss, or insect-loss estimates are the goal of the models which focused on seed-yield maximization. While the relationship for defoliation level yield reduction in soybean were under






7



development, new research needs surfaced. Quantitative descriptions of dry-matter accumulation for yield components were required for soybean models dealing with plant growth. From the 1960's and continuing through

today, mathematical models of dry-matter accumulation for soybean have been published. Shibles and Weber (72, 73) were pioneers in these studies, establishing that soybean plant dry-matter accumulation was proportional to leaf area. The early work by Shibles and Weber has been further documented by numerous workers (8, 20, 21, 22, 28, 29, 31, 71). The linear relationship between the dry-matter accumulation for entire soybean plants versus time has been documented (28, 31, 71). The linear relationship for the dry-matter accumulation for the seed versus time (8, 20, 21, 28) has also been described. The development of quantitative descriptions of dry-matter accumulation for soybean yield components provided the data for soybean modeling.

In modeling efforts, the soybean is a relatively new crop, when compared to potatoes or cereals. To date, soybean models, especially soybean disease models, are lacking the sophistication and accuracy of those of potato and cereal crops. Much progress on modeling of the soybean has been made in the last twenty years, and with the ever-increasing importance of the soybean as a crop, progress toward maximization of soybean yields will continue to be made.













III. DEVELOPMENT OF THE MODEL



A.) Introduction



Holistic experiments were conducted in 1980, and repeated during the 1981 growing season. The experiments were designed to follow the host growth during the season and to observe the development and progress of all foliar-disease epidemics. On selected plants, all leaves were regularly examined for disease incidence and severity and for leaf area. All measurements were made by nondestructive methods. Fungicides were applied frequently, or not at all, to provide a range of diseases and disease intensities. Frequent fungicide applications were aimed at providing as complete disease control as possible. Some plots were left untreated by fungicides to allow disease epidemics to progress without man-made interference. For both growing seasons, the plots were located within a 2 hectare soybean field, with approximately 4 to 6 additional hectares of soybeans grown in close proximity. Soybeans had been grown continuously in the general area for over 10 years, assuring some presence of inoculum for diseases commonly occurring in Florida.



8






9



The growth model was derived from host

measurements. Disease intensity measurements over time

provide an account of disease progress, which could be converted into a disease model. The separation of host and disease is a useful approach for the determination of economic threshold levels for diseases. Mathematical separation of host and disease could be accomplished by mathematically increasing the disease intensity in the disease model and removing the increased amounts of diseased tissue from the total host tissue.



B.) Materials and Methods



The soybean breeding line F76-4486 was chosen for the experiments. The breeding line is susceptible to

some foliar diseases and is an F5 line from the cross Centennial x (Forrest x {Cobb x D68-2161) (K. Hinson, personal communication); the cultivar Foster (F76-8827) is a sibling to the chosen breeding line. The experimental fields were located on the University of Florida campus, Gainesville, Florida. The plots were arranged in a randomized-complete-block design, with five replications of fungicide treatments. The

fungicide treatments were benomyl, benomyl plus

metalaxyl, metalaxyl, and an untreated check (Appendix A). The plots were four 6.1-meter long rows with






10



0.91-meter row spacing and were seeded at the rate of 39 seeds/meter. The center two rows were used as multiple observations from each experimental unit. This allowed for testing of block by treatment interaction. The field was fertilized and an insecticide applied as

recommended for the crop (2). Benomyl was applied (586.5 g/ha) at 14-day intervals; metalaxyl was applied (1137 g/ha) at 40-day intervals. All fungicide applications were made over the top of the canopy with a hand-held, two-row, six-nozzle, boom sprayer delivering the equivalent of 396 ls/ha at 276 kilopascals (Appendix B). Frequent fungicide applications were used to

provide optimal disease control. Metalaxyl and benomyl were chosen because their selectivity of action would provide a difference in disease severity and intensity in the plots. Metalaxyl was chosen to control downy

mildew. Benomyl was chosen to control other diseases, primarily pod and stem blight, anthracnose, frogeye leaf spot, and purple stain.

In each of the center two rows of a plot, plants were randomly selected and labeled. Starting three weeks from date of sowing, weekly measurements of leaf area and disease incidence and severity were recorded for each leaf of the labeled plants. Leaf emergence, leaf senescence, insect damage, and growth stage (23, 24) also were recorded weekly. For each leaf, the






11



disease and insect damage was expressed as a percent of leaf area for that leaf. All measurements were comparisons against leaf-area diagrams and insect- and disease-rating scales developed for soybeans (Appendix C). Total photosynthetic area of the leaves was

calculated by subtracting the senescent, insect-damaged, and diseased area from total leaf area.

At maturity, each of the labeled plants was harvested. The dry weights for pods, seeds, and stems were measured from each plant. The disease severity on the stems and pods from these plants was rated on a scale from 0 to 10. The rating scale consisted of 11 evenly spaced ratings with a rating of 0 for 0% of the pods or main stem covered with symptoms or signs of pathogens; and a rating of 10 for 100% of the pods or main stem covered with symptoms or signs of pathogens. Because the visual ratings had a binomial distribution, an angular transformation (arcsine (disease

proportion)**{1/2)) was used where the ratings of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 were equivalent to 0, 2.5 10, 21, 35, 50, 65, 79, 90, 97.5, 100%, respectively (42). Seeds from the labeled, individually harvested plants were surface sterilized in a 10% Clorox (Appendix D) solution for one minute and plated onto acidified potato dextrose agar (Appendix D) and observed within seven days for presence of seed-borne fungal pathogens. After






12



the labeled plants were individually harvested, the center 4.88 meters of the center two rows were harvested for seed yield.



1.) Field Plots. 1980



The field was planted on 27 June and harvested 125 days later on 4 November. Benomyl was first applied 4 July, and sunsequent applications were made every 14 days through harvest. Metalaxyl was first applied 30 June, and sunsequent applications were made every 40 days through harvest. Leaf area and disease intensity data were collected from five plants in each of the center two plot rows.



2.) Field Plots, 1981



The field was planted on 15 June and harvested 124 days later on 16 October. Benomyl was first applied 22 June, and sunsequent applications were made every 14 days through harvest. Metalaxyl was first applied 22 June, and sunsequent applications were made every 40 days through harvest. Leaf area and disease intensity data were collected from two plants in each of the center two plot rows.






13



In a separate experiment, the soybean breeding line F76-884b was planted on the University of Florida campus, Gainesville, Florida. The separate experiment was conducted to ascertain if the scheme of benomyl application affected the disease severity or yield. The treatments were arranged in a randomized-complete-block design with five replications of benomyl (586.5 glha) applied i) at planting, ii) at 11 and 13 weeks from planting, iii) at planting and at 11 and 13 weeks from planting, iv) or not at all. The plots, fungicide applications, and harvested plant matter were treated as described above.



C.) Results



1.) Field Plots, 1980



The block by treatment interaction was

nonsignificant (P=0.23) for all measured variables; so the plots were treated as an entity, not as two individual rows. The seed yields from the plots were

not significantly different among the treatments (Table 1). Dry weight yields from the labeled, individually harvested plants were not significantly different among treatments (Table 2) when viewed as entities (P=0.38) or when separated into seeds (P=0.39), stems (P=0.35), and






14





Table 1. Soybean seed yields from plots, 1980.




Treatmenty Seed yield
g/plot kg/ha

Benomyl + z
metalaxyl 2676 3200

Benomyl 2564 3067

Metalaxyl 2128 2545

Check 2393 2862

Duncan-Waller
k-ratio (k=100)
LSD NS



YBenomyl was applied at the rate of 586.5 g/ha at 14-day intervals from 27 June 1980 to 4 November 1980. Metalaxyl was applied at the rate of 1137 g/ha at 40-day intervals from 27 June 1980 to 4 November 1980. Check plots received no treatment. ZMean of five plots.






15





Table 2. Dry-matter yields from individually harvested soybean plants, 1980.




TreatmenJ Yield/plant (g)Z
Total Partitioned
Pods Stems Seeds

Benomyl +

metalaxyl 22.10 4.21 6.98 10.91

Benomyl 19.20 3.59 5.86 9.75

Metalaxyl 20.54 3.96 6.92 9.66

Check 16.40 3.08 5.57 7.75

Duncan-Waller
k-ratio (k=100)
LSD NS NS NS NS



YBenomyl was applied at the rate of 586.5 g/ha at 14-day intervals from 27 June 1980 to 4 November 1980. Metalaxyl was applied at the rate of 1137 g/ha at 40-day intervals from 27 June 1980 to 4 November 1980. Check plots received no treatment.
z
Mean of 50 plants.






16



pods (P=0.42). The quality of the stems and pods from

the labeled, individually harvested plants, as

determined by visual rating, varied significantly in response to the treatments. Treatments of benomyl and benomyl plus metalaxyl had significantly better disease control on pods (P=0.0001) and stems (P=0.0001) than did treatments without benomyl (Table 3). Individually

harvested plants from the benomyl treatment had the lowest percent seed infection (5%) and the untreated check had the highest percent seed infection (15%) (Table 4). The ratios of the percent seed infection caused by Fusarium spp., Phmo..pis spp., and C. kikuchii were similar across the treatments. This was also true when the seed from the individually harvested plants were plated (Table 5).



2.) Field Plots, 1981



The block by treatment interaction was

nonsignificant (P=0.25) for the seed yield from the Plots, so plots were treated as an entity, not as two individual rows (Table 6). A significant block by treatment interaction was present- for the dry-weight yields of the labeled, individually harvested plants when separated into seeds (P=0.04), pods (P=0.04), or when the dry weights of the seeds, pods, and stems were






17





Table 3. Pod and stem quality ratings from individually harvested soybean plants, 1980.



Treatments RatingY
Pod Stem

Benomyl +
metalaxyl 2z 4

Benomyl 2 4

Metalaxyl 7 8

Check 7 8

Duncan-Waller
k-ratio (k=100)
LSD 1 1

x
Benomyl was applied at the rate of 586.5 g/ha at 14-day intervals from 27 June 1980 to 4 November 1980. Metalaxyl was applied at the rate of 1137 g/ha at 40-day intervals from 27 June 1980 to 4 November 1980. Check plots received no treatment.

YRated on a scale of 0 to 10 and transformed with an angular transformation (arcsine (disease proportion)**{1/2}) where the ratings of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 were equivelent to 0, 2.5 10, 21, 35, 50, 65, 79, 90, 97.5, 100%, respectively (42). z Mean of 50 plants.






18





Table 4. Soybean seed infection from plots, 1980.

v W
Treatment x Per ent seed infection
T F P C 0

Benomyl plus z
metalyxl 07 82 08 02 08

Benomyl 21 60 07 02 31

Metalaxyl 05 48 20 28 04

Check 05 78 06 06 11


VBenomyl was applied at the rate of 586.5 g/ha at 14-day intervals from 27 June 1980 to 4 November 1980. Metalaxyl was applied at the rate of 1137 g/ha at 40-day intervals from 27 June 1980 to 4 November 1980. Check plots received no treatment. W Seven hundred seed plated onto acidified potato dextrose agar and observed 3 to 5 days later. XT=total seed infection.

YTotal seed infection partitioned into specific pathogens: F=Fusarium spp.; P=Phomopsis spp.; C=Cercospora kikuchii; O=Others, primarily Rhizoctonia spp. and Colletotrichum spp. ZRound off error present.





19






Table 5. Soybean seed infection from individually harvested plants, 1980.


Treatment Peycent seed infection
T F P C 0

Benomyl plus
metalyxl 10 67 12 12 09

Benomyl 05 66 17 17 00

Metalaxyl 08 60 20 20 00

Check 15 69 20 11 00


Benomyl was applied at the rate of 586.5 g/ha at 14-day intervals from 27 June 1980 to 4 November 1980. Metalaxyl was applied at the rate of 1137 g/ha at 40-day intervals from 27 June 1980 to 4 November 1980. Check plots received no treatment. XFour hundred seed plated onto acidified potato dextrose agar and observed 3 to 5 days later. T=total seed infection.
ZTotal seed infection partitioned into specific pathogens: F=Fusarium spp.; P=Phomopsis spp.; C=Cercospora kikuchii; O=Others, primarily Rhizoctonia spp. and Colletotrichum spp.





20






Table 6. Soybean seed yields from plots, 1981.



Treatment Seed yieldy
g/plot kg/ha

Benomyl + z
metalaxyl 1071 1281

Benomyl 898 1074

Metalaxyl 771 922

Check 1002 1198

Duncan-Waller
k-ratio (k=100)
LSD 197


xBenomyl was applied at the rate of 586.5 g/ha at 14-day intervals from 22 June 1981 to 16 October 1981. Metalaxyl was applied at the rate of 1137 g/ha at 40-day intervals from 22 June 1981 to 16 October 1981. Check plots received no treatment. YMean of five plots. zRoundoff error present.
Round-off error present.






21



summed (P=0.07); a significant block by treatment interaction was absent for the dry weight of stems (P=0.36). Much of the block by treatment interaction was attributable to block 3 (Table 7). With block 3 removed from the calculations (taking a mean of the remaining four blocks), block by treatment interactions were nonsignificant for dry-weight yields of the labeled, individually harvested plants when separated into seeds (P-0.19), pods (P=0.16), stems (P=0.59), or when the dry weights of the seeds, pods, and stems were summed (P=0.26). With blocks 1, 2, 4, and 5 summed, there were significant differences in the labeled, individually harvested plants when separated into stems (P=0.02), pods (P=0.02), and seeds (P=0.03), or when summed (P=0.02); the nonsignificant block by treatment interaction was used as an error term for these tests (Table 8). The visible quality of the stems and pods from the labeled, individually harvested plants varied significantly in response to treatments. Block by treatment interaction was nonsignificant for visual ratings of quality for pods (P=0.27) and stems (P=0.81). Treatments with benomyl (benomyl alone, and benomyl plus metalaxyl) had significantly less (P=0.0001) symptoms and signs of pathogens than did treatments without benomyl (metalaxyl alone, and check), when the

nonsignificant block by treatment interaction was used






22





Table 7. Dry-matter yields from individually harvested soybean plants, 1981.


Portion Yield/plant (g)WX
Block
1 2 3 4 5

Pods MYl4.65az M 1.88a B 4.37 M 13.55a M 7.93
O 9.82 b 0 9.25ab C 3.92 B 5.16 b B 6.98 C 3.61 c B 6.30 b M 3.91 C 4.77 b C 4.99 B 3.53 c C 5.76 b 0 3.32 0 4.28 b 0 4.75
NS NS


Seeds M 32.43a M 26.14a B 9.86 M 29.74a M 17.45
0 22.79 b 0 21.42ab 0 8.27 B 12.70 b B 16.12 B 8.83 c B 15.85 bc C 7.89 C 10.39 b C 11.94 C 8.53 c C 13.20 c M 6.40 0 9.58 b 0 11.55 NS NS


Stems M 15.63a M 13.32a B 5.50 M 16.02a M 11.14
0 11.39 b 0 12.45a C 4.91 C 7.49 b B 9.69 B 5.98 c B 8.37 b M 4.70 0 6.24 b C 8.23 C 5.57 c C 8.14 b 0 4.52 B 5.83 b 0 7.91 NS NS


Total M 62.71a M 51.34a B 19.73 M 59.31a M 36.52
0 44.00 b 0 43.12ab C 16.72 B 23.68 b B 32.79 B 18.34 c B 30.52 b 0 16.11 C 22.65 b C 25.16 C 17.70 c C 27.10 c M 15.00 0 20.09 b 0 24.20 NS NS
WRoundoff error present.

XMean of four plants.

YBzbenomyl-treated plants; Mfimetalaxyl-treated plants; Ofbenomyl plus metalaxyl-treated plants; Cfcheck plants. Benomyl was applied at the rate of 586.5 g/ha at 14-day intervals from 22 June 1981 to 16 October 1981. Metalaxyl was applied at the rate of 1137 g/ha at 40-day intervals from 22 June 1981 to 16 October 1981. Check plots received no treatment. ZNumbers in the same column, within a row, followed by
the same letter are not significantly different according to Duncan's new multiple range test (P=0.05).






23





Table 8. Dry-matter yields from individually harvested soybean plants (analyzed with block three removed), 1981.



Treatment Yield/plot (g)X
Total Partitioned
Pods Stems Seeds

Benomyl +

metalaxyl 32.85ayz 7.03a 9.50a 16.34a

Benomyl 26.33a 5.49a 7.47a 13.38a

Metalaxyl 52.47 b 12.03 b 14.03 b 26.44 b

Check 23.15a 4.78a 7.36a 11.02a


WBenomyl was applied at the rate of 586.5 g/ha at 14-day intervals from 22 June 1981 to 16 October 1981. Metalaxyl was applied at the rate of 1137 g/ha at 40-day intervals from 22 June 1981 to 16 October 1981. Check plots received no treatment. XMean of 16 plants.

YNumbers within a column followed by the same letter are not significantly different according to Duncan's New Multiple Range Test (P=0.05). ZRoundoff error present.






24



as an error term (Table 9). Seed infection from the individually harvested plants was low. The most likely reason for the low infection levels would be the weather conditions (57-61) which were highly unfavorable for pathogen development. The same soybean line was used in 1980 and 1981 and the plots were located about 100 meters from where the 1980 plots had been planted; so inoculum present during 1981 should have been similar to that of 1980. A range of 6% in seed infection levels was present (Table 10). Viewed differently,

benomyl-treated versus non-benomyl-treated, the

percentages of seed infection were 3% versus 4%. True differences would be expressed in this comparison. Another test to determine if random infection existed would be to compare the percent of seed infection from metalaxyl-treated (benomyl plus metalaxyl, and metalaxyl alone) versus non-metalaxyl-treated (benomyl alone, and check) plants, 3% versus 3% in this case. The percent of infected seed from the individually harvested plants (Table 11) was similar to that from the plots. The low level of infection present in 1981 precluded meaningful analysis.

In the separate experiment on the time of application of benomyl, the block by treatment interaction was significant (P=0.03) for the seed yield; so the seed yield was analyzed separately for each block






25





Table 9. Pod and stem quality ratings from individually harvested soybean plants, 1981.



Treatment Rat ingxy
Pod Stem

Benomyl +

metalaxyl laz la

Benomyl la la

Metalaxyl 2 b 7 b

Check 2 b 7 b

WBenomyl was applied at the rate of 586.5 g/ha at 14-day intervals from 22 June 1981 to 16 October 1981. Metalaxyl was applied at the rate of 1137 g/ha at 40-day intervals from 22 June 1981 to 16 October 1981. Check plots received no treatment. XMean of 20 plants.

YRated on a scale of 0 to 10 and transformed with an angular transformation (arcsine (disease proportion)**{I/2}) where the ratings of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 were equivelent to 0, 2.5 10, 21, 35, 50, 65, 79, 90, 97.5, 100%, respectively (42). z Numbers followed by the same letter are not significantly different according to Duncan's New Multiple Range Test (P=0.05).






26





Table 10. Soybean seed infection from plots, 1981.



Treatment y Pecent seed infectionx
T F P C 0

Benomyl plus
metalyxl 02 64 27 09 00

Benomyl 03 31 62 07 00

Metalaxyl 04 32 26 37 05

Check 02 00 88 12 00


w
Benomyl was applied at the rate of 586.5 g/ha at 14-day intervals from 22 June 1981 to 16 October 1981. Metalaxyl was applied at the rate of 1137 g/ha at 40-day intervals from 22 June 1981 to 16 October 1981. Check plots received no treatment. xFive hundred seed plated onto acidified potato dextrose agar and observed 3 to 5 days later. YT=total seed infection. ZTotal seed infection partitioned into specific pathogens: F=Fusarium spp.; P=Phomopsis spp.; C=Cercospora kikuchii; O=Others, primarily Rhizoctonia spp.






27





Table 11. Soybean seed infection from individually harvested plants, 1981.

w x
Treatment Pecent eed infection
T F P C

Benomyl plus
metalyxl 02 50 00 50

Benomyl 03 50 50 00

Metalaxyl 01 100 00 00

Check 07 00 67 33


W
Benomyl was applied at the rate of 586.5 g/ha at 14-day intervals from 22 June 1981 to 16 October 1981. Metalaxyl was applied at the rate of 1137 g/ha at 40-day intervals from 22 June 1981 to 16 October 1981. Check plots received no treatment. xOne hundred seed plated onto acidified potato dextrose agar and observed 3 to 5 days later. YT=total seed infection. Total seed infection partitioned into specific pathogens: F=Fusarium spp.; P=Phomopsis spp.; C=Cercospora kikuchii.






28



(Table 12). The block by treatment interaction was

nonsignificant for the visual ratings of the pods

(P=0.62) and stems (P=0.70); so the plots were treated as an entity, not as two individual rows. Plots treated with benomyl at weeks 11 and 13 yielded significantly higher quality pods (P=0.0004) and stems (P=0.0001) than those plots treated at planting only or not treated at all; data are presented in Table 13. Seed from the harvested rows were plated as described, and results appear in Table 14. The low level of seed infection

prevented meaningful analysis.



D.) Discussion



1.) Field Plots, 1980



The foliar diseases observed were purple stain, frogeye leaf spot, downy mildew, target spot, and

Rhizoctonia blight. The actual amount of foliar disease on individual plants ranged from less than 0.01% to 10.0%. The 10% disease severity was approached

immediately prior to final leaf drop.

Throughout the growing season, few individual leaves reached a 10% disease level; generally, senescence would occur and the leaf would be removed from the canopy. It was not possible to partition the






29






Table 12. Soybean seed yields from separate experiment, 1981.



Benomyl 1
application ~ Yield/plot (g)
Block
1 2 3 4 5


Planting 801 b z1243a 815 1113a 1154
Planting,
weeks 11&13 1154a 999 b 877 807 b 1224

Weeks 11&13 798 b 836 b 956 lOO2ab 1083

Check 1203a 778 b 727 lO5lab 1242

NS NS



YBenomyl was applied at the rate of 586.5 g/ha; the field was planted on 15 June 1981. Check plots received no treatment.

zNumbers within the same column followed by the same letter are not significantly different according to Duncan's new multiple range test (P=0.05).






30





Table 13. Soybean pod and stem quality ratings from separate experiment, 1981.



Benomyl w x
application Rating
Pod Stem


Planting 2 ayz 5 b

Planting,
weeks 1l&13 1 b 2 c

Weeks 11&13 1 b 2 c

Check 3 a 7 a


wBenomyl was applied at the rate of 586.5 g/ha; the field was planted on 15 June 1981. Check plots received no treatment.
x
Mean of 10 ratings. YNumbers within the same column followed by the same letter are not significantly different according to Duncan's new multiple range test (P=0.05).
z
Roundoff error present.






31





Table 14. Soybean seed infection from separate experiment, 1981.



Benomyl1
application Percent seed infection
T Fz P C


Planting 03 54 23 23
Planting, weeks
11 and 13 05 55 35 10

Weeks 11 and 13 03 71 29 00

Check 03 50 29 21



Benomyl was applied at the rate of 586.5 g/ha; the field was planted on 15 June 1981. Check plots received no treatment.
XFive hundred seed plated onto acidified potato dextrose agar and observed 3 to 5 days later. YT=total seed infection. ZTotal seed infection partitioned into specific pathogens: F=Fusarium spp.; P=Phomopsis spp.; C=Cercospora kikuchii.






32



senescent leaf area into disease-induced senescence and normal senescence. The low levels of foliar disease

present throughout the growing season could have been a direct result of the dry environmental conditions (51-56) and may have been the reason why seed yields from the plots were not significantly different when the Duncan-Waller k-ratio (k=100) LSD test was used. All yields were high -- about 3000 kg per hectare. Plant-portion dry weights, partitioned into pods, stems, and seeds, or combined as whole plants, were not significantly different among treatments. The nonsignificant differences in the dry weights were expected when seed yields from the plots were not significantly different. High variability present in

plants grown under field conditions may partially account for the nonsignificant differences among weights of plants from the treatments. The weight differences were not large enough to be significantly different at P=0.05, probably because of low disease levels.

The weather conditions for the 1980 growing season (51-56) were not excessively conducive to spread of foliar diseases. Foliar diseases did not cause

appreciable plant stress, and neither did water deficiency during the growing season. Overhead irrigation was applied three times during the growing season. The timing of the irrigation applications






33



undoubtedly was not optimal, as soil tensiometers were not used. No irrigation management scheme was followed, so it would be improper to conclude that irrigation was applied to produce optimal yields or favor disease spread. The foliar disease levels ranged from less than 0.01% to 1.0% throughout most of the growing season and the nonsignificant differences in seed yield of plots as a result of fungicide treatments were expected.

The lack of a yield response as a result of disease control manifested itself in soybean fungicide trials conducted by others during the season (5, 19, 65, 66, 67, 83). In some reports, foliar disease levels were

not significantly different (P=0.05) for frogeye leaf spot (65, 67), purple stain (66), or for pod discoloration (66). Pod discoloration (67), purple stain (67), and frogeye leaf spot (66) levels were significantly different (P=0.05) for other tests. No significant (P=0.05) yield response as a result of fungicide treatment was present across most fungicide trials during that year. Plots with treatments which controlled diseases generally yielded better than those plots which did not have a fungicide treatment, although not always significantly (P=0.05). The general trend observed was the highest control of foliar disease provided the highest yield of plant mass. I also

observed the same trend of highest yield associated with






34



greater control of disease.

The seed yields were not significantly different among the treatments. Treatments which received benomyl produced stems and pods with significantly fewer signs and symptoms of pathogens than did treatments without benomyl. Low levels of disease were present during the growing season but highly significant differences in the presence of symptoms and signs of pathogens on the stem and seed were present. The low disease levels during the growing season resulted in low seed-infection levels. Had more disease been present, the range of the percent infected seed may have been wider than 10% between seed from untreated-check plants and seed from fungicide-protected plants. Seed from the individually harvested plants of different treatments was infected by fungi to varing degrees. Fungicide application reduced the percentage of seed infection, but did not reduce the relative importance of the pathogenic fungi. Fusarium spp. was responsible for about 65% of the seed infection, PhomRosis spp. for about 17%, and C. kikuchii for about 15%, irrespective of the treatment. Plants which received a benomyl treatment, with or without metalaxyl, had 8% seed infection, compared to 12% for seeds from plants which had not received a benomyl treatment. The majority of pathogens cultured from the surface-sterilized seeds were inhibited by the presence






35



of benomyl, but the low numbers of infected seeds precluded meaningful analyses; benomyl treatments had 4% lower seed infection than non-benomyl treatments, but this was considered inconsequential. Seed from plants which received a metalaxyl treatment (with or without benomyl) had 9% infection compared to 10% for seeds from plants which had not received a metalaxyl treatment. These values should be similar, because in each case,

half of the plots received benomyl and half did not. Metalaxyl, specific-acting toward Pythiacious fungi, had no effect on Fusarium spp., Phomopsis spp., or C.

kikuchii. Metalaxyl-treated plants would not be

expected to have reduced seed infection when compared to the untreated plants because P. manshurica will not grow on acidified potato dextrose agar. Seed pathogens

occurred at similar ratios, irrespective of the treatment. Pathogen escapes would be expected to occur at similar frequencies to pathogens present in seeds from the untreated-check plants.



2.) Field Plots, 1981



Seed yields from the metalaxyl-treated plots were significantly less (k=100) than from the

benomyl-treated, benomyl plus metalaxyl-treated, or the untreated-check plots. Yields were quite low -- about






36



11 quintals per hectare, or 38% of the 1980 plot seed yield. No yield response to applications of benomyl was present in other fungicide trials during that year (63, 70, 87).

Plants from block three were not similar to plants from the rest of the blocks. No logical explanation for block three being completely different from the remaining blocks was evident from field observation. The block did not have uneven stress of water, insect, nutritional, or disease. It is possible that block

three accurately described the metalaxyl-treated plants and the remainder of blocks did not. When the majority of the block by treatment interaction was removed (Table 8), the metalaxyl-treated plants were significantly (P-0.05) larger than all the rest of the plants. It is my feeling that the selected individual plants from the metalaxyl-treated plots did not reflect the true

population. Metalaxyl-treated plots produced the lowest seed yield, but the selected plants produced the highest yields. With the exception of the metalaxyl-treated plants, there were no significant (P-0.05) differences present in the entire, individually harvested plants, or when the plants were separated into pods, seeds, and stems. These results, with the exception of the

metalaxyl-treated plants, were similar to 1980 results of no significant (P=0.05) differences between plants,






37



or the plant parts among treatments (Table 2). Possibly, the sample size (four) from each of the 1981 season experimental plots was inadequate to describe the population accurately.

Again in 1981, benomyl-treated plants, with or without metalaxyl, had significantly (P=0.05) fewer symptoms and signs of pathogens than plants which had not received a benomyl treatment. Seed infection levels were low in 1981. The extremely dry weather was undoubtedly the reason for the unusually healthy seed. The seed infection levels for the individually harvested plants ranged from 2% to 4% and from 1% to 7% for the plots (Tables 10, 11). Pathogen ratios, as occurred in 1980 (Tables 4, 5), would not be expected to occur. Small changes in raw numbers drastically change ratios when the values are less than 5%.

In the separate experiment, selected applications of benomyl improved pod and stem quality over that of the controls. Yields were low, and there were no consistant significant differences among the treatments. However, pod and stem quality was significantly improved with the application of benomyl. Applications around flowering (weeks 11 and 13) provided significantly better protection against the presence of disease symptoms and signs of the pathogen than application at planting or than no application at all. Flowering






38



triggers drastic physiological changes in the soybean plant. It is possible that the period of flowering is when the pathogens, already present in the soybean plant, proliferate throughout the stem. If this hypothesis is correct, it would explain why the benomyl treatments at 11 and 13 weeks significantly improved stem and pod quality. An experiment specifically

designed to investigate the growth of systemic plant pathogens would have to be undertaken before any generalizations could be drawn.

The block by treatment interaction present in the seed yields from the separate experiment can not be well explained. No pattern of one treatment producing higher seed yield was present. The conclusion from this study, under the conditions of that year (57-61), would be that benomyl treatments did not increase yield. The

recommended benomyl treatment (2) was for applications to be made at 11 and 13 weeks from planting. This treatment did not produce increased yields. Benomyl applications during years unfavorable for pathogens did not increase seed yields (Tables 1, 6, 12), but did significantly improve stem and pod quality (Tables 3, 9, 13). It would seem logical to conclude that seed infection would also be reduced with benomyl applications and result in higher stem and pod quality, but more disease than was present for these years would






39



be needed for verification. Possibly, under more disease than existed in 1980 and 1981, benomyl

treatments would also improve seed yield.















IV. DESCRIPTION OF THE MODEL



A.) Introduction



Growth models exist for crops (11, 14, 15, 35, 50, 76, 88), specific aspects of crop growth (4, 16, 35, 77), or crop pest interactions (6, 11, 12, 17, 38, 44, 45, 47, 48, 61, 68, 69, 74, 81, 82). The models vary in sophistication, accuracy, purpose, and applicability. Growth models for soybean exist (15, 33, 50, 84, 88), but applying the models to investigate disease threshold levels and the disease intensity yield loss relationship would be outside the scope of the intended application of these models. Problems arise when a model is used for an application for which it was not intended.

The soybean plant growth model developed from this work was specifically designed to evaluate disease threshold levels and the disease intensity yield loss relationship.

The ex post facto approach was used for this model for a number of reasons. The model was designed to be exceedingly simple -- a set of regression equations. The approach would permit easy changes from year to year



40






41



and would have wide applicability among locations.

Regression analysis is ideally suited to the ex 2 st fact approach, and large data sets can be handled efficiently. The presence of large data sets, along with the use of regression analysis (32) to construct a continuous function from discrete points of a quantitative variable, facilitated the choice of this mathematical technique for the model.

A continuous mathematical function to describe the biological nature of the crop or crop pest interaction was not considered for the basic model. Holistic

experiments contain numerous uncontrolled and unmeasured variables. Water stress, nematode infestation of soil, soil-borne insects, and nutritional stress would be included in the unmeasured variables. It is imperative that these variables be included in a

biological-function model.



B.) Materials and Methods



During 1981, whole-plant samples were collected for 16 weeks, starting three weeks from the date of planting and continuing through harvest (124 days from planting) from a soybean field planted to breeding line F76-8846. The disease damage and insect damage were expressed as percent of total leaf area for each leaf. All






42



measurements were comparisons against leaf-area diagrams and insect- and disease-rating scales developed for soybeans (Appendix E). On each sampling date, the above-ground plant was separated into stems, leaves, petioles, pods, and seeds. The plant parts were dried and weighed. The relationship between leaf area and

leaf dry weight was determined from these plants. A separate regression equation was developed for each dependent variable; time was used as the quantitative independent variable, with up to 15 degrees of freedom available for the regression equation.

The equation which described the leaf dry-matter accumulation over time was used to drive the model. The separate regression equations which described dry-matter accumulation by pods, stems, seeds, and petioles at each day, were related mathematically to the equation which described dry-matter accumulation by leaves alone. The relationship was strictly a ratio. The ratios of stems : leaves, seeds : leaves, pods : leaves, and petioles : leaves were established for each day of the model. The equation which described leaf dry-matter accumulation over time produced stems, seeds, pods, and petioles, varying in dry-matter accumulation proportional to leaf dry-matter accumulation. Problems associated with mathematical descriptions of biological data were handled as they arose. Dry matter of the plant organs





43



was not permitted to be negative, it was set to zero when this condition occurred. No dry weight was accumulated for seven days after planting. This time period was reserved for seed germination and seedling emergence.



-C.) Results



The linear relationship between leaf area and leaf dry-matter (Fig. 1) was highly correlated (r- 0.97). The dry-matter accumulation of stems over time was also well (r=0.89) described by a straight line (Fig. 2). The dry-matter accumulation of seeds over time was described by a cubic equation with an associated r = 0.94 (Fig. 3). The dry-matter accumulation of pods over time was described by a quadratic equation with an r 0.89 (Fig. 4). The dry-matter accumulation over time of petioles and leaves was described by separate cubic equations with r = 0.87 for petiole (Fig. 5) and r = 0.89 for leaf dry-matter accumulation over time (Fig. 6). The dry-matter accumulation for whole plants over time is presented in Fig. 7, where a linear equation with an r = 0.89 described the response. Values of r = 0.48, 0.61, 0.72 corresponded to P = 0.05, 0.01, 0.001 for 15 degrees of freedom (42).




























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58



Figures 2 through 7 represent the positive dry-matter accumulation over time and associated coefficients of determination for soybean plant organs. When a mathematical equation described negative dry-matter accumulation, the dry matter was set to zero. The model had a flexible harvest date, determined by the progression of leaf dry-matter accumulation, but generally was run 123 or fewer days from sowing.



D.) Discussion



To have a soybean model driven by leaf dry-matter accumulation over time seems a reasonable approach, as leaves produce photosynthate to fill pods and seeds and to grow stems and petioles. Shibles and Weber (72, 73) have reported soybean dry-matter accumulation was proportional to leaf area. The proportionality of

dry-matter accumulation to leaf area is not unique to soybeans. Allen and Scott (1) described a linear relationship between dry-matter accumulation in potato and interception of solar radiation; interception of solar radiation was proportional to leaf area. Peanut canopies under various disease and insect stresses had a linear leaf area to leaf dry-weight relationship; LAI values from the work ranged from 0.32 to 3.55 (9).






59



The described model is not intended to be an all-encompassing model, as others have attempted (50). The regression equations are not intended to be viewed as stimulus response situations. The flow chart for this model (Fig. 8) is simple and readily adaptable compared to SOYMOD (50) or SIMED (35). Changes in the regression coefficients, or in the regression equations, can describe different soybean varieties, different locations, or different years (Figs. 9, 10). This

flexibility is desirable in the basic framework of a model.

The time reserved for seedling emergence can be easily changed to more or less than seven days. This parameter would be location dependent. The seven day's for seedling emergence for northern Florida climatic conditions was adequate. The model could be refined to have the time required for seedling emergence linked to soil temperature and moisture or planting date. This refinement would be better than setting the time as a fixed value. Plant dry weight was not permitted to be

negative, as a negative measurement of dry weight is biologically meaningless. The regression equations were continuous with respect to the time variable. This, along with the equations not intending to describe a biologic phenomenon but to explain a phenomenon, can lead to negative values. Time was continuous in the

















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66



equations and days were integers in the model; dry weight can increase from 0.0 g to 0.03 g or higher in one day. Linear extrapolation to zero was performed on the four days previous to measurable dry-weight appearance (and disappearance) to smooth out the curve. The adjustment did not affect the performance of the model; the model-derived curves more closely represented the biology of the system. The model was set to run 123 days from planting. The time duration was set by the equation describing the leaf dry-weight accumulation; the soybean fields under intensive study for two consecutive seasons were harvested 123 and 124 days after sowing.

The correlation coefficients and the coefficients of determination were not 1.00 for any of the regression equations. The field data may be biased, which would produce a less-than-perfect fit. The field data may not be accurate or may not accurately represent the actual plants, again introducing bias. Random variation, a

common obstacle with field data, likely accounts for most of the variation. Had the correlation coefficients been less than 0.80 or the coefficients of determination less than 0.60, some concern as to whether- the regression equations accurately described the field data might be warranted. The data were well fitted by the

presented equations (Figures 1 7).















V. VALIDATION AND VERIFICATION OF THE MODEL



A.) Introduction



Validation is a continuing process; a model is really never finished, it can always be improved, adjusted, and expanded. Validation is the application of the model to conditions different from those under which the model was developed. The different conditions can range from different plants to different hosts, depending on the type of model. Validation data for this model are from different plants of the same cultivar, different growing seasons, and different soybean cultivars. The soybean cultivar, soil type, general cultural practices (fertilization, insect control, disease control, cultivation) remained unchanged between the two seasons. Host growth differences (Figs. 9, 10; Tables 2, 7), seed yield

differences (Tables 1, 6), differences in disease

intensity (Tables 3, 9), and incidence (Tables 4, 5, 10, 11) can be crudely attributed to weather conditions (51-61).

Far more validation data than appear here are needed to discern which specific parameter(s) are



67






68



responsible for yield and disease differences. This type of further refinement could take many, many growing seasons to substantiate.

Verification must be performed on the model. Verification assures the model properly mimics the biological system under one set of conditions, namely, the set of conditions under which it was developed. Further model verification with published data from literature is useful. Often, published data are the

sole source for physiologically-based models. Because of the nature of this model, published data did not aid in the development or adjustment of the model, they only verify that data used to develop and validate the model were similar to published data.



B.) Materials and Methods



The soybean growth model was validated with 200 data sets from 1980 and 80 data sets from 1981; all 280 data sets were independent of the data set used to develop the model, but were the same soybean cultivar. The validation data sets consisted of nondestructive leaf-area measurements throughout the growing season and final measurements of dry weight for above-ground plant parts. The final measurements were destructive. Leaf area was converted to leaf dry matter (Fig. 1). Leaf



















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dry matter was regressed on time, with up to 15 degrees of freedom available for time, the independent variable. The resultant regression equation was used to drive the model (Fig. 8). The model predictions of final dry

weight of the plant portions were compared against the measured data (Figs. 11-16).

Weekly nondestructive measurements of leaf area and disease incidence and severity were recorded for each leaf of five randomly selected soybean plants, variety Cobb, and five randomly selected soybean plants, variety Bragg. The plants were grown under overhead irrigation, with a water management scheme directed toward zero water stress (L. Hammond, personal communication). At maturity, the individual plants were harvested and the dry-weights for pods, seeds, and stems were measured.

The accuracy of the model was verified with published data (43, 72, 73, 78, 79). Published

regression parameters and agronomic values such as slope of dry-matter accumulation of plant portions, dry-weight ratios between plant portions, and dry-matter accumulation for the plant parts were compared against model predictions.






82



C. ) Results



Validation data of model-predicted versus actual yield of stems, pods, and seeds for 1980 are presented in Figs 11-13. Model-predicted versus actual yield for 1981 appear in Figs. 14-16. Not all growth simulations were ceased on the same day. Since the plants were harvested at 123 or 124 days from planting, theoretically, the growth simulations should cease on the same day.

Final plant-portion dry-weight ratios for Cobb and Bragg soybean varieties, grown under an intensive overhead irrigation scheme, are presented in Table 15.

Generally in the literature, instead of the profile of an entire growing season, sections of the growth curve for plant organs were analyzed where their growth was linear. The seed dry-matter accumulation was analyzed after 83 days from planting, where a linear equation accurately fitted the data. When my data were treated similarly, analyzing from day 83 through day 123, the slope coefficient for the simulated data was 0.42, for the raw data was 0.45, and was 0.41 (Table 16) for the published data (28). The pod dry-matter accumulation over time also could be described by a linear equation, when 77 days from planting through harvest were analyzed. When my data were treated






83





Table 15. Harvested above-ground plant dry matter proportioned into seeds, stems, and pods for two soybean cultivars, 1981.



Soybean cultivar Plant portion (%) z
Seeds Stems Pods



Bragg 52 33 15

Cobb 53 34 13

ZMean of three plants.






84





Table 16. Published values, model predictions, and 1980 and 1981 raw data for the same parameters.




Whole-plant Parameter Published Simulated Raw 1980 1981


Seedz
dry-matter accumulation (g/day) 0.41-0.47 0.42 0.45

Podsz
dry-matter accumulation (g/day) 0.19 0.11 0.11

Seed:Pod dry-matter ratios 2.47-2.63:1 2.56:1 2.27:1

Seed:stem dry-matter ratios 1.53-1.59:1 1.50:1 1.66:1


YAfter day 86. ZAfter day 77.






85



similarly (analyzing 77 days from planting through day 123, harvest), my slope coefficient for the simulated and the raw data was 0.11, compared to 0.19 for the published value (28). The final ratio of seedpod dry-matter for 1980 was 2.56:1. Published values range from 2.47:1 to 2.63:1 (Table 16) for commercially-grown soybean varieties in the United States (22, 28,); the 1981 seedpod dry-matter ratio was 2.27:1. The final ratio of seed:stem dry-matter for 1980 was 1.50:1, compared to published ratios of 1.53:1 to 1.59:1 for commercially-grown soybean varieties (28); in 1981, the ratio was 1.66:1 (Table 16). The 1980 to 1981 variations in final plant dry-matter ratios were reflected in the proportions of plant dry-matter ratios. For 1980 and 1981, 49% of the final-plant dry-matter by weight was seeds, 19% was pods in 1980 compared to 22% in 1981; 32% was stems in 1980 compared to 29% in 1981 (Table 17). The higher percentage of pods and lower percentage of stems in 1981 were reflected in a lower seedpod dry-matter ratio and a higher seed:stem

dry-matter ratio.



D.) Discussion



The model predictions of final dry matter for seeds (Figs. 11, 14), pods (Figs. 12, 15), and stems (Figs.






86





Table 17. Harvested, above-ground, soybean plant dry-matter proportioned into seeds, stems, and pods for two seasons.




Season Plant portion M%
Seeds Stems Pods



1.980Y 49 32 19

1981lz 49 29 22


YMean of 200 plants. Zmean of 80 plants.






87



13, 16) were well within a reasonable range, especially considering cumulative error. The leaf area to leaf dry-matter equation had 94% of the variation in the data explained by the linear relationship (Fig. 1), leaving 6% as unexplained error. A linear relationship between leaf area and leaf dry matter for soybeans (39) and for alfalfa (64) has been published. Likewise, the stem, pod, and leaf dry-matter accumulation equations have 79% of the variation in the data explained (Figs. 2, 4, 6), leaving 21% of the variation as unexplained error. The seed dry-matter accumulation had 88% of the variation explained by the relationship (Fig. 3), leaving 12% as unexplained error. Thus the model-predicted dry-matter accumulation for seeds starts with 18% (6% + 12%) absolute error. The model-predicted pod and stem dry-matter accumulation starts with 27% (6% + 21%) absolute error, and have whatever portion of the

unexplained error the leaf area equations conta in in addition. Clearly, one can rapidly increase the error to over 100%. The error mentioned is absolute error. The 27% error could be as low as 15% if the 6% leaf area to leaf dry-matter accumulation error cancels a portion of the 21% error of the pod or stem dry-matter accumulation. The leaf area equation (Figs. 9, 10) added to this could possibly cancel the 21% completely, or add completely to it. Obviously, the cumulative






88



error must be followed, but no cause effect

relationship can be assessed to the cumulative error.

The final plant-portion dry-matter ratios from Cobb and Bragg soybean cultivars (Table 16) were similar to the ratios obtained from plants used in model

verification (Table 17). In view of this evidence, using ratios, updated daily, to produce growth of stems, seeds, and pods in the model is a reasonable approach. The seed:stem dry-matter ratio for Cobb and Bragg soybean cultivars (Table 18) was very similar to the ratios obtained for a different soybean cultivar grown under different conditions (Table 16), and also similar to published ratios of totally different soybean cultivars (28). The seed:pod ratio from the Cobb and

Bragg soybean cultivars (Table 18) were much higher than published ratios (22, 28) or the ratios from another soybean cultivar (Table 16) grown under a less intensive water management scheme. Again, the pod dry-matter accumulation, as discussed earlier, may be more

sensitive to environmental changes, which includes water, than are the seeds or the stems.

The slopes from the linear equations describing the seed dry-matter accumulated (Table 16) for the

simulation and published data (28) were similar (0.42, 0.41), but the Y-intercepts were not (0.43, 1.61). 1 interpret the Y-intercept to be location dependent,




Full Text
LIST OF FIGURES
1. The dry-matter accumulation for soybean
leaves of known area over time 45
2. The dry-matter accumulation for soybean
stems over time 47
3. The dry-matter accumulation for soybean
seeds over time 49
4. The dry-matter accumulation for soybean
pods over time 51
5. The dry-matter accumulation for soybean
petioles over time 53
6. The dry-matter accumulation for soybean
leaves over time 55
7. The dry-matter accumulation for entire
soybean plants over time 57
8. Flow chart of the soybean growth model
(N = number of days; 0 = rate of change) 61
9. The dry-matter accumulation for soybean leaves,
converted from leaf area (Fig. 1),
from individually harvested
plants over time, 1980 63
10. The dry-matter accumulation for soybean leaves,
converted from leaf area (Fig. 1),
from individually harvested
plants over time, 1981 65
11. Model-predicted versus actual dry-matter
accumulation for seeds, 1 980 70
12. Model-predicted versus actual dry-matter
accumulation for stems, 1 980 72
13. Model-predicted versus actual dry-matter
accumulation for pods, 1980 74
vii


61
END


23
Table 8
soybean
1981 .
Dry-matter yields from individually harvested
plants (analyzed with block three removed),
w
Treatment
Yield/plot (g)
Total Partitioned
Pods Stems Seeds
Benomyl +
meta 1axy1
Benomy1
Metalaxy1
Check
32.85ayz 7.03a 9.50a 16.34a
26.33a 5.49a 7.47a 13.38a
52.47 b 12.03 b 14.03 b 26.44 b
23.15a 4.78a 7.36a 11.02a
WBenomyl was applied at the rate of 586.5 g/ha at 14-day
intervals from 22 June 1981 to 16 October 1981.
Metalaxyl was applied at the rate of 1137 g/ha at 40-day
intervals from 22 June 1981 to 16 October 1981. Check
plots received no treatment.
x
Mean of 16 plants.
y
Numbers within a column followed by the same letter are
not significantly different according to Duncan's New
Multiple Range Test (P=0.05).
z
Roundoff error present.


126


LEAF AREA


39
be needed for verification. Possibly
disease than existed in 1980 and
treatments would also improve seed yield.
, under more
1981, benomy1


W)


150
87. Whitney, N. G. 1982. Evaluation of fungicides for
soybean disease control, 1981. Fungcide and Nematacide
Tests 37:107-108.
88. Wilkerson, G.
Ingram, K. T., and
soybean growth for
press) .
G., Jones, J. W., Boote, K. J.,
Mishoe, J. W. 1982. Modeling
crop management. Trans. ASAE (in
V


117
D ) Discussion
Any of the proposed submodels can be linked to the
soybean growth model mathematically by either
subtraction or multiplication. This ease of application
makes the model and submodels attractive for a basic
framework. The disease severity was not high enough to
test the foliar disease submodel or to determine injury
threshold levels. There are published reports involving
defoliation levels and yield reductions (9, 13, 17, 25,
26, 34, 36, 37, 40, 41, 43, 46, 80, 81, 85, 86). Many
of the reports involve non-pathogen-induced defoliation
and consequent yield reduction (9, 25, 26, 34, 46, 80,
81). The studies on defoliation and yield reduction
lacked adequate spacing of treatments and lacked
accurate quantitation of defoliation levels (9, 25, 26,
34, 46, 80, 81). The unfortunate results of these
shortcomings in experimental design are that these data
cannot be
used to
test
or modify the foliar
disease
submode 1,
and
the
threshold level
for
defoliation-
induced
loss
cannot be extracted
. As
previously mentioned, the threshold level for loss from
disease cannot be extracted from my work, owing to
inadequate disease. As previously mentioned, a
threshold level for disease has not been considered in


32
senescent leaf area into disease-induced senescence and
normal senescence. The low levels of foliar disease
present throughout the growing season could have been a
direct result of the dry environmental conditions
(51-56) and may have been the reason why seed yields
from the plots were not significantly different when the
Duncan-Waller k-ratio (k=100) LSD test was used. All
yields were
high -- about 3000
kg per hectare.
Plant-port ion
dry weight s,
partitioned
into pods stems,
and seeds ,
or combined
as whole
plant s, were
not
signif icantly
different
among
treatment s.
The
nonsignificant
differences
in the
dry weights
were
expected when
seed yields
from the
plots were
not
significantly different. High variability present in
plants grown under field conditions may partially
account for the nonsignificant differences among weights
of plants from the treatments. The weight differences
were not large enough to be significantly different at
P=0.05, probably because of low disease levels.
The weather conditions for the 1980 growing season
(51-56) were not excessively conducive to spread of
foliar diseases. Foliar diseases did not cause
appreciable plant stress, and neither did water
deficiency during the growing season. Overhead
irrigation was applied three times during the growing
season. The timing of the irrigation applications


Fig. 5 .
The dry-matter accumulation for soybean petioles over time.


26
Table 10. Soybean seed infection from plots, 1981.
w
Treatment
T7
Pej cen t
F
seed
P
infectionx
C
0
Benomyl plus
metalyxl
02
64
27
09
00
Benomy1
03
31
62
07
00
Metalaxyl
04
32
26
37
05
Check
02
00
88
12
00
w
Benomyl was applied at the rate of 586.5 g/ha at 14-day
intervals from 22 June 1981 to 16 October 1981.
Metalaxyl was applied at the rate of 1137 g/ha at 40-day
intervals from 22 June 1981 to 16 October 1981. Check
plots received no treatment.
X
Five hundred seed plated onto acidified potato dextrose
agar and observed 3 to 5 days later.
y
T=total seed infection.
2
Total seed infection partitioned into specific
pathogens: F=Fusarium spp.; P=Phomopsis spp.;
C = Cercospora kikuchii; 0 = 0thers, primarily Rhizoctonia
spp.


Fig. 13.
Model-predicted versus actual dry-matter accumulation for pods, 1980


144
A new model to measure yield losses caused by stem rust
in spring wheat. Minn. Exp. Sta. Tech. Bull. 307. 23
PP
12. Castor, L. L., Ayers, J. E., MacNab, A. A., and
Krause, R. A. 1975. Computerized forcasting system for
Stewart's bacterial disease on corn. Plant Dis. Rep.
59 : 533-536 .
13. Chester, K. S. 1945. Defoliation and crop loss.
Plant Dis. Rep. 29:162-168.
14. Curry, R. B. 1971. Dynamic simulation of plant
growth I. Development of a model. Trans. ASAE
14:945-949,959.
15. Curry, R. B., Baker, C. H., and Streeter, J. G.
1975. SOYMOD I: A dynamic simulator of soybean growth
and development. Trans. ASAE 18:963-968,974.
16. Curry, R. B., and Chen, L. H. 1971. Dynamic
simulation of plant growth part II. Incorporation of
actual daily weather and partitioning of net
photosynthsate. Trans. ASAE 14:1170-1174.
17. Dunleavy, J. M. 1980. Yield loss in soybeans
induced by powdery mildew. Plant Disease 64:291-292.
18. Dunleavy, J. M., Chamberlain, D. W., and Ross, J.
P. 1966. Soybean diseases. U.S. Dept. Agrie. Handb.
302. 38 pp.
19. Edwards, N. C., and Sciumbato, G. L. 19*82.
Evaluation of fungicides on soybeans, 1980. Fungicide
and Nematacide Tests 37:104.
20. Egli, D. B. 1975. Rate of accumulation of dry
weight in seed of soybeans and its relationship to
yield. Can. J. Plant Sci. 55:215-219.
21. Egli, D. B., and Leggett, J. E. 1976. Rate of dry
matter accumulation in soybean seeds with varing
source-sink ratios. Agron. J. 68:371-374.
22. Egli, D. B., Leggett, J. E., and Duncan, W. G.
1978. Influence of N stress on leaf senescence and N
redistribution in soybeans. Agron. J. 70:43-47.
23. Fehr, W. R., and Caviness, C. E. 1980. Stages of
soybean development. Iowa St. Univ. Spec. Rep. 80. 11
PP


LIST OF TABLES
1. Soybean seed yields from plots, 1980 14
2. Dry-matter yields from individually harvested
soybean plants, 1980 15
3. Pod and stem quality ratings from
individually harvested soybean plants, 1980 17
4. Soybean seed infection from plots, 1980 .... 18
5. Soybean seed infection from individually
harvested plants, 1980 19
6. Soybean seed yields from plots, 1981 20
7. Dry-matter yields from individually
harvested soybean plants, 1981 22
8. Dry-matter yields from individually harvested
soybean plants (analyzed with
block three removed), 1981 23
9. Pod and stem quality ratings from individually
harvested soybean plants, 1981 25
10. Soybean seed infection from plots, 1981 26
11. Soybean seed infection from individually
harvested plants, 1981 27
12. Soybean seed yields from
separate experiment, 1981 29
13. Soybean pod and stem quality
ratings from separate experiment, 1981 30
14. Soybean seed infection from
separate experiment, 1981 31
15. Harvested above-ground plant dry matter
proportioned into seeds, stems, and pods for
two soybean cultivars, 1981 83
v


IV. DESCRIPTION OF THE MODEL
A.) Introduction
Growth models exist for crops (11, 14, 15, 35, 50,
76, 88), specific aspects of crop growth (4, 16, 35,
77), or crop pest interactions (6, 11, 12, 17, 38, 44,
45, 47, 48, 61, 68, 69, 74, 81, 82). The models vary in
sophistication, accuracy, purpose, and applicability.
Growth models for soybean exist (15, 33, 50, 84, 88),
but applying the models to investigate disease threshold
levels and the disease intensity yield loss
relationship would be outside the scope of the intended
application of these models. Problems arise when a
model is used for an application for which it was not
intended.
The soybean plant growth model developed from this
work was specifically designed to evaluate disease
threshold levels and the disease intensity yield loss
relationship.
The ^x post facto approach was used for this model
for a number of reasons. The model was designed to be
exceedingly simple -- a set of regression equations.
The approach would permit easy changes from year to year
40


57
TIME (days)


105
DRY MATTER


16
pods (P=0.42). The quality of the stems and pods from
the labeled, individually harvested plants, as
determined by visual rating, varied significantly in
response to the treatments. Treatments of benomyl and
benomyl plus metalaxyl had significantly better disease
control on pods (P=0.0001) and stems (P=0.0001) than did
treatments without benomyl (Table 3). Individually
harvested plants from the benomyl treatment had the
lowest percent seed infection (5%) and the untreated
check had the highest percent seed infection (15%)
{Table 4). The ratios of the percent seed infection
caused by F u s a r i um spp., Phomops i s spp., and C^. kikuchii
were similar across the treatments. This was also true
when the seed from the individually harvested plants
were plated (Table 5).
2.) Field Plots, 1981
The block by treatment interaction was
nonsignificant (P=0.25) for the seed yield from the
plots, so plots were treated as an entity, not as two
individual rows (Table 6). A significant block by
treatment interaction was present for the dry-weight
yields of the labeled, individually harvested plants
when separated into seeds (P=0.04), pods (P=0.04), or
when the dry weights of the seeds, pods, and stems were


DRY WEIGHT (g)
53
TIME (days)


Fig. 7. The dry-matter accumulation for entire soybean plants over time.


A narrow range of disease intensities resulted from
the application of the fungicides and, consequently,
yield differences were nonsignificant. However, quality
of the soybean pods and stems from the individually
monitored plants were significantly improved with the
application of a fungicide.
A regression-derived soybean growth model was
developed from the holistic field experiments. The
model was driven by the dry-matter accumulation of
soybean leaves over time. Separate equations which
described the dry-matter accumulation of soybean stems,
pods, petioles, and seeds were developed and related to
the leaf dry-matter accumulation equation by ratios,
updated with each time step.
Model validation was performed with measurements
taken from holistic field experiments conducted over two
growing seasons. The measurements were independent of
the measurements used to develop the model. Disease
intensities were too low over both growing seasons for a
true yield difference to be realized from the fungicide
applications .
Model verification was performed with published
values. Dry-matter ratios and slopes of dry-matter
accumulation for soybean organs, as described by the
model, were comparable with published values.
xi




III. DEVELOPMENT OF THE MODEL
A.) Introduction
Holistic experiments were conducted in 1980, and
repeated during the 1981 growing season. The
experiments were designed to follow the host growth
during the season and to observe the development and
progress of all foliar-disease epidemics. On selected
plants, all leaves were regularly examined for disease
incidence and severity and for leaf area. All
measurements were made by nondestructive methods.
Fungicides were applied frequently, or not at all, to
provide a range of diseases and disease intensities.
Frequent fungicide applications were aimed at providing
as complete disease control as possible. Some plots
were left untreated by fungicides to allow disease
epidemics to progress without man-made interference.
For both growing seasons, the plots were located within
a 2 hectare soybean field, with approximately 4 to 6
additional hectares of soybeans grown in close
proximity. Soybeans had been grown continuously in the
general area for over 10 years, assuring some presence
of inoculum for diseases commonly occurring in Florida.
8


18
Table 4. Soybean seed infection from plots, 1980.
v
Treatment
TX
Percent
Fy
seed
P
w
infection
C
0
Benomyl plus
me talyxl
07Z
82
08
02
08
Benomy1
21
60
07
02
31
Meta 1axy1
05
48
20
28
04
Check
05
78
06
06
11
vBenomyl was applied at the rate of 586.5 g/ha at 14-day
intervals from 27 June 1980 to 4 November 1980.
Metalaxyl was applied at the rate of 1137 g/ha at 40-day
intervals from 27 June 1980 to 4 November 1980. Check
plots received no treatment.
WSeven hundred seed plated onto acidified potato
dextrose agar and observed 3 to 5 days later.
T=total seed infection.
yTotal seed infection partitioned into specific
pathogens: F=Fusarium spp.; P = Phomopsis spp.;
C Cercospora kikuchii; 0 = 0thers, primarily Rhizoctonia
spp. and Colletotrichum spp.
z _
Round off error present.


93
lowering the seed proportion of final plant dry-matter
ratio would probably also cause the slope of the seed
dry-matter accumulation curve (from day 86 through
harvest) to be different from 0.42. The increased
proportion of final ratio of pods during 1981 (3%
increase over 1980) may account for the decreased slope
and increased Y-intercepts over the published values.


87
13, 16) were well within a reasonable range, especially
considering cumulative error. The leaf area to leaf
dry-matter equation had 94% of the variation in the data
explained by the linear relationship (Fig. 1), leaving
6% as unexplained error. A linear relationship between
leaf area and leaf dry matter for soybeans (39) and for
alfalfa (64) has been published. Likewise, the stem,
pod, and leaf dry-matter accumulation equations have 79%
of the variation in the data explained (Figs. 2, 4, 6),
leaving 21% of the variation as unexplained error. The
seed dry-matter accumulation had 88% of the variation
explained by the relationship (Fig. 3), leaving 12% as
unexplained error. Thus the model-predicted dry-matter
accumulation for
seeds
starts with
18% (6%
+
12%)
absolute
error.
The
model-predicted pod
and
stem
dry-matter
accumulation
starts with
27% (6%
+
21%)
absolute
error ,
and
have whatever
portion
of
the
unexplained error the leaf area equations contain in
addition. Clearly, one can rapidly increase the error
to over 100%. The error mentioned is absolute error.
The 27% error could be as low as 15% if the 6% leaf area
to leaf dry-matter accumulation error cancels a portion
of the 21% error of the pod or stem dry-matter
accumulation. The leaf area equation (Figs. 9, 10)
added to this could possibly cancel the 21% completely,
or add completely to it. Obviously, the cumulative




19
Table 5. Soybean seed infection from individually
harvested plants, 1980.
w
Treatment
y
Percent
seed
infectionX
Ty
F
P
C
0
Benomyl plus
metalyxl
10
67
12
12
09
Benomy1
05
66
17
17
00
Metalaxy1
08
60
20
20
00
Check
15
69
20
11
00
w
Benomyl was applied at the rate of
586 .5
g/ha at
14-day
intervals from
27
June
1980 to
4 November
1980 .
Metalaxyl was
applied
at the rate of 1137
g/ha at
40-day
intervals from
27
June
1980 to
4 November
1980 .
Check
plots received no treatment.
Four hundred seed plated onto acidified potato dextrose
agar and observed 3 to 5 days later.
y
T=total seed infection.
2
Total seed infection partitioned into specific
pathogens: F=Fusarium spp.; P = Phomopsis spp.;
C=Cercospora kikuchii; 0=0thers, primarily Rhizoctonia
spp. and Co 11 etotrichum spp.


122
The description and modeling of the physiology and
biochemistry of disease development, plant development,
and disease plant interactions must start with
holistic experiments designed to determine the responses
of these interactions. I consider the models for
soybean growth and for disease intensity yield loss as
an initial step toward the development of more accurate
models. It is work on these models which I have
inititaed and have described here.


PREDICTED DRY MATTER (g)
76
ACTUAL
DRY MATTER
(g)


103
optimal ripeness that the seed was harvested would
accommodate this change. The incorporation of equations
2 and 3 into the flow chart of the soybean growth model
is presented in Fig. 18.
3.) Soil-borne Pathogens
Yield losses caused by soil-borne pathogens would
be difficult to incorporate into the present form of the
model. Soybean root growth was not used in the model.
Yield losses resulting from soil-borne diseases need to
be handled with a root submodel. A model of fusarium
root rot has been published (6, 7); a similar model
would be adequate for soybeans. In keeping with the ex
post facto nature of the model, root growth could be
incorporated in a way similar to the stems, pods, seeds,
and petioles. Ratios from published curves of
dry-matter accumulation for roots and leaves (50) could
be extracted, and added to the existing model. The root
model would not alone explain the pathogen root
system. In continuing this approach, attack by
soil-borne pathogens could be simulated using the Monte
Carlo method (27). Severe attack by, for instance,
Fusarium spp., kills the individual plant. The
percentage of plant-kill, determined by the severity of
soil infestation by Fusarium spp.,
could be removed from


Fig. 11. Mode1-predicted versus actual dry-matter accumulation for seeds, 1980.


14. Model-predicted versus actual dry-matter
accumulation for seeds, 1981 76
15. Model-predicted versus actual dry-matter
accumulation for stems, 1981 78
16. Mode1-predicted versus actual dry-matter
accumulation for pods, 1981 80
17. Incorporation of a foliar-disease submodel
into the soybean growth model (Fig. 8) 100
18. Incorporation of an above-ground, non-foliar
disease submodel into the soybean growth
model (Fig. 8) 105
19. Incorporation of a soil-borne disease
submodel into the soybean growth
model (Fig. 8) 108
20. Incorporation of a foliage-feeding insect
submodel into the soybean growth
model (Fig. 8) 110
21. Incorporation of a seed-feeding insect
submodel into the soybean growth
model (Fig 8 ) 114
viii


III. VALIDATION AND VERIFICATION OF THE MODEL 67
A.) Introduction 67
B.) Materials and Methods... 68
C.) Results 82
D.) Discussion 85
IV. APPLICATIONS FOR THE MODEL 94
A.) Introduction 94
B.) Uses For The Model 96
1.) Foliar Pathogens 96
2.) Above-ground Non-foliar Pathogens 98
3.) Soil-borne Pathogens 103
4.) Foliage-feeding Insects 106
5.) Seed-feeding Insects Ill
C.) Results 115
D.) Discussion 117
SUMMARY 121
APPENDICES 123
A: FUNGICIDES USED 123
B: EQUIPMENT USED 124
C: LEAF-AREA, DISEASE- AND INSECT-RATING SCALES...125
D: MATERIALS USED 142
LITERATURE CITED 143
BIOGRAPHICAL SKETCH 151
iv


116
rated on a scale of 0 to 10, the 1980 growing season
mean pod and stem quality rating was 3 for
benomy1-treated plots, and 8 (roundoff error present)
for non-benomy1-treated plots (Table 3). If the maximum
dry-matter loss to above-ground, non-foliar, plant
pathogens was 15%, there would be 7.3% more seed yield
lost in the non-benomy1-treated plots when compared to
benomy1-treated plots (7.3% = {1 ({3**3 / 10**3} *
.15)} {1 ({8**3 / 10**3} .15)}, roundoff error
present). Similarily, in 1981, there would be a 2%
increase in yield with mean pod and stem quality ratings
of 1 and 5 for benomyl-treated and non-benomy1-treated
plots (Table 9).
The quality of seed harvested is reduced,
proportional to the square of the mean pod and stem
quality rating (Eq. 3). Primarily, {Q} is a measure of
how appropriate the harvested seed would be for
planting. If the maximum quality loss from
above-ground, non-foliar, plant pathogens would be 20%,
there was a 11% reduction in quality in 1980 (11% = {1 -
({3**2 / 10**2} .20)} {1 ({8**2 / 10**2} .20)}).
Mean pod and stem ratings of 1 for benomyl-treated and 5
for non-benomy1-treated plots in 1981 (Table 9) would
reflect a 5% reduction in quality from the
non-benomy1-treated plots when compared to the
benomyl-treated plots.


LIST OF ABBREVIATIONS
In
base e (natural) logarithm
log
base 10 logarithm
m
slope of linear regression equations
R
coefficient of determination
r
correlation coefficient
Yo
initial disease
Ymax
maximum disease level
*
mult ip 1ica tion
**
exponentation
exp
base of natural logarithm
k
epidemic rate for Gompertz transformation
b
(-ln{Yo}) in Gompertz transformation
t
time
P
probability level
LSD
least significant difference
LAI
leaf area index
g
gram
ha
hectare
1
liter
ix


>
PREDICTED DRY MATTER (g)
00


Fig. 8. Flow chart of the soybean growth model (N = number of days; 0 rate of
change).


14
Table 1. Soybean seed yields from plots, 1980.
y
Treatment
Seed
g/plot
yield
kg/ha
Benomyl +
me t a 1axy1
2676Z
3200
B enomy1
2564
3067
Metalaxyl
2128
2545
Check
2393
2862
Duncan-Waller
k-ratio (k=100)
LSD
NS
^Benomyl was applied at the rate of 586.5 g/ha at 14-day
intervals from 27 June 1980 to 4 November 1980.
Metalaxyl was applied at the rate of 1137 g/ha at 40-day
intervals from 27 June 1980 to 4 November 1980. Check
plots received no treatment.
z
Mean of five plots.


6
from hail (25, 85). More recently, insect damage (9,
34, 80, 81) and disease damage (43) have been modeled.
McAlister and Krober (46) approached the situation
differently; they measured the yield changes and the
changes in the biochemical components of the soybean
plant parts in response to artificial defoliation. The
recent soybean modeling work has focused on seed yield
maximization, as soybean production is now almost
exclusively a seed crop. Soybean workers have
investigated several diseases and their relation to
yield loss (17, 36, 40, 41, 86). At present, the models
are, at best, restricted to a particular location for a
particular season. A flexible model for soybean growth
which would give loss estimates from diseases does not
exist. None of the models for soybean disease loss have
been incorporated into growth models.
Paralleling the interest in defoliation yield
loss relationships for soybeans were those of other
crops. Chester (13) published an article on the nature
of artificial defoliation experiments to provide a basis
for disease-loss estimates. Chester drew from studies
involving wheat, corn, oats, barley, and onion.
Disease-loss, hail-loss, or insect-loss estimates are
the goal of the models which focused on seed-yield
maximization. While the relationship for defoliation
level yield reduction in soybean were under


Fig. 18. Incorporation of an above-ground, non-foliar disease submodel into the
soybean growth model (Fig. 8).


66
equations and days were integers in the model; dry
weight can increase from 0.0 g to 0.03 g or higher in
one day. Linear extrapolation to zero was performed on
the four days previous to measurable dry-weight
appearance (and disappearance) to smooth out the curve.
The adjustment did not affect the performance of the
model; the model-derived curves more closely represented
the biology of the system. The model was set to run 123
days from planting. The time duration was set by the
equation describing the leaf dry-weight accumulation;
the soybean fields under intensive study for two
consecutive seasons were harvested 123 and 124 days
after sowing.
The correlation coefficients and the coefficients
of determination were not 1.00 for any of the regression
equations. The field data may be biased, which would
produce a 1ess-than-perfect fit. The field data may not
be accurate or may not accurately represent the actual
plants, again introducing bias. Random variation, a
common obstacle with field data, likely accounts for
most of the variation. Had the correlation coefficients
been less than 0.80 or the coefficients of determination
less than 0.60, some concern as to whether' the
regression equations accurately described the field data
might be warranted. The data were well fitted by the
presented equations (Figures 1 7).


31
Table 14. Soybean seed infection from separate
experiment, 1981.
B enomy1
application
Ty
Percent seed
F2
infectionX
P
C
Planting
03
54
23
23
Planting, weeks
11 and 13
05
55
35
10
Weeks 11 and 13
03
71
29
00
Check
03
50
29
21
w
Benomyl was applied at the rate of 586.5 g/ha;
field was planted on 15 June 1981. Check plots
no treatment.
X
Five hundred seed plated onto acidified potato
agar and observed 3 to 5 days later.
y
T=total seed infection.
Total seed infection partitioned into specific
pathogens: F=Fusarium spp.; P = Phomopsis spp.;
C=Cercospora kikuchii.
the
received
dextrose


82
C ) Results
Validation data of model-predicted versus actual
yield of stems, pods, and seeds for 1980 are presented
in Figs 11-13. Model-predicted versus actual yield for
1981 appear in Figs. 14-16. Not all growth simulations
were ceased on the same day. Since the plants were
harvested at 123 or 124 days from planting,
theoretically, the growth simulations should cease on
the same day.
Final plant-portion dry-weight ratios for Cobb and
Bragg soybean varieties, grown under an intensive
overhead irrigation scheme, are presented in Table 15.
Generally in the literature, instead of the profile
of an entire growing season, sections of the growth
curve for plant organs were analyzed where their growth
was linear. The seed dry-matter accumulation was
analyzed after 83 days from planting, where a linear
equation accurately fitted the data. When my data were
treated similarly, analyzing from day 83 through day
123, the slope coefficient for the simulated data was
0.42, for the raw data was 0.45, and was 0.41 (Table 16)
for the published data (28). The pod dry-matter
accumulation over time also could be described by a
linear equation, when 77 days from planting through
harvest were analyzed. When my data were treated


PREDICTED DRY MATTER (g)
(g)


28
(Table 12). The block by treatment interaction was
nonsignificant for the visual ratings of the pods
(P-0
.62) and
stems (P=0
.70); so the plots
were
treated
a s
an entity,
no t
as two
individual rows.
Plots
treated
with
benomy1
at
weeks
11 and 13 yielded
significantly
higher quality pods (P=0.0004) and stems (P=0.0001) than
those plots treated at planting only or not treated at
all; data are presented in Table 13. Seed from the
harvested rows were plated as described, and results
appear in Table 14. The low level of seed infection
prevented meaningful analysis.
D.) Discussion
1 .) Field Plots. 1980
The foliar diseases observed were purple stain,
frogeye leaf spot, downy mildew, target spot, and
Rhizoctonia blight. The actual amount of foliar disease
on individual plants ranged from less than 0.01% to
10.0%. The 10% disease severity was approached
immediately prior to final leaf drop.
Throughout the growing season, few individual
leaves reached a 10% disease level; generally,
senescence would occur and the leaf would be removed
from the canopy.
It was not possible to partition the


APPENDIX A
FUNGICIDES USED
Fungicide
Tradename, source, chemical name
percent active ingredient
Benomy1
Benlate 50W, Biochemicals Department, E.
I. duPont De Nemours and Company, Inc.,
Wilmington, Delaware 19898. Methyl 1-
(butylcarbamoyl)-2-benzimidazole
carbamate, 50% a.i.
Metalaxy1
Ridomil 2E, Agricultural Division, CIBA-
GEIGY Corporation, Greensboro, North
Carolina 27409, N-(2,6-dimethylpheny1)-N
(methoxyacety1) alanine methyl ester
25.11% a.i.
123


Ill
5.) Seed-feeding Insects
Southern green stink bug is the major seed-feeding
insect which annually causes damage in soybean fields.
Damage this pest causes could be described by equation
4.
D= I (T-86) 0.42 Y Z + 0.43 (Eq. 4)
D= reduced dry-matter accumulation by the seed
1= insect population per area
T= time from planting in days
Y= number of seed destroyed per insect per day
Z= dry-matter weight of one seed
Reduced dry-matter accumulation by seed (D) is removed
directly from the accumulation of any one day after 86
days from planting. Eighty-six days from planting is
suggested as a reference point because this is where a
published linear equation describes the seed dry-matter
accumulation (28), and my data (Table 15) are in good
accord. Appearing in equation 4 is a 0.42 factor which
describes the plant dry-matter accumulation per day for
the seeds after 86 days from planting, in grams. Also
appearing in equation 4 is a 0.43 factor added for the
Y-intercept value, in grams, from the linear equation
(Table 15). The number of seed destroyed per insect per
day (Y) would have to be determined experimentally. The


112
dry-matter weight of one seed (Z) is important to keep
the equation to scale. The scaling permits removal of
numbers of destroyed seed, not percentage of destroyed
seed. The insect population per area (I) can be
determined from "row shakes" a standard sampling
procedure for entomological studies. However, the
equation is such that the insect population would have
to be updated daily after day 86 from planting. Daily
sampling to describe southern green stink bug
populations is not practical, so an approach similar to
the velvetbean caterpillar model (48) could be used.
The insect growth from egg through instars to adult is
modeled for velvetbean caterpillar (48). The same
model, with modifications, could be used to update daily
the southern green stink bug populations. Modifications
would be necessary for differences in growth stages and
respective damage caused by each growth stage between
southern green stink bug and velvetbean caterpillar.
Again, an insecticide submodel could be easily
incorporated. The incorporation of equation 4 into the
flow chart of the soybean growth model is presented in
Fig. 21.


102
The reduction in seed quality (Q) could be a measure of
field emergence, or a combination of germination before
and after accelerated aging, field emergence, and
electrolyte conductivity. For these purposes, the
specific measure of seed quality is unimportant. The
squared mean plant quality rating (S) divided by the
maximum quality rating squared would likely yield a more
representative curve than a cubic equation for seed
quality. Any infection, evidenced by symptoms and signs
of pathogens on the stems and pods, could lead to seed
infection and reduced seed quality. However, the higher
the disease severity, the better the chance that the
infection has reached the seed, hence the squared term
to describe this type of relationship. The maximum
quality reduction (P) would have to be determined
experimentally. By whatever means used to measure {Q},
be it
on
a
scale
of 0
to 25 or
in
percent
, {P} would
also
have
to
appear
in
the same
form. An
appropriate
value
for
{P>
could
be
100% of
the
scale used, with a
much delayed harvest. Under normal conditions, 20% of
the range of the {S} scale would be a reasonable value.
The seed quality reduction from infection by pathogens
would be difficult to separate from physiological
decline, and both may have to be included in equation 3.
A factor multipled by the number of days after the




27
Table 11. Soybean seed infection from individually
harvested plants, 1981.
w
Treatment
Pe$
T
cent geed
infection
X
F
P
C
Benomyl plus
metalyxl
02
50
00
50
Benomy1
03
50
50
00
Metalaxyl
01
100
00
00
Check
07
00
67
33
WBenomyl was applied at the rate of 586.5 g/ha at 14-day
intervals from 22 June 1981 to 16 October 1981.
Metalaxyl was applied at the rate of 1137 g/ha at 40-day
intervals from 22 June 1981 to 16 October 1981. Check
plots received no treatment.
One hundred seed plated onto acidified potato dextrose
agar and observed 3 to 5 days later.
y
T=total seed infection.
z ... .
Total seed infection partitioned into specific
pathogens: F =Fusarium s p p ; P = Phomo psis s p p.;
C=Cercospora kikuchii


91
The slope of pod dry-matter accumulation from this
study (0.11) was different from a previously
reported(28) slope of pod dry-matter accumulation
(0.19). My Y-intercept (-1.21) for pod dry-matter
accumulation was also different from the value I
calculated from published data (-2.92). I expect pod
dry-matter accumulation to be influenced by the same
factors that influenced seed dry-matter accumulation.
Had Hanway and Weber (28) included data points between
70 and 75 days from planting in regression (which were
omitted), the slope for the pod dry-matter accumulation
curve would be lower than 0.19, perhaps even close to
0.11. The Y-intercepts also may be closer to the ones I
found with these data points included in the regression.
The coefficient of determination for the published pod
dry-matter accumulation curve (28) is 0.92; including
data points between days 70 and 75 in the regression
analysis will lower the coefficient of determination as
well as the slope. Any damage to the pods by insects or
plant pathogens, which was present in published studies
and was different from what was experienced in my
studies, would account for some variation between the
slopes of the pod dry-matter accumulation.


Fig. 9. The dry-matter accumulation for soybean leaves, converted from leaf area
(Fig. 1), from individually harvested plants over time, 1980.


Fig. 16. Model-predicted versus actual dry-matter accumulation for pods, 1981.


Fig. 21. Incorporation of a seed-feeding insect submodel into the soybean growth
mode 1 (Fig. 8) .


43
was not permitted to be negative, it was set to zero
when this condition occurred. No dry weight was
accumulated for seven days after planting. This time
period was reserved for seed germination and seedling
emergence.
C.) Results
The linear relationship between leaf area and leaf
dry-matter (Fig. 1) was highly correlated (r= 0.97).
The dry-matter accumulation of stems over time was also
well (r=0.89) described by a straight line (Fig. 2).
The dry-matter accumulation of seeds over time was
described by a cubic equation with an associated r =
0.94 (Fig. 3). The dry-matter accumulation of pods over
time was described by a quadratic equation with an r =
0.89 (Fig. 4). The dry-matter accumulation over time of
petioles and leaves was described by separate cubic
equations with r = 0.87 for petiole (Fig. 5) and r =
0.89 for leaf dry-matter accumulation over time (Fig.
6). The dry-matter accumulation for whole plants over
time is presented in Fig. 7, where a linear equation
with an r = 0.89 described the response. Values of r =
0.48, 0.61, 0.72 corresponded to P = 0.05, 0.01, 0.001
for 15 degrees of freedom (42).


LITERATURE CITED
1. Allen, E. J., and Scott, R. K. 1980. An analysis
of growth of the potato crop. J. Agrie. Sci., Camb.
94:583-606.
2. Anonymous. 1980. Soybean production guide.
Florida Coop. Ext. Serv. Circular 277E. 17pp.
3. Berger, R. D. 1981. Comparison of Gompertz and
logistic equations to describe plant disease progress.
Phytopathology 71:716-719.
4. Blacklow, W. M. 1973. Simulation model to predict
germination and emergence of corn (Zea mays L.) in an
environment of changing temperature. Crop Sci. 13:
604-608.
5. Blackman, C. H. 1980. Fungicide evaluation on
soybeans, 1980. Fungicide and Nematacide Tests 36:93.
6. Bloomberg, W. J. 1979. A model of damping-off of
Douglas-fir seedlings caused by Fusarium oxysporum.
Phytopathology 69:74-81.
7. Bloomberg, W. J. 1979. Model simulations of
infection of Douglas-fir seedlings by Fusarium
oxysporum. Phytopathology 69:1072-1077.
8. Boote, K. J., Gallaher, R. N., Robertson, W. K.,
Hinson, K., and Hammond, L. C. 1978. Effect of foliar
fertilization on photosynthesis, leaf nutrition, and
yield of soybeans. Agron. J. 70:787-791.
9. Boote, K. J., Jones, J. W., Smerage, G. H.,
Barfield, C. S., and Berger, R. D. 1980.
Photosynthesis of peanut canopies as affected by
leafspot and artifical defoliation. Agron. J.
72:247-252.
10. Caldwell, B. E. (e_d.) 1973 Soybeans:
Improvemnt, Production, Uses. Amer. Soc. Agron.,
Madison. 681 pp.
11. Calpouzos, L., Roelfs, A. P., Madson, M. E.,
Martin, F. B., Welsh, J. R., and Wilcoxson, R. D. 1976.
143


84
Table 16. Published values, model predictions, and 1980
and 1981 raw data for the same parameters.
Whole-plant
Parameter Published Simulated Raw 1980 1981
z
Seed
dry-mat ter
accumulation
(g/day) 0.41-0.47
Pods2
dry-mat ter
accumulation
(g/day) 0.19
Seed:Pod
dry-mat ter
ratios 2.47-2.63:1 -- 2.56:1 2.27:1
Seed:stem
dry-mat ter
ratios 1.53-1.59:1 1.50:1 1.66:1
0.42 0.45
0.11 0.11
^After day 86.
2
After day 77.


R)


92
The linearity of the entire plant (sum, Fig. 7) has
also been previously reported (31, 71).
The 1980 final dry-matter ratio for seeds :pods was
similar to published values (28), but the 1981 ratio was
not. Weather conditions much different from those in
1980 prevailed during 1981; there was more water and
more photosynthetica1ly-active radiation during the 1980
growing season than during the 1981 growing season
(51-61). The environmental conditions which prevailed
in 1980 more closely resembled the long-time averages
than did the 1981 environmental conditions. The 1980
environmental conditions can then be considered more
"normal," or closer to "normal" than the 1981
environmental conditions. As expected in the seed:stem
dry-mat ter
ratios,
the
1980
data were similar to
published
data, and
the
1981
data are not. Again,
environmental conditions were different during the two
seasons.
The seeds were the same proportion of the total dry
matter for both the 1980 and the 1981 growing season.
This further supports the rate of seed dry-matter
accumulation being relatively unaffected by
environmental changes. Had the 1980 to 1981
environmental variation been more pronounced, the seed
proportion of the final plant dry-matter ratio may have
been lower. Environmental conditions responsible for


LEAF AREA (cm2)
45


15
Table 2. Dry-matter yields from individually harvested
soybean plants, 1980.
Treatment^ Yield/plant (g)z
Total Partitioned
Pods
S t ems
Seeds
Benomyl +
metalaxyl
22.10
4.21
6.98
10.91
Benomy1
19.20
3.59
5.86
9.75
Metalaxyl
20.54
3.96
6.92
9.66
Check
16.40
3 .08
5.57
7.75
Duncan-Wa Her
k-ratio (k=100)
LSD
NS
NS
NS
NS
yBenomyl was applied at the rate of 586.5 g/ha at 14-day
intervals from 27 June 1980 to 4 November 1980.
Metalaxyl was applied at the rate of 1137 g/ha at 40-day
intervals from 27 June 1980 to 4 November 1980. Check
plots received no treatment.
z
Mean of 50 plants.


95
reduction in leaf area by foliar diseases or by
foliage-feeding insects (velvetbean ca11erpi1 lar ,
Anticarsia gemmatalis Hubner ; green cloverworm,
Plathypena scabra Fabricus; soybean looper, Pseudoplusia
includens Walker) would result in directly reducing the
product ion
of carbohydrates.
The
reduction
in
carbohydrat e
production would
cause
reduction
in
dry-matter
accumulation in stems,
seeds,
and pods.
The
southern green stink bug (Nezara viridula L.) pierces
the soybean pod and destroys the seed within the pod. A
specific equation to reduce the seed dry-matter
accumulation dependent upon the numbers of southern
green stink bugs could be developed and incorporated
into the seed dry-matter accumulation equation.
Subtraction of damaged seed would give a resultant yield
loss associated with various levels of this insect.
Similarly, the intensity of non-foliar diseases such as
pod and stem blight or anthracnose could be incorporated
into the model. The disruption of the normal growth
process in the stem, pod, and seed could be quantitated,
and the resultant terms introduced into the equations
for dry-matter accumulation. Mathematical separation of
dry-matter accumulation for seeds, stems, and pods
permitted each individual plant portion to be weighted
differently for pathogen intensity yield loss
reduction. Undoubtedly, different equations would be


17
Table 3. Pod and stem quality ratings from individually
harvested soybean plants, 1980.
Treatment Rating^
Pod Stem
Benomyl +
metalaxyl 2Z 4
Benomyl 2 4
Metalaxyl 7 8
Check 7 8
Duncan-Waller
k-ratio (k=100)
LSD 1 1
Benomyl was applied at the rate of 586.5 g/ha at 14-day
intervals from 27 June 1980 to 4 November 1980.
Metalaxyl was applied at the rate of 1137 g/ha at 40-day
intervals from 27 June 1980 to 4 November 1980. Check
plots received no treatment.
y
'Rated on a scale of 0 to 10 and transformed with an
angular transformation (arcsine (disease
proportion)**{1/2}) where the ratings of 0, 1, 2, 3, 4,
5, 6, 7, 8, 9, 10 were equivelent to 0, 2.5 10, 21, 35,
50, 65, 79, 90, 97.5, 100%, respectively (42).
2
Mean of 50 plants.


101
of the mean plant quality rating (S) divided by the cube
of the maximum quality rating is suggested to mimic
observations from the field that the most infected
plants in a field yield the smallest amount of dry
matter, but not on a 1:1 relationship between percent
infection and reduced yield. Often, moderately infected
stems and pods yield as much plant dry matter as clean,
or nearly clean plants. The cubic-shaped curve would
remove proportionally more dry-matter accumulation at
higher percent disease than at lower percent disease.
The maximum percent dry-matter reduction (M)
attributable to pod and stem blight and anthracnose
would have to be determined experimentally. The purpose
of {M} is to place a limit on the amount of damage
attributable to these type of plant pathogens. It is
very possible that {M} may change from season to season,
dependent upon the environmental conditions. A
reasonable value for {M} would be <15%.
Similarly, seed quality (as opposed to quantity,
above) could be evaluated with equation 3.
Q= (S**2 / Smax**2) P (Eq. 3)
Q= reduction in seed quality
S= average of stem and pod rating (based
on percent infection) at harvest
P= maximum quality reduction by pod
and stem blight and anthracnose
Smax= maximum pod and stem rating possible


42
measurements were comparisons against leaf-area diagrams
and insect- and disease-rating scales developed for
soybeans (Appendix E). On each sampling date, the
above-ground plant was separated into stems, leaves,
petioles, pods, and seeds. The plant parts were dried
and weighed. The relationship between leaf area and
leaf dry weight was determined from these plants. A
separate regression equation was developed for each
dependent variable; time was used as the quantitative
independent variable, with up to 15 degrees of freedom
available for the regression equation.
The equation which described the leaf dry-matter
accumulation over time was used to drive the model. The
separate regression equations which described dry-matter
accumulation by pods, stems, seeds, and petioles at each
day, were related mathematically to the equation which
described dry-matter accumulation by leaves alone. The
relationship was strictly a ratio. The ratios of stems
: leaves, seeds : leaves, pods : leaves, and petioles :
leaves were established for each day of the model. The
equation which described leaf dry-matter accumulation
over time produced stems, seeds, pods, and petioles,
varing in dry-matter accumulation proportional to leaf
dry-matter accumulation. Problems associated with
mathematical descriptions of biological data were
handled as they arose. Dry matter of the plant organs


34
greater control of disease.
The seed yields were not significantly different
among the treatments. Treatments which received benomyl
produced stems and pods with significantly fewer signs
and symptoms of pathogens than did treatments without
benomyl. Low levels of disease were present during the
growing season but highly significant differences in the
presence of symptoms and signs of pathogens on the stem
and seed were present. The low disease levels during
the growing season resulted in low seed-infection
levels. Had more disease been present, the range of the
percent infected seed may have been wider than 10%
between seed from untreated-check plants and seed from
fungicide-protected plants. Seed from the individually
harvested plants of different treatments was infected by
fungi to varing degrees. Fungicide application reduced
the percentage of seed infection, but did not reduce the
relative importance of the pathogenic fungi. Fusarium
spp. was responsible for about 65% of the seed
infection, Phompo sis spp. for about 17%, and _C_. kikuchii
for about 15%, irrespective of the treatment. Plants
which
received
a
benomy1
treatment
, with
or
without
metalaxyl, had
8%
seed
infection,
compared
t 0
12% for
seeds
from plant s
which
had not
received
a
benomy1
treatment. The majority of pathogens cultured from the
surface-steri1ized seeds were inhibited by the presence


24
as an error term (Table 9). Seed infection from the
individually harvested plants was low. The most likely
reason for the low infection levels would be the weather
conditions (57-61) which were highly unfavorable for
pathogen development. The same soybean line was used in
1980 and 1981 and the plots were located about 100
meters from where the 1980 plots had been planted; so
inoculum present during 1981 should have been similar to
that of 1980. A range of 6% in seed infection levels
was present (Table 10). Viewed differently,
benomy1-treated versus non-benomy1-treated, the
percentages of seed infection were 3% versus 4%. True
differences would be expressed in this comparison.
Another test to determine if random infection existed
would be to compare the percent of seed infection from
metalaxyl-treated (benomyl plus metalaxyl, and metalaxyl
alone) versus non-metalaxy1-treated (benomyl alone, and
check) plants, 3% versus 31 in this case. The percent
of infected seed from the individually harvested plants
(Table 11) was similar to that from the plots. The low
level of infection present in 1981 precluded meaningful
analy s is.
In the separate experiment on the time of
application of benomyl, the block by treatment
interaction was significant (P=0.03) for the seed yield;
so the seed yield was analyzed separately for each block


190cm2
(V-W)


Fig. 3 .
The dry-matter accumulation for soybean seeds over time.


81
dry matter was regressed on time, with up to 15 degrees
of freedom available for time, the independent variable.
The resultant regression equation was used to drive the
model (Fig. 8). The model predictions of final dry
weight of the plant portions were compared against the
measured data (Figs. 11-16).
Weekly nondestructive measurements of leaf area and
disease incidence and severity were recorded for each
leaf of five randomly selected soybean plants, variety
Cobb, and five randomly selected soybean plants, variety
Bragg. The plants were grown under overhead irrigation,
with a water management scheme directed toward zero
water stress (L. Hammond, personal communication). At
maturity, the individual plants were harvested and the
dry-weights for pods, seeds, and stems were measured.
The accuracy of the model was verified with
published data (43, 72, 73, 78, 79). Published
regression parameters and agronomic values such as slope
of dry-matter accumulation of plant portions, dry-weight
ratios between plant portions, and dry-matter
accumulation for the plant parts were compared against
model predictions.


APPENDIX D
MATERIALS USED
Material
Source
Acidified
potato
dextrose agar
Potatoes, 200 g; dextrose, 20 g; agar,
20 g; 50% lactic acid, 3 ml; deionized
water, 1 1
Clorox
The Clorox Company, Oakland, California
94612, 5.25% sodium hypochlorite
142


Horticultural Society, Soil and Crop Science Society of
Florida, Alpha Zeta Agricultural Honor Society, and
Gamma Sigma Delta Agricultural Honor Society. He is a
candidate for the degree of Doctor of Philosophy in
plant pathology at the University of Florida.


24. Fehr, W. R., Caviness, C. E., Burmood, D. T., and
Pennington, J. S. 1971. Stage of development
descriptions of soybeans, Glycine max (L.) Merrill.
Crop Sci. 11:929-931.
25. Fehr, W. R., Caviness, C. E., and Vorst, J. J.
1977. Response of indeterminate and determinate soybean
cultivars to defoliation and half-plant cut-off. Crop
Sci. 17:913-917.
26. Gibson, R. M., Lovvorn, R. L., and Smith, B. W.
1944. Response of soybeans to experimental defolation.
J. Amer. Soc. Agron. 36:768-778.
27. Hajek, J., and Dupac, V. 1967. Probability in
Science and Engineering. Academic Press, New York. 120
pp.
28. Hanway, J. J., and Weber, C. R. 1971. Dry matter
accumulation in eight soybean (Glycine max (L.) Merrill)
variets. Agron. J. 63:227-230.
29. Hanway, J. J., and Weber, C. R. 1971. Dry matter
accumulation in soybean (Glycine max (L.) Merrill)
plants as influenced by N, P, and K fertilization.
Agron. J. 63:263-266.
30. Heady, J. C. 1972. Defining the economic
threshold. Pages 100-108 jja: Pest Control Strategies
for the Future. National Academy of Sciences, New York.
31. Heilman, J. L. Kanemasu, E. T., and Paulson, G. M.
1977. Estimating dry-matter accumulation in soybean.
Can. J. Bot. 55:2196-2201.
32. Helwig, J. T., and Council, K. A. (ed s ) 1979 .
SAS User's Guide, 1979 Edition. SAS Institute Inc,
Raleigh. 494 pp.
33. Hill, R. W., Johnson, D. R., and Ryan, K. H. 1979.
A model for predicting soybean yields from climatic
data. Agron J. 71:251-256.
34. Hinson, K., Nino, R. H., and Boote, K. J. 1977.
Characteristics of removed leaflets and yield response
of artifically defoliated soybeans. Proc. Fla. Soil
Crop Sci. 37:104-109.
35. Holt, D. A., Bula, R. J., Miles, G. E., Schreibner,
M. M., and Peart, R. M. 1975. Environmental physiology
modeling and simulation of alfalfa growth. I.
Conceptual development of SIMED. Purdue Agr. Exp. Sta.
Bull. 907. 26 pp.


II. LITERATURE SURVEY
Morse (62), in reviewing the ancient history of the
soybean, claimed that the first written record of the
soybean was 2838 B. C. It was not until around 1900
that commercial soybean acreage became established in
the United States. At that time, the soybean acreage
was grown mainly for forage. As late as 1934, only 25%
of the
soybe
an
acreage
in
the
United
States
was
harvested
for
seed
By 1941,
more
soybean
acreage
was
harvested
for
seed
than for
forage.
Today ,
the soybean
acreage
grown
for
forage
in
the
United
States
is
minima1.
A model is a simplifed representation of a system.
A system is a collection of components and their
interrelationships. A model, therefore, represents a
collection of components, or more often a component and
its input s
and
output s. A
model
which covers all
aspects of
crop
growth defeats its
purpose
. Such a
model would
be
too large to
solve
detailed
prob1ems
which arise under field conditions. The simpler the
model is, while retaining accuracy, the more effective
the model becomes. Simple models are easier to evaluate
critically, and easier to apply to wide ranges of
4


DEVELOPMENT AND VALIDATION OF A GROWTH MODEL FOR
FLORIDA-GROWN SOYBEANS WITH DISEASE STRESS
BY
STEVEN BOYD JOHNSON
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE
UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1982

ACKNOWLEDGMENTS
I wish to acknowledge the assistance of Dr. Richard
D. Berger, major advisor for the studies and for the
dissertation, who unselfishly contributed incalculable
hours in these capacities. His dedication to science,
his critical and independent thinking, and his approach
to problems have earned my deepest respect. Special
recognition for general assistance throughout the
program of study and for critically reading and offering
valuable suggestions on this dissertation is in order
for the remainder of my supervisory committee: Drs. T.
E. Freeman, H. H. Luke, and S. H. West. I would also
like to recognize all the persons, too numerous to
mention by name, that have in some way contributed to
the completion of this dissertataion. I also wish to
acknowledge my wife, Jennifer, for she was the true
sufferer through the long hours of the studies and
preparation of the dissertation. The work was supported
by funds from EPA grant no. CR-806277-020-0 and research
funds from Dr. Berger.
ii

TABLE OF CONTENTS
LIST OF TABLES v
LIST OF FIGURES vii
LIST OF ABBREVIATIONS ix
ABSTRACT x
GENERAL INTRODUCTION 1
LITERATURE SURVEY 4
I. DEVELOPMENT OF THE MODEL 8
A.) Introduction 8
B.) Materials and Methods 9
1.) Field Plots, 1980 12
2 .) Field Plots 1981 12
C ) Results 13
1 .) Field Plots 1980 13
2.) Field Plots, 1981 16
D.) Discussion 28
1 .) Field Plots 1980 28
2 ) Field Plots 1981 35
II. DESCRIPTION OF THE MODEL 40
A.) Introduction 40
B.) Materials and Methods 41
C.) Results 43
D.) Discussion 58
iii

III. VALIDATION AND VERIFICATION OF THE MODEL 67
A.) Introduction 67
B.) Materials and Methods... 68
C.) Results 82
D.) Discussion 85
IV. APPLICATIONS FOR THE MODEL 94
A.) Introduction 94
B.) Uses For The Model 96
1.) Foliar Pathogens 96
2.) Above-ground Non-foliar Pathogens 98
3.) Soil-borne Pathogens 103
4.) Foliage-feeding Insects 106
5.) Seed-feeding Insects Ill
C.) Results 115
D.) Discussion 117
SUMMARY 121
APPENDICES 123
A: FUNGICIDES USED 123
B: EQUIPMENT USED 124
C: LEAF-AREA, DISEASE- AND INSECT-RATING SCALES...125
D: MATERIALS USED 142
LITERATURE CITED 143
BIOGRAPHICAL SKETCH 151
iv

LIST OF TABLES
1. Soybean seed yields from plots, 1980 14
2. Dry-matter yields from individually harvested
soybean plants, 1980 15
3. Pod and stem quality ratings from
individually harvested soybean plants, 1980 17
4. Soybean seed infection from plots, 1980 .... 18
5. Soybean seed infection from individually
harvested plants, 1980 19
6. Soybean seed yields from plots, 1981 20
7. Dry-matter yields from individually
harvested soybean plants, 1981 22
8. Dry-matter yields from individually harvested
soybean plants (analyzed with
block three removed), 1981 23
9. Pod and stem quality ratings from individually
harvested soybean plants, 1981 25
10. Soybean seed infection from plots, 1981 26
11. Soybean seed infection from individually
harvested plants, 1981 27
12. Soybean seed yields from
separate experiment, 1981 29
13. Soybean pod and stem quality
ratings from separate experiment, 1981 30
14. Soybean seed infection from
separate experiment, 1981 31
15. Harvested above-ground plant dry matter
proportioned into seeds, stems, and pods for
two soybean cultivars, 1981 83
v

16. Published values, model predictions, and
1980 and 1981 raw data for the same parameters ... 84
17. Harvested, above-ground soybean-plant dry-matter
proportioned into seeds, stems, and pods
for two seasons 86
18. Final plant dry-matter ratios for two
soybean cultivars, 1981 89

LIST OF FIGURES
1. The dry-matter accumulation for soybean
leaves of known area over time 45
2. The dry-matter accumulation for soybean
stems over time 47
3. The dry-matter accumulation for soybean
seeds over time 49
4. The dry-matter accumulation for soybean
pods over time 51
5. The dry-matter accumulation for soybean
petioles over time 53
6. The dry-matter accumulation for soybean
leaves over time 55
7. The dry-matter accumulation for entire
soybean plants over time 57
8. Flow chart of the soybean growth model
(N = number of days; 0 = rate of change) 61
9. The dry-matter accumulation for soybean leaves,
converted from leaf area (Fig. 1),
from individually harvested
plants over time, 1980 63
10. The dry-matter accumulation for soybean leaves,
converted from leaf area (Fig. 1),
from individually harvested
plants over time, 1981 65
11. Model-predicted versus actual dry-matter
accumulation for seeds, 1 980 70
12. Model-predicted versus actual dry-matter
accumulation for stems, 1 980 72
13. Model-predicted versus actual dry-matter
accumulation for pods, 1980 74
vii

14. Model-predicted versus actual dry-matter
accumulation for seeds, 1981 76
15. Model-predicted versus actual dry-matter
accumulation for stems, 1981 78
16. Mode1-predicted versus actual dry-matter
accumulation for pods, 1981 80
17. Incorporation of a foliar-disease submodel
into the soybean growth model (Fig. 8) 100
18. Incorporation of an above-ground, non-foliar
disease submodel into the soybean growth
model (Fig. 8) 105
19. Incorporation of a soil-borne disease
submodel into the soybean growth
model (Fig. 8) 108
20. Incorporation of a foliage-feeding insect
submodel into the soybean growth
model (Fig. 8) 110
21. Incorporation of a seed-feeding insect
submodel into the soybean growth
model (Fig 8 ) 114
viii

LIST OF ABBREVIATIONS
In
base e (natural) logarithm
log
base 10 logarithm
m
slope of linear regression equations
R
coefficient of determination
r
correlation coefficient
Yo
initial disease
Ymax
maximum disease level
*
mult ip 1ica tion
**
exponentation
exp
base of natural logarithm
k
epidemic rate for Gompertz transformation
b
(-ln{Yo}) in Gompertz transformation
t
time
P
probability level
LSD
least significant difference
LAI
leaf area index
g
gram
ha
hectare
1
liter
ix

Abstract of Dissertation Presented to the Graduate
Council of the University of Florida in Partial
Fulfillment of the Requirements for the Degree of
Doctor of Philosophy
DEVELOPMENT AND VALIDATION OF A GROWTH MODEL FOR
FLORIDA-GROWN SOYBEANS WITH DISEASE STRESS
By
Steven Boyd Johnson
December, 1982
Chairman: Dr. Richard D. Berger
Major Department: Plant Pathology
Holistic field experiments with soybean were
conducted over two growing seasons, in which fungicides
were applied to achieve various disease intensities.
The experiments were monitored at weekly intervals from
planting through harvest. Each week, the disease
intensity of five different foliar diseases, the insect
damage, and the area of each individual leaf were
measured from representative plants. The above-ground
portion of the plants, which had been measured through
the growing season, were harvested for dry-matter
yields. The experiments continued after harvest when
the pathogen presence in the seed from the individually
monitored plants and in the seed from the plots was
de t ermined .
x

A narrow range of disease intensities resulted from
the application of the fungicides and, consequently,
yield differences were nonsignificant. However, quality
of the soybean pods and stems from the individually
monitored plants were significantly improved with the
application of a fungicide.
A regression-derived soybean growth model was
developed from the holistic field experiments. The
model was driven by the dry-matter accumulation of
soybean leaves over time. Separate equations which
described the dry-matter accumulation of soybean stems,
pods, petioles, and seeds were developed and related to
the leaf dry-matter accumulation equation by ratios,
updated with each time step.
Model validation was performed with measurements
taken from holistic field experiments conducted over two
growing seasons. The measurements were independent of
the measurements used to develop the model. Disease
intensities were too low over both growing seasons for a
true yield difference to be realized from the fungicide
applications .
Model verification was performed with published
values. Dry-matter ratios and slopes of dry-matter
accumulation for soybean organs, as described by the
model, were comparable with published values.
xi

Theoretical submodels were developed for foliar
pathogens, above-ground non-foliar pathogens,
foliage-feeding insects, and seed-feeding insects.
Possible applications for the model are to develop
disease intensity yield loss relationships and
threshold levels of disease-induced loss.
XI1

I. GENERAL INTRODUCTION
The soybean (Glycine max (L.) Merrill), an annual
plant, is included in the kingdom Planta, phylum
Tracheophyta, class Angiospermae, order Rosales, family
Leguminosae, and is one of the oldest cultivated crops.
The geographic adaptability, high oil content, and high
nutritive value of the pressed seed mash have placed the
soybean into prominence in United States agriculture.
Since 1954, the United States has been one of the
world's largest producer of soybeans.
Throughout the geographical distribution of the
soybean, diseases reduce yield quality and quantity.
The most prevalent fungal diseases of soybean in Florida
are purple stain (Cercospora kikuchii Matsumoto &
Tomoyasu), frogeye leaf spot (Cercospora so jina Hara. ) ,
downy mildew (Peronospora man shurica (Naoum.) Syd. ex
Gaum.), target spot (Corynespora cassiicola (Berk, and
Curt.) Wei.), Rhizoctonia blight (Rhizoctonia solani
Kuehn), anthracnose (Colletotrichum truncatum (Schw.)
Andrus and W. D. Moore), and pod and stem blight
(Phomo p sis so j ae L e h {Diaporthe so jae Leh.}) {10, 18,
75). Diseases which cause yield reduction and plant
defoliation in other soybean growing regions are not
1

2
present (rust {Phakopsora pachyrhizi Sydow}) or not
prevalent in some portions of Florida (brown spot
{Septoria glycines Hemmi.}). The devastation of soybean
in areas of the world by diseases, some presently in
Florida, necessitates the establishment of disease
intensity-yield loss relationships.
The relationship between foliar diseases and yield
of soybeans has not been characterized. One approach to
determine
the disease
intensity-
yield loss relationship
would be
to measure
the host
growth
without stress
(diseases,
insects,
drought ,
poor
nutrition) and
concurrently subject other host plants to various levels
of stress and measure the resulting change in yield.
Both the host growth and stress components can be
described mathematically. The host growth model, with
and without the stress factors, would need validation
and verification to prove its applicability for decision
processes in soybean crop management. In the case of
this project, the controlled stress factors were
diseases. In the growth model, leaf area could be
mathematically removed to simulate stress. The
influence of disease on yield can be examined by
removing leaf area from fungicide-treated plants
equivalent to the disease levels on non-treated plants.
The approach of modeling will help field projects
become more efficient, or at least can help direct

3
investigations toward aspects of the pathosystem which
need clarification.
Any model is the simplified representation of a
system. The soybean growth model developed with disease
stress, described here, does not cover all aspects of
plant growth, but that was not its intended purpose.
The purpose of this new model was to be a beginning
framework for a disease intensity yield loss model.
Further model refinements could incorporate pathogen
response to environmental conditions and growth of
systemic, non-foliar pathogens.
Data were analyzed on an Amdahl 470 V6 and an IBM
3033N at the facilities of the Northeast Regional Data
Center of the State University System of Florida, and on
an APPLE II Plus microcomputer (48 K memory); all
computers were located on the University of Florida
campus, Gainesville, Florida.

II. LITERATURE SURVEY
Morse (62), in reviewing the ancient history of the
soybean, claimed that the first written record of the
soybean was 2838 B. C. It was not until around 1900
that commercial soybean acreage became established in
the United States. At that time, the soybean acreage
was grown mainly for forage. As late as 1934, only 25%
of the
soybe
an
acreage
in
the
United
States
was
harvested
for
seed
By 1941,
more
soybean
acreage
was
harvested
for
seed
than for
forage.
Today ,
the soybean
acreage
grown
for
forage
in
the
United
States
is
minima1.
A model is a simplifed representation of a system.
A system is a collection of components and their
interrelationships. A model, therefore, represents a
collection of components, or more often a component and
its input s
and
output s. A
model
which covers all
aspects of
crop
growth defeats its
purpose
. Such a
model would
be
too large to
solve
detailed
prob1ems
which arise under field conditions. The simpler the
model is, while retaining accuracy, the more effective
the model becomes. Simple models are easier to evaluate
critically, and easier to apply to wide ranges of
4

5
conditions. A model can be used to predict the system
response to various changes in inputs, without going to
the actual system. The usefulness of models for
research programs, whether for identification of
problems or solving problems, cannot be overstated.
Modeling of systems dates back as far as records
were kept, and yet is as current as today. Development
of maps, models of land or water masses, continuing
through the development of laws of physics, modeling the
effect of gravity, etc., to today's high-speed
digital-computer simulations of biochemical processes,
are examples of models. Likewise, soybeans are one of
the world's oldest cultivated crops, yet today are under
intensive investigation to increase yields. Soybeans,
like modeling, can be viewed as rich in tradition and
yet extremely modern.
Soybeans as a crop and modeling as a science
started to converge with the interest of agricultural
scientists in yield maximization. Early modelers of
soybean growth were concerned with production of
soybeans as a forage source, and the effect of
defoliation (cattle grazing) on leaf, stem, and seed
yield (26). The maximization of the entire soybean
plant was investigated in this work, because the soybean
was grown as a forage source. Interest shifted from
modeling the injury from grazing to modeling the injury

6
from hail (25, 85). More recently, insect damage (9,
34, 80, 81) and disease damage (43) have been modeled.
McAlister and Krober (46) approached the situation
differently; they measured the yield changes and the
changes in the biochemical components of the soybean
plant parts in response to artificial defoliation. The
recent soybean modeling work has focused on seed yield
maximization, as soybean production is now almost
exclusively a seed crop. Soybean workers have
investigated several diseases and their relation to
yield loss (17, 36, 40, 41, 86). At present, the models
are, at best, restricted to a particular location for a
particular season. A flexible model for soybean growth
which would give loss estimates from diseases does not
exist. None of the models for soybean disease loss have
been incorporated into growth models.
Paralleling the interest in defoliation yield
loss relationships for soybeans were those of other
crops. Chester (13) published an article on the nature
of artificial defoliation experiments to provide a basis
for disease-loss estimates. Chester drew from studies
involving wheat, corn, oats, barley, and onion.
Disease-loss, hail-loss, or insect-loss estimates are
the goal of the models which focused on seed-yield
maximization. While the relationship for defoliation
level yield reduction in soybean were under

7
development, new research needs surfaced. Quantitative
descriptions of dry-matter accumulation for yield
components were required for soybean models dealing with
plant growth. From the 1960's and continuing through
today, mathematical models of dry-matter accumulation
for soybean have been published. Shibles and Weber (72,
73) were pioneers in these studies, establishing that
soybean plant dry-matter accumulation was proportional
to leaf area. The early work by Shibles and Weber has
been further documented by numerous workers (8, 20, 21,
22, 28, 29, 31, 71). The linear relationship between
the dry-matter accumulation for entire soybean plants
versus time has been documented (28, 31, 71). The
linear relationship for the dry-matter accumulation for
the seed versus time (8, 20, 21, 28) has also been
described. The development of quantitative descriptions
of dry-matter accumulation for soybean yield components
provided the data for soybean modeling.
In modeling efforts, the soybean is a relatively
new crop, when compared to potatoes or cereals. To
date, soybean models, especially soybean disease models,
are lacking the sophistication and accuracy of those of
potato and cereal crops. Much progress on modeling of
the soybean has been made in the last twenty years, and
with the ever-increasing importance of the soybean as a
crop, progress toward maximization of soybean yields
will continue to be made.

III. DEVELOPMENT OF THE MODEL
A.) Introduction
Holistic experiments were conducted in 1980, and
repeated during the 1981 growing season. The
experiments were designed to follow the host growth
during the season and to observe the development and
progress of all foliar-disease epidemics. On selected
plants, all leaves were regularly examined for disease
incidence and severity and for leaf area. All
measurements were made by nondestructive methods.
Fungicides were applied frequently, or not at all, to
provide a range of diseases and disease intensities.
Frequent fungicide applications were aimed at providing
as complete disease control as possible. Some plots
were left untreated by fungicides to allow disease
epidemics to progress without man-made interference.
For both growing seasons, the plots were located within
a 2 hectare soybean field, with approximately 4 to 6
additional hectares of soybeans grown in close
proximity. Soybeans had been grown continuously in the
general area for over 10 years, assuring some presence
of inoculum for diseases commonly occurring in Florida.
8

9
The growth model was derived from host
measurements. Disease intensity measurements over time
provide an account of disease progress, which could be
converted into a disease model. The separation of host
and disease is a useful approach for the determination
of economic threshold levels for diseases. Mathematical
separation of host and disease could be accomplished by
mathematically increasing the disease intensity in the
disease model and removing the increased amounts of
diseased tissue from the total host tissue.
B.) Materials and Methods
The soybean breeding line F76-4486 was chosen for
the experiments. The breeding line is susceptible to
some foliar diseases and is an F5 line from the cross
Centennial x (Forrest x {Cobb x D68-216}) (K. Hinson,
personal communication); the cultivar Foster (F76-8827 )
is a sibling to the chosen breeding line. The
experimental fields were located on the University of
Florida campus, Gainesville, Florida. The plots were
arranged in a randomized-comp1ete-b1ock design, with
five replications of fungicide treatments. The
fungicide treatments were benomyl, benomyl plus
metalaxyl, metalaxyl, and an untreated check (Appendix
A). The plots were four 6.1-meter long rows with

10
0.91-meter row spacing and were seeded at the rate of 39
seeds/meter. The center two rows were used as multiple
observations from each experimental unit. This allowed
for
testing
of
block
by
treatment interaction. The
field
was
fertilized
and
an
insecticide
applied as
recommended
for
the
crop
(2)
. Benomyl
was applied
(586.5 g/ha) at 14-day intervals; metalaxyl was applied
(1137 g/ha) at 40-day intervals. All fungicide
applications were made over the top of the canopy with a
hand-held, two-row, six-nozzle, boom sprayer delivering
the equivalent of 396 ls/ha at 276 kilopascals (Appendix
B). Frequent fungicide applications were used to
provide optimal disease control. Metalaxyl and benomyl
were chosen because their selectivity of action would
provide a difference in disease severity and intensity
in the plots. Metalaxyl was chosen to control downy
mildew. Benomyl was chosen to control other diseases,
primarily pod and stem blight, anthracnose, frogeye leaf
spot, and purple stain.
In each of the center two rows of a plot, plants
were randomly selected and labeled. Starting three
weeks from date of sowing, weekly measurements of leaf
area and disease incidence and severity were recorded
for each leaf of the labeled plants. Leaf emergence,
leaf senescence, insect damage, and growth stage (23,
24) also were recorded weekly.
For each leaf, the

11
disease and insect damage was expressed as a percent of
leaf area for that leaf. All measurements were
comparisons against leaf-area diagrams and insect- and
disease-rating scales developed for soybeans (Appendix
C). Total photosynthetic area of the leaves was
calculated by subtracting the senescent, insect-damaged,
and diseased area from total leaf area.
At maturity, each of the labeled plants was
harvested. The dry weights for pods, seeds, and stems
were measured from each plant. The disease severity on
the stems and pods from these plants was rated on a
scale from 0 to 10. The rating scale consisted of 11
evenly spaced ratings with a rating of 0 for 0% of the
pods or main stem covered with symptoms or signs of
pathogens; and a rating of 10 for 100% of the pods or
main stem covered with symptoms or signs of pathogens.
Because the visual ratings had a binomial distribution,
an angular transformation (arcsine (disease
proport ion)**{1/2}) was used where the ratings of 0, 1,
2, 3, 4, 5, 6, 7, 8, 9, 10 were equivelent to 0, 2.5 10,
21, 35, 50, 65, 79, 90, 97.5, 100%, respectively (42).
Seeds from the labeled, individually harvested plants
were surface sterilized in a 10% Clorox (Appendix D)
solution for one minute and plated onto acidified potato
dextrose agar (Appendix D) and observed within seven
days for presence of seed-borne fungal pathogens. After

12
the labeled plants were individually harvested, the
center 4.88 meters of the center two rows were harvested
for seed yield.
1 ) Field Plots 1980
The field was planted on 27 June and harvested 125
days later on 4 November. Benomyl was first applied 4
July, and sunsequent applications were made every 14
days through harvest. Metalaxyl was first applied 30
June, and sunsequent applications were made every 40
days through harvest. Leaf area and disease intensity
data were collected from five plants in each of the
center two plot rows.
2 ) Field Plots 1981
The field was planted on 15 June and harvested 124
days
later
on 16 October. Benomyl
was
f irst applied
22
June ,
and
sunsequent
applications
were made every
14
days
through harvest
. Metalaxyl
was
first applied
22
June ,
and
sunsequent
applications
were made every
40
days
through harvest
. Leaf area
and
disease intensity
data
were
collected
f rom two plants
in each of
the
center two plot rows.

13
In a separate experiment, the soybean breeding line
F76-884b was planted on the University of Florida
campus, Gainesville, Florida. The separate experiment
was conducted to ascertain if the scheme of benomyl
application affected the disease severity or yield. The
treatments were arranged in a randomized-complete-block
design with five replications of benomyl (586.5 g/ha)
applied i) at planting, ii) at 11 and 13 weeks from
planting, iii) at planting and at 11 and 13 weeks from
planting, iv) or not at all. The plots, fungicide
applications, and harvested plant matter were treated as
described above.
C.) Results
1.) Field Plots, 1980
The block by treatment interaction was
nonsignificant (P=0.23) for all measured variables; so
the plots were treated as an entity, not as two
individual rows. The seed yields from the plots were
not significantly different among the treatments (Table
1). Dry weight yields from the labeled, individually
harvested plants were not significantly different among
treatments (Table 2) when viewed as entities (P=0.38) or
when separated into seeds (P=0.39), stems (P=0.35), and

14
Table 1. Soybean seed yields from plots, 1980.
y
Treatment
Seed
g/plot
yield
kg/ha
Benomyl +
me t a 1axy1
2676Z
3200
B enomy1
2564
3067
Metalaxyl
2128
2545
Check
2393
2862
Duncan-Waller
k-ratio (k=100)
LSD
NS
^Benomyl was applied at the rate of 586.5 g/ha at 14-day
intervals from 27 June 1980 to 4 November 1980.
Metalaxyl was applied at the rate of 1137 g/ha at 40-day
intervals from 27 June 1980 to 4 November 1980. Check
plots received no treatment.
z
Mean of five plots.

15
Table 2. Dry-matter yields from individually harvested
soybean plants, 1980.
Treatment^ Yield/plant (g)z
Total Partitioned
Pods
S t ems
Seeds
Benomyl +
metalaxyl
22.10
4.21
6.98
10.91
Benomy1
19.20
3.59
5.86
9.75
Metalaxyl
20.54
3.96
6.92
9.66
Check
16.40
3 .08
5.57
7.75
Duncan-Wa Her
k-ratio (k=100)
LSD
NS
NS
NS
NS
yBenomyl was applied at the rate of 586.5 g/ha at 14-day
intervals from 27 June 1980 to 4 November 1980.
Metalaxyl was applied at the rate of 1137 g/ha at 40-day
intervals from 27 June 1980 to 4 November 1980. Check
plots received no treatment.
z
Mean of 50 plants.

16
pods (P=0.42). The quality of the stems and pods from
the labeled, individually harvested plants, as
determined by visual rating, varied significantly in
response to the treatments. Treatments of benomyl and
benomyl plus metalaxyl had significantly better disease
control on pods (P=0.0001) and stems (P=0.0001) than did
treatments without benomyl (Table 3). Individually
harvested plants from the benomyl treatment had the
lowest percent seed infection (5%) and the untreated
check had the highest percent seed infection (15%)
{Table 4). The ratios of the percent seed infection
caused by F u s a r i um spp., Phomops i s spp., and C^. kikuchii
were similar across the treatments. This was also true
when the seed from the individually harvested plants
were plated (Table 5).
2.) Field Plots, 1981
The block by treatment interaction was
nonsignificant (P=0.25) for the seed yield from the
plots, so plots were treated as an entity, not as two
individual rows (Table 6). A significant block by
treatment interaction was present for the dry-weight
yields of the labeled, individually harvested plants
when separated into seeds (P=0.04), pods (P=0.04), or
when the dry weights of the seeds, pods, and stems were

17
Table 3. Pod and stem quality ratings from individually
harvested soybean plants, 1980.
Treatment Rating^
Pod Stem
Benomyl +
metalaxyl 2Z 4
Benomyl 2 4
Metalaxyl 7 8
Check 7 8
Duncan-Waller
k-ratio (k=100)
LSD 1 1
Benomyl was applied at the rate of 586.5 g/ha at 14-day
intervals from 27 June 1980 to 4 November 1980.
Metalaxyl was applied at the rate of 1137 g/ha at 40-day
intervals from 27 June 1980 to 4 November 1980. Check
plots received no treatment.
y
'Rated on a scale of 0 to 10 and transformed with an
angular transformation (arcsine (disease
proportion)**{1/2}) where the ratings of 0, 1, 2, 3, 4,
5, 6, 7, 8, 9, 10 were equivelent to 0, 2.5 10, 21, 35,
50, 65, 79, 90, 97.5, 100%, respectively (42).
2
Mean of 50 plants.

18
Table 4. Soybean seed infection from plots, 1980.
v
Treatment
TX
Percent
Fy
seed
P
w
infection
C
0
Benomyl plus
me talyxl
07Z
82
08
02
08
Benomy1
21
60
07
02
31
Meta 1axy1
05
48
20
28
04
Check
05
78
06
06
11
vBenomyl was applied at the rate of 586.5 g/ha at 14-day
intervals from 27 June 1980 to 4 November 1980.
Metalaxyl was applied at the rate of 1137 g/ha at 40-day
intervals from 27 June 1980 to 4 November 1980. Check
plots received no treatment.
WSeven hundred seed plated onto acidified potato
dextrose agar and observed 3 to 5 days later.
T=total seed infection.
yTotal seed infection partitioned into specific
pathogens: F=Fusarium spp.; P = Phomopsis spp.;
C Cercospora kikuchii; 0 = 0thers, primarily Rhizoctonia
spp. and Colletotrichum spp.
z _
Round off error present.

19
Table 5. Soybean seed infection from individually
harvested plants, 1980.
w
Treatment
y
Percent
seed
infectionX
Ty
F
P
C
0
Benomyl plus
metalyxl
10
67
12
12
09
Benomy1
05
66
17
17
00
Metalaxy1
08
60
20
20
00
Check
15
69
20
11
00
w
Benomyl was applied at the rate of
586 .5
g/ha at
14-day
intervals from
27
June
1980 to
4 November
1980 .
Metalaxyl was
applied
at the rate of 1137
g/ha at
40-day
intervals from
27
June
1980 to
4 November
1980 .
Check
plots received no treatment.
Four hundred seed plated onto acidified potato dextrose
agar and observed 3 to 5 days later.
y
T=total seed infection.
2
Total seed infection partitioned into specific
pathogens: F=Fusarium spp.; P = Phomopsis spp.;
C=Cercospora kikuchii; 0=0thers, primarily Rhizoctonia
spp. and Co 11 etotrichum spp.

20
Table 6. Soybean seed yields from plots, 1981.
X
Treatment
Seed
g/plot
yield ^
kg/ha
Benomyl +
metalaxyl
107 1 Z
1281
Benomy1
898
1074
Metalaxyl
771
922
Check
1002
1198
Duncan-Waller
k-ratio (k=100)
LSD
197
XBenomyl was applied at the rate of 586.5 g/ha at 14-day
intervals from 22 June 1981 to 16 October 1981.
Metalaxyl was applied at the rate of 1137 g/ha at 40-day
intervals from 22 June 1981 to 16 October 1981. Check
plots received no treatment.
y
Mean of five plots,
z
Round-off error present.

21
summed (P=0.07); a significant block by treatment
interaction was absent for the dry weight of stems
(P=0.36). Much of the block by treatment interaction
was attributable to block 3 (Table 7). With block 3
removed from the calculations (taking a mean of the
remaining four blocks), block by treatment interactions
were nonsignificant for dry-weight yields of the
labeled, individually harvested plants when separated
into seeds (P=0.19), pods (P=0.16), stems (P=0.59), or
when the dry weights of the seeds, pods, and stems were
summed (P=0.26). With blocks 1, 2, 4, and 5 summed,
there were significant differences in the labeled,
individually harvested plants when separated into stems
(P=0.02), pods (P=0.02), and seeds (P=0.03), or when
summed (P = 0.02); the nonsignificant block by treatment
interaction was used as an error term for these tests
(Table 8). The visible quality of the stems and pods
from the labeled, individually harvested plants varied
significantly in response to treatments. Block by
treatment interaction was nonsignificant for visual
ratings of quality for pods (P=0.27) and stems (P=0.81).
Treatments with benomyl (benomyl alone, and benomyl plus
metalaxyl) had significantly less (P=0.0001) symptoms
and signs of pathogens than did treatments without
benomyl (metalaxyl alone, and check), when the
nonsignificant block by treatment interaction was used

22
Table 7. Dry-matter yields from individually harvested
soybean plants, 1981.
Portion Yield/plant (g)*
Block
1
2
3
4
5
Pods M7
14.6 5aZ
M
11.88a
B
4.37
M
13.55a
M
7.93
0
9.82b
0
9.25ab
C
3.92
B
5.16 b
B
6.98
C
3.61 c
B
6.30 b
M
3.91
C
4.77 b
C
4.99
B
3.53 c
C
5.76 b
0
3.32
NS
0
4.28 b
0
4.75
NS
Seeds M
32.43a
M
26.14a
B
9.86
M
29.74a
M
17 .45
0
22.79 b
0
21 .42ab
0
8.27
B
12.70 b
B
16.12
B
8.83
c B
15.85 be
C
7 .89
C
10.39 b
C
11 .94
C
8.53
c C
13.20 c
M
6 .40
NS
0
9.58 b
0
11.55
NS
Stems M
15.63a
M
13 .32a
B
5.50
M
16 .02a
M
11.14
0
11.39 b
0
12.45a
C
4.91
C
7.49 b
B
9.69
B
5.98
c B
8.37 b
M
4.70
0
6.24b
C
8.23
C
5.57
c C
8.14 b
0
4.52
NS
B
5.83 b
0
7.91
NS
Total M
62.71a
M
51.34a
B
19.73
M
59.31a
M
36.52
0
44.00 b
0
43.12ab
C
16.72
B
23 .68
b
B
32.79
B
18.34 c
B
30.52 b
0
16.11
C
22.65
b
C
25.16
C
17.70 c
C
27.10 c
M
15.00
0
20.09
b
0
24.20
NS NS
w
Roundoff error present.
Mean of four plants.
y
B=benomy1-treated plants; M=metalaxy1-treated plants;
O=benomyl plus meta1axy1-treated plants; C=check plants.
Benomyl was applied at the rate of 586.5 g/ha at 14-day
intervals from 22 June 1981 to 16 October 1981.
Metalaxyl was applied at the rate of 1137 g/ha at 40-day
intervals from 22 June 1981 to 16 October 1981. Check
plots received no treatment.
z .
Numbers in the same column, within a row, followed by
the same letter are not significantly different
according to Duncan's new multiple range test (P=0.05).

23
Table 8
soybean
1981 .
Dry-matter yields from individually harvested
plants (analyzed with block three removed),
w
Treatment
Yield/plot (g)
Total Partitioned
Pods Stems Seeds
Benomyl +
meta 1axy1
Benomy1
Metalaxy1
Check
32.85ayz 7.03a 9.50a 16.34a
26.33a 5.49a 7.47a 13.38a
52.47 b 12.03 b 14.03 b 26.44 b
23.15a 4.78a 7.36a 11.02a
WBenomyl was applied at the rate of 586.5 g/ha at 14-day
intervals from 22 June 1981 to 16 October 1981.
Metalaxyl was applied at the rate of 1137 g/ha at 40-day
intervals from 22 June 1981 to 16 October 1981. Check
plots received no treatment.
x
Mean of 16 plants.
y
Numbers within a column followed by the same letter are
not significantly different according to Duncan's New
Multiple Range Test (P=0.05).
z
Roundoff error present.

24
as an error term (Table 9). Seed infection from the
individually harvested plants was low. The most likely
reason for the low infection levels would be the weather
conditions (57-61) which were highly unfavorable for
pathogen development. The same soybean line was used in
1980 and 1981 and the plots were located about 100
meters from where the 1980 plots had been planted; so
inoculum present during 1981 should have been similar to
that of 1980. A range of 6% in seed infection levels
was present (Table 10). Viewed differently,
benomy1-treated versus non-benomy1-treated, the
percentages of seed infection were 3% versus 4%. True
differences would be expressed in this comparison.
Another test to determine if random infection existed
would be to compare the percent of seed infection from
metalaxyl-treated (benomyl plus metalaxyl, and metalaxyl
alone) versus non-metalaxy1-treated (benomyl alone, and
check) plants, 3% versus 31 in this case. The percent
of infected seed from the individually harvested plants
(Table 11) was similar to that from the plots. The low
level of infection present in 1981 precluded meaningful
analy s is.
In the separate experiment on the time of
application of benomyl, the block by treatment
interaction was significant (P=0.03) for the seed yield;
so the seed yield was analyzed separately for each block

25
Table 9. Pod and stem quality ratings from individually
harvested soybean plants, 1981.
Treatment*7 Rating3^
Pod
Stem
Benomyl +
meta 1axy1
la
1 a
Benomy1
1 a
1 a
Me talaxy1
2 b
7 b
Check
2 b
7 b
wBenomyl was applied at the rate of 586.5 g/ha at 14-day
intervals from 22 June 1981 to 16 October 1981.
Metalaxyl was applied at the rate of 1137 g/ha at 40-day
intervals from 22 June 1981 to 16 October 1981. Check
plots received no treatment.
Mean of 20 plants.
Rated on a scale of 0 to 10 and transformed with an
angular transformation (arcsine (disease
proportion)**{1/2}) where the ratings of 0, 1, 2, 3, 4,
5, 6, 7, 8, 9, 10 were equivelent to 0, 2.5 10, 21, 35,
50, 65, 79, 90, 97.5, 100%, respectively (42).
2
Numbers followed by the same letter are not
significantly different according to Duncan's New
Multiple Range Test (P=0.05).

26
Table 10. Soybean seed infection from plots, 1981.
w
Treatment
T7
Pej cen t
F
seed
P
infectionx
C
0
Benomyl plus
metalyxl
02
64
27
09
00
Benomy1
03
31
62
07
00
Metalaxyl
04
32
26
37
05
Check
02
00
88
12
00
w
Benomyl was applied at the rate of 586.5 g/ha at 14-day
intervals from 22 June 1981 to 16 October 1981.
Metalaxyl was applied at the rate of 1137 g/ha at 40-day
intervals from 22 June 1981 to 16 October 1981. Check
plots received no treatment.
X
Five hundred seed plated onto acidified potato dextrose
agar and observed 3 to 5 days later.
y
T=total seed infection.
2
Total seed infection partitioned into specific
pathogens: F=Fusarium spp.; P=Phomopsis spp.;
C = Cercospora kikuchii; 0 = 0thers, primarily Rhizoctonia
spp.

27
Table 11. Soybean seed infection from individually
harvested plants, 1981.
w
Treatment
Pe$
T
cent geed
infection
X
F
P
C
Benomyl plus
metalyxl
02
50
00
50
Benomy1
03
50
50
00
Metalaxyl
01
100
00
00
Check
07
00
67
33
WBenomyl was applied at the rate of 586.5 g/ha at 14-day
intervals from 22 June 1981 to 16 October 1981.
Metalaxyl was applied at the rate of 1137 g/ha at 40-day
intervals from 22 June 1981 to 16 October 1981. Check
plots received no treatment.
One hundred seed plated onto acidified potato dextrose
agar and observed 3 to 5 days later.
y
T=total seed infection.
z ... .
Total seed infection partitioned into specific
pathogens: F =Fusarium s p p ; P = Phomo psis s p p.;
C=Cercospora kikuchii

28
(Table 12). The block by treatment interaction was
nonsignificant for the visual ratings of the pods
(P-0
.62) and
stems (P=0
.70); so the plots
were
treated
a s
an entity,
no t
as two
individual rows.
Plots
treated
with
benomy1
at
weeks
11 and 13 yielded
significantly
higher quality pods (P=0.0004) and stems (P=0.0001) than
those plots treated at planting only or not treated at
all; data are presented in Table 13. Seed from the
harvested rows were plated as described, and results
appear in Table 14. The low level of seed infection
prevented meaningful analysis.
D.) Discussion
1 .) Field Plots. 1980
The foliar diseases observed were purple stain,
frogeye leaf spot, downy mildew, target spot, and
Rhizoctonia blight. The actual amount of foliar disease
on individual plants ranged from less than 0.01% to
10.0%. The 10% disease severity was approached
immediately prior to final leaf drop.
Throughout the growing season, few individual
leaves reached a 10% disease level; generally,
senescence would occur and the leaf would be removed
from the canopy.
It was not possible to partition the

29
Table 12. Soybean seed yields from separate experiment,
1981 .
Benomy1
application^ Yield/plot (g)
Block
1
2
3
4
5
Planting
801 bZ
1243a
815
1113a
1154
Planting ,
weeks 11 & 13
1154a
999 b
877
807 b
1224
Weeks 11 & 13
798 b
836 b
956
1002ab
1083
Check
1203a
77 8 b
727
10 51ab
1242
NS NS
y
Benomyl was applied at the rate of 586.5 g/ha; the
field was planted on 15 June 1981. Check plots received
no treatment.
2
Numbers within the same column followed by the same
letter are not significantly different according to
Duncan's new multiple range test (P=0.05).

30
Table 13. Soybean pod and stem quality ratings from
separate experiment, 1981.
Benomyl w
application
x
Rating
Pod Stem
Planting
Planting,
weeks 11&13
Weeks 11&13
Check
2 ayZ
1 b
1 b
3 a
5 b
2 c
2 c
7 a
Benomyl was applied at the rate of 586.5 g/ha; the
field was planted on 15 June 1981. Check plots received
no treatment.
x
Mean of 10 ratings.
y
Numbers within the same column followed by the same
letter are not significantly different according to
Duncan's new multiple range test (P=0.05).
z
Roundoff error present.

31
Table 14. Soybean seed infection from separate
experiment, 1981.
B enomy1
application
Ty
Percent seed
F2
infectionX
P
C
Planting
03
54
23
23
Planting, weeks
11 and 13
05
55
35
10
Weeks 11 and 13
03
71
29
00
Check
03
50
29
21
w
Benomyl was applied at the rate of 586.5 g/ha;
field was planted on 15 June 1981. Check plots
no treatment.
X
Five hundred seed plated onto acidified potato
agar and observed 3 to 5 days later.
y
T=total seed infection.
Total seed infection partitioned into specific
pathogens: F=Fusarium spp.; P = Phomopsis spp.;
C=Cercospora kikuchii.
the
received
dextrose

32
senescent leaf area into disease-induced senescence and
normal senescence. The low levels of foliar disease
present throughout the growing season could have been a
direct result of the dry environmental conditions
(51-56) and may have been the reason why seed yields
from the plots were not significantly different when the
Duncan-Waller k-ratio (k=100) LSD test was used. All
yields were
high -- about 3000
kg per hectare.
Plant-port ion
dry weight s,
partitioned
into pods stems,
and seeds ,
or combined
as whole
plant s, were
not
signif icantly
different
among
treatment s.
The
nonsignificant
differences
in the
dry weights
were
expected when
seed yields
from the
plots were
not
significantly different. High variability present in
plants grown under field conditions may partially
account for the nonsignificant differences among weights
of plants from the treatments. The weight differences
were not large enough to be significantly different at
P=0.05, probably because of low disease levels.
The weather conditions for the 1980 growing season
(51-56) were not excessively conducive to spread of
foliar diseases. Foliar diseases did not cause
appreciable plant stress, and neither did water
deficiency during the growing season. Overhead
irrigation was applied three times during the growing
season. The timing of the irrigation applications

33
undoubtedly was not optimal, as soil tensiometers were
not used. No irrigation management scheme was followed,
so it would be improper to conclude that irrigation was
applied to produce optimal yields or favor disease
spread. The foliar disease levels ranged from less than
0.01% to 1.0% throughout most of the growing season and
the nonsignificant differences in seed yield of plots as
a result of fungicide treatments were expected.
The lack of a yield response as a result of disease
control manifested itself in soybean fungicide trials
conducted by others during the season (5, 19, 65, 66,
67, 83). In some reports, foliar disease levels were
not significantly different (P=0.05) for frogeye leaf
spot (65, 67), purple stain (66), or for pod
discoloration (66). Pod discoloration (67), purple
stain (67), and frogeye leaf spot (66) levels were
significantly different (P=0.05) for other tests. No
significant (P=0.05) yield response as a result of
fungicide treatment was present across most fungicide
trials during that year. Plots with treatments which
controlled diseases generally yielded better than those
plots which did not have a fungicide treatment, although
not always significantly (P=0.05). The general trend
observed was the highest control of foliar disease
provided the highest yield of plant mass. I also
observed the same trend of highest yield associated with

34
greater control of disease.
The seed yields were not significantly different
among the treatments. Treatments which received benomyl
produced stems and pods with significantly fewer signs
and symptoms of pathogens than did treatments without
benomyl. Low levels of disease were present during the
growing season but highly significant differences in the
presence of symptoms and signs of pathogens on the stem
and seed were present. The low disease levels during
the growing season resulted in low seed-infection
levels. Had more disease been present, the range of the
percent infected seed may have been wider than 10%
between seed from untreated-check plants and seed from
fungicide-protected plants. Seed from the individually
harvested plants of different treatments was infected by
fungi to varing degrees. Fungicide application reduced
the percentage of seed infection, but did not reduce the
relative importance of the pathogenic fungi. Fusarium
spp. was responsible for about 65% of the seed
infection, Phompo sis spp. for about 17%, and _C_. kikuchii
for about 15%, irrespective of the treatment. Plants
which
received
a
benomy1
treatment
, with
or
without
metalaxyl, had
8%
seed
infection,
compared
t 0
12% for
seeds
from plant s
which
had not
received
a
benomy1
treatment. The majority of pathogens cultured from the
surface-steri1ized seeds were inhibited by the presence

35
of benomyl, but the low numbers of infected seeds
precluded meaningful analyses; benomyl treatments had 4%
lower seed infection than non-benomyl treatments, but
this was considered inconsequential. Seed from plants
which received a metalaxyl treatment (with or without
benomyl) had 9% infection compared to 10% for seeds from
plants which had not received a metalaxyl treatment.
These values should be similar, because in each case,
half of the plots received benomyl and half did not.
Metalaxyl, specific-acting toward Pythiacious fungi, had
no effect on Fu sari um spp., Phomop s i s spp., or C_.
kikuchii. Metalaxy1-treated plants would not be
expected to have reduced seed infection when compared to
the untreated plants because P. manshurica will not grow
on acidified potato dextrose agar. Seed pathogens
occurred at similar ratios, irrespective of the
treatment. Pathogen escapes would be expected to occur
at similar frequencies to pathogens present in seeds
from the untreated-check plants.
2.) Field Plots. 1981
Seed yields from the meta 1axy1-1reated plots were
significantly less (k=100) than from the
benomy1-1reated, benomyl plus meta 1axy1-1reated, or the
untreated-check plots. Yields were quite low about

36
11 quintals per hectare, or 38% of the 1980 plot seed
yield. No yield response to applications of benomyl was
present in other fungicide trials during that year (63,
70, 87).
Plants from block three were not similar to plants
from the rest of the blocks. No logical explanation for
block three being completely different from the
remaining blocks was evident from field observation.
The block did not have uneven stress of water, insect,
nutritional, or disease. It is possible that block
three accurately described the metalaxyl-treated plants
and the remainder of blocks did not. When the majority
of the block by treatment interaction was removed (Table
8), the metalaxyl-treated plants were significantly
(P=0.05) larger than all the rest of the plants. It is
my feeling that the selected individual plants from the
metalaxyl-treated plots did not reflect the true
population. Metalaxyl-treated plots produced the lowest
seed yield, but the selected plants produced the highest
yields. With the exception of the metalaxyl-treated
plants, there were no significant (P=0.05) differences
present in the entire, individually harvested plants, or
when the plants were separated into pods, seeds, and
stems. These results, with the exception of the
metalaxyl-treated plants, were similar to 1980 results
of no significant (P=0.05) differences between plants,

37
or the plant parts among treatments (Table 2).
Possibly, the sample size (four) from each of the 1981
season experimental plots was inadequate to describe the
population accurately.
Again in 1981, benomy1-treated plants, with or
without metalaxyl, had significantly (P=0.05) fewer
symptoms and signs of pathogens than plants which had
not received a benomyl treatment. Seed infection levels
were low in 1981. The extremely dry weather was
undoubtedly the reason for the unusually healthy seed.
The seed infection levels for the individually harvested
plants ranged from 2% to 4% and from 1% to 7% for the
plots (Tables 10, 11). Pathogen ratios, as occurred in
1980 (Tables 4, 5), would not be expected to occur.
Small changes in raw numbers drastically change ratios
when the values are less than 5%.
In the separate experiment, selected applications
of benomyl improved pod and stem quality over that of
the controls. Yields were low, and there were no
consistant significant differences among the treatments.
However, pod and stem quality was significantly improved
with the application of benomyl. Applications around
flowering (weeks 11 and 13) provided significantly
better protection against the presence of disease
symptoms and signs of the pathogen than application at
planting or than no application at all. Flowering

38
triggers drastic physiological changes in the soybean
plant. It is possible that the period of flowering is
when the pathogens, already present in the soybean
plant, proliferate throughout the stem. If this
hypothesis is correct, it would explain why the benomyl
treatments at 11 and 13 weeks significantly improved
stem and pod quality. An experiment specifically
designed to investigate the growth of systemic plant
pathogens would have to be undertaken before any
generalizations could be drawn.
The block by treatment interaction present in the
seed yields from the separate experiment can not be well
explained. No pattern of one treatment producing higher
seed yield was present. The conclusion from this study,
under the conditions of that year (57-61), would be that
benomyl treatments did not increase yield. The
recommended benomyl treatment (2) was for applications
to be made at 11 and 13 weeks from planting. This
treatment did not produce increased yields. Benomyl
applications during years unfavorable for pathogens did
not increase seed yields (Tables 1, 6, 12), but did
significantly improve stem and pod quality (Tables 3, 9,
13). It would seem logical to conclude that seed
infection would also be reduced with benomyl
applications and result in higher stem and pod quality,
but more disease than was present for these years would

39
be needed for verification. Possibly
disease than existed in 1980 and
treatments would also improve seed yield.
, under more
1981, benomy1

IV. DESCRIPTION OF THE MODEL
A.) Introduction
Growth models exist for crops (11, 14, 15, 35, 50,
76, 88), specific aspects of crop growth (4, 16, 35,
77), or crop pest interactions (6, 11, 12, 17, 38, 44,
45, 47, 48, 61, 68, 69, 74, 81, 82). The models vary in
sophistication, accuracy, purpose, and applicability.
Growth models for soybean exist (15, 33, 50, 84, 88),
but applying the models to investigate disease threshold
levels and the disease intensity yield loss
relationship would be outside the scope of the intended
application of these models. Problems arise when a
model is used for an application for which it was not
intended.
The soybean plant growth model developed from this
work was specifically designed to evaluate disease
threshold levels and the disease intensity yield loss
relationship.
The ^x post facto approach was used for this model
for a number of reasons. The model was designed to be
exceedingly simple -- a set of regression equations.
The approach would permit easy changes from year to year
40

41
and would have wide applicability among locations.
Regression analysis is ideally suited to the ex_ post
facto approach, and large data sets can be handled
efficiently. The presence of large data sets, along
with the use of regression analysis (32) to construct a
continuous function from discrete points of a
quantitative variable, facilitated the choice of this
mathematical technique for the model.
A continuous mathematical function to describe the
biological nature of the crop or crop pest interaction
was not considered for the basic model. Holistic
experiments contain numerous uncontrolled and unmeasured
variables. Water stress, nematode infestation of soil,
soil-borne insects, and nutritional stress would be
included in the unmeasured variables. It is imperative
that these variables be included in a
biological-function model.
B.) Materials and Methods
During 1981, whole-plant samples were collected for
16 weeks, starting three weeks from the date of planting
and continuing through harvest (124 days from planting)
from a soybean field planted to breeding line F76-8846.
The disease damage and insect damage were expressed as
percent of total leaf area for each leaf. All

42
measurements were comparisons against leaf-area diagrams
and insect- and disease-rating scales developed for
soybeans (Appendix E). On each sampling date, the
above-ground plant was separated into stems, leaves,
petioles, pods, and seeds. The plant parts were dried
and weighed. The relationship between leaf area and
leaf dry weight was determined from these plants. A
separate regression equation was developed for each
dependent variable; time was used as the quantitative
independent variable, with up to 15 degrees of freedom
available for the regression equation.
The equation which described the leaf dry-matter
accumulation over time was used to drive the model. The
separate regression equations which described dry-matter
accumulation by pods, stems, seeds, and petioles at each
day, were related mathematically to the equation which
described dry-matter accumulation by leaves alone. The
relationship was strictly a ratio. The ratios of stems
: leaves, seeds : leaves, pods : leaves, and petioles :
leaves were established for each day of the model. The
equation which described leaf dry-matter accumulation
over time produced stems, seeds, pods, and petioles,
varing in dry-matter accumulation proportional to leaf
dry-matter accumulation. Problems associated with
mathematical descriptions of biological data were
handled as they arose. Dry matter of the plant organs

43
was not permitted to be negative, it was set to zero
when this condition occurred. No dry weight was
accumulated for seven days after planting. This time
period was reserved for seed germination and seedling
emergence.
C.) Results
The linear relationship between leaf area and leaf
dry-matter (Fig. 1) was highly correlated (r= 0.97).
The dry-matter accumulation of stems over time was also
well (r=0.89) described by a straight line (Fig. 2).
The dry-matter accumulation of seeds over time was
described by a cubic equation with an associated r =
0.94 (Fig. 3). The dry-matter accumulation of pods over
time was described by a quadratic equation with an r =
0.89 (Fig. 4). The dry-matter accumulation over time of
petioles and leaves was described by separate cubic
equations with r = 0.87 for petiole (Fig. 5) and r =
0.89 for leaf dry-matter accumulation over time (Fig.
6). The dry-matter accumulation for whole plants over
time is presented in Fig. 7, where a linear equation
with an r = 0.89 described the response. Values of r =
0.48, 0.61, 0.72 corresponded to P = 0.05, 0.01, 0.001
for 15 degrees of freedom (42).

Fig. 1. The dry-matter accumulation for soybean leaves of known area over time.

LEAF AREA (cm2)
45

Fig. 2.
The dry-matter accumulation for soybean stems over time.

47

Fig. 3 .
The dry-matter accumulation for soybean seeds over time.

22
20
I 8
I 6
14
I 2
I 0
8
6
4
2
0
49
SEEDS
9 = -3.447 +0.2767x 0.00644x 2
+ (4.444* 10"5)x3
Rz = 0.88
20 40 60 80 100 I 20
TIME (days)

Fig. 4 .
The dry-matter accumulation for soybean pods over time.

51

Fig. 5 .
The dry-matter accumulation for soybean petioles over time.

DRY WEIGHT (g)
53
TIME (days)

Fig 6 .
The dry-matter accumulation for soybean leaves over time.

55
TIME (days)

Fig. 7. The dry-matter accumulation for entire soybean plants over time.

57
TIME (days)

58
Figures 2 through 7 represent the positive
dry-matter accumulation over time and associated
coefficients of determination for soybean plant organs.
When a mathematical equation described negative
dry-matter accumulation, the dry matter was set to zero.
The model had a flexible harvest date, determined by the
progression of leaf dry-matter accumulation, but
generally was run 123 or fewer days from sowing.
D ) Pis cus sion
To have a soybean model driven by leaf dry-matter
accumulation over time seems a reasonable approach, as
leaves produce photosynthate to fill pods and seeds and
to grow stems and petioles. Shibles and Weber (72, 73)
have reported soybean dry-matter accumulation was
proportional to leaf area. The proportionality of
dry-matter accumulation to leaf area is not unique to
soybeans. Allen and Scott (1) described a linear
relationship between dry-matter accumulation in potato
and interception of solar radiation; interception of
solar radiation was proportional to leaf area. Peanut
canopies under various disease and insect stresses had a
linear leaf area to leaf dry-weight relationship; LAI
values from the work ranged from 0.32 to 3.55 (9).

59
The described model is not intended to be an
all-encompassing
model,
as others
have attempted (50).
The regression
equations
are not
intended to
be viewed
as stimulus
-
response
situations
. The flow
chart for
this model
(Fig. 8) is
simp 1e
and readily
adaptable
compared to
SOYMOD (50)
or SIMED
(35). Changes in the
regression
coefficient s ,
or in the
regression
equations,
can describe
different
soybean
varieties ,
different
locations,
or
different
years (Figs. 9, 10). This
flexibility
is
desirable
in the
basic framework of a
model.
The time reserved for seedling emergence can be
easily changed to more or less than seven days. This
parameter would be location dependent. The seven days
for seedling emergence for northern Florida climatic
conditions was adequate. The model could be refined to
have the time required for seedling emergence linked to
soil temperature and moisture or planting date. This
refinement would be better than setting the time as a
fixed value. Plant dry weight was not permitted to be
negative, as a negative measurement of dry weight is
biologically meaningless. The regression equations were
continuous with respect to the time variable. This,
along with the equations not intending to describe a
biologic phenomenon but to explain a phenomenon, can
lead to negative values. Time was continuous in the

Fig. 8. Flow chart of the soybean growth model (N = number of days; 0 rate of
change).

61
END

Fig. 9. The dry-matter accumulation for soybean leaves, converted from leaf area
(Fig. 1), from individually harvested plants over time, 1980.


Fig. 10. The dry-matter accumulation for soybean leaves, converted from leaf area
(Fig. 1), from individually harvested plants over time, 1981.

9

66
equations and days were integers in the model; dry
weight can increase from 0.0 g to 0.03 g or higher in
one day. Linear extrapolation to zero was performed on
the four days previous to measurable dry-weight
appearance (and disappearance) to smooth out the curve.
The adjustment did not affect the performance of the
model; the model-derived curves more closely represented
the biology of the system. The model was set to run 123
days from planting. The time duration was set by the
equation describing the leaf dry-weight accumulation;
the soybean fields under intensive study for two
consecutive seasons were harvested 123 and 124 days
after sowing.
The correlation coefficients and the coefficients
of determination were not 1.00 for any of the regression
equations. The field data may be biased, which would
produce a 1ess-than-perfect fit. The field data may not
be accurate or may not accurately represent the actual
plants, again introducing bias. Random variation, a
common obstacle with field data, likely accounts for
most of the variation. Had the correlation coefficients
been less than 0.80 or the coefficients of determination
less than 0.60, some concern as to whether' the
regression equations accurately described the field data
might be warranted. The data were well fitted by the
presented equations (Figures 1 7).

V. VALIDATION AND VERIFICATION OF THE MODEL
A.) Introduction
Validation is a continuing process; a model is
really never finished, it can always be improved,
adjusted, and expanded. Validation is the application
of the model to conditions different from those under
which the model was developed. The different conditions
can range from different plants to different hosts,
depending on the type of model. Validation data for
this model are from different plants of the same
cultivar, different growing seasons, and different
soybean cultivars. The soybean cultivar, soil type,
general
cultural practices (fertilization, insect
control,
disease control, cultivation) remained
unchanged
between the two seasons. Host growth
differences (Figs. 9, 10; Tables 2, 7), seed yield
differences (Tables 1, 6), differences in disease
intensity
(Tables 3, 9), and incidence (Tables 4, 5, 10,
11) can
be crudely attributed to weather conditions
(51-61) .
Far more validation data than appear here are
to discern which specific parameter(s) are
needed
67

68
responsible for yield and disease differences. This
type of further refinement could take many, many growing
seasons to substantiate.
Verification must be performed on the model.
Verification assures the model properly mimics the
biological system under one set of conditions, namely,
the set of conditions under which it was developed.
Futher model verification with published data from
literature is useful. Often, published data are the
sole source for physiologically-based models. Because
of the nature of this model, published data did not aid
in the development or adjustment of the model, they only
verify that data used to develop and validate the model
were similar to published data.
B.) Materials and Methods
The soybean growth model was validated with 200
data sets from 1980 and 80 data sets from 1981; all 280
data sets were independent of the data set used to
develop the model, but were the same soybean cultivar.
The validation data sets consisted of nondestructive
leaf-area measurements throughout the growing season and
final measurements of dry weight for above-ground plant
parts. The final measurements were destructive. Leaf
area was converted to leaf dry matter (Fig. 1). Leaf

Fig. 11. Mode1-predicted versus actual dry-matter accumulation for seeds, 1980.

PREDICTED DRY MATTER (g)
0 10 20 30 40
ACTUAL DRY MATTER
(g)

Fig. 12. Model-predicted versus actual dry-matter accumulation for stems,
1980 .

PREDICTED DRY MATTER (g)
72
(g)

Fig. 13.
Model-predicted versus actual dry-matter accumulation for pods, 1980

PREDICTED DRY MATTER (g)
(g)

Fig. 14. Model-predicted versus actual dry-matter accumulation for seeds, 1981.

PREDICTED DRY MATTER (g)
76
ACTUAL
DRY MATTER
(g)

Fig. 15. Model-predicted versus actual dry-matter accumulation for stems, 1981

>
PREDICTED DRY MATTER (g)
00

Fig. 16. Model-predicted versus actual dry-matter accumulation for pods, 1981.

80
ACTUAL DRY MATTER
(9)

81
dry matter was regressed on time, with up to 15 degrees
of freedom available for time, the independent variable.
The resultant regression equation was used to drive the
model (Fig. 8). The model predictions of final dry
weight of the plant portions were compared against the
measured data (Figs. 11-16).
Weekly nondestructive measurements of leaf area and
disease incidence and severity were recorded for each
leaf of five randomly selected soybean plants, variety
Cobb, and five randomly selected soybean plants, variety
Bragg. The plants were grown under overhead irrigation,
with a water management scheme directed toward zero
water stress (L. Hammond, personal communication). At
maturity, the individual plants were harvested and the
dry-weights for pods, seeds, and stems were measured.
The accuracy of the model was verified with
published data (43, 72, 73, 78, 79). Published
regression parameters and agronomic values such as slope
of dry-matter accumulation of plant portions, dry-weight
ratios between plant portions, and dry-matter
accumulation for the plant parts were compared against
model predictions.

82
C ) Results
Validation data of model-predicted versus actual
yield of stems, pods, and seeds for 1980 are presented
in Figs 11-13. Model-predicted versus actual yield for
1981 appear in Figs. 14-16. Not all growth simulations
were ceased on the same day. Since the plants were
harvested at 123 or 124 days from planting,
theoretically, the growth simulations should cease on
the same day.
Final plant-portion dry-weight ratios for Cobb and
Bragg soybean varieties, grown under an intensive
overhead irrigation scheme, are presented in Table 15.
Generally in the literature, instead of the profile
of an entire growing season, sections of the growth
curve for plant organs were analyzed where their growth
was linear. The seed dry-matter accumulation was
analyzed after 83 days from planting, where a linear
equation accurately fitted the data. When my data were
treated similarly, analyzing from day 83 through day
123, the slope coefficient for the simulated data was
0.42, for the raw data was 0.45, and was 0.41 (Table 16)
for the published data (28). The pod dry-matter
accumulation over time also could be described by a
linear equation, when 77 days from planting through
harvest were analyzed. When my data were treated

83
Table 15. Harvested above-ground plant dry matter
proportioned into seeds, stems, and pods for two soybean
cultivars 1981.
Soybean cultivar
Bragg
Cobb
z
Mean of three plants.
Plant
portion
(%)Z
Seeds
Stems
Pods
52
33
15
53
34
13

84
Table 16. Published values, model predictions, and 1980
and 1981 raw data for the same parameters.
Whole-plant
Parameter Published Simulated Raw 1980 1981
z
Seed
dry-mat ter
accumulation
(g/day) 0.41-0.47
Pods2
dry-mat ter
accumulation
(g/day) 0.19
Seed:Pod
dry-mat ter
ratios 2.47-2.63:1 -- 2.56:1 2.27:1
Seed:stem
dry-mat ter
ratios 1.53-1.59:1 1.50:1 1.66:1
0.42 0.45
0.11 0.11
^After day 86.
2
After day 77.

85
similarly (analyzing 77 days from planting through day
123, harvest), my slope coefficient for the simulated
and the raw data was 0.11, compared to 0.19 for the
published value (28). The final ratio of seed:pod
dry-matter for 1980 was 2.56:1. Published values range
from 2.47:1 to 2.63:1 (Table 16) for commercially-grown
soybean varieties in the United States (22, 28,); the
1981 seed:pod dry-matter ratio was 2.27:1. The final
ratio of seed:stem dry-matter for 1980 was 1.50:1,
compared to published ratios of 1.53:1 to 1.59:1 for
commercially-grown soybean varieties (28); in 1981, the
ratio was 1.66:1 (Table 16). The 1980 to 1981
variations in final plant dry-matter ratios were
reflected in the proportions of plant dry-matter ratios.
For 1980 and 1981, 49% of the final-plant dry-matter by
weight was seeds, 19% was pods in 1980 compared to 22%
in 1981; 32% was stems in 1980 compared to 29% in 1981
(Table 17). The higher percentage of pods and lower
percentage of stems in 1981 were reflected in a lower
seed:pod dry-matter ratio and a higher seed:stem
dry-matter ratio.
D.) Discussion
The model predictions of final dry matter for seeds
(Figs. 11, 14), pods (Figs. 12, 15), and stems (Figs.

86
Table 17. Harvested, above-ground, soybean plant
dry-matter proportioned into seeds, stems, and pods for
two seasons .
Season
Plant
portion
(%)
Seeds
Stems
Pods
1980y
49
32
19
1 981z
49
29
22
yMean of 200 plants,
^ean of 80 plants.

87
13, 16) were well within a reasonable range, especially
considering cumulative error. The leaf area to leaf
dry-matter equation had 94% of the variation in the data
explained by the linear relationship (Fig. 1), leaving
6% as unexplained error. A linear relationship between
leaf area and leaf dry matter for soybeans (39) and for
alfalfa (64) has been published. Likewise, the stem,
pod, and leaf dry-matter accumulation equations have 79%
of the variation in the data explained (Figs. 2, 4, 6),
leaving 21% of the variation as unexplained error. The
seed dry-matter accumulation had 88% of the variation
explained by the relationship (Fig. 3), leaving 12% as
unexplained error. Thus the model-predicted dry-matter
accumulation for
seeds
starts with
18% (6%
+
12%)
absolute
error.
The
model-predicted pod
and
stem
dry-matter
accumulation
starts with
27% (6%
+
21%)
absolute
error ,
and
have whatever
portion
of
the
unexplained error the leaf area equations contain in
addition. Clearly, one can rapidly increase the error
to over 100%. The error mentioned is absolute error.
The 27% error could be as low as 15% if the 6% leaf area
to leaf dry-matter accumulation error cancels a portion
of the 21% error of the pod or stem dry-matter
accumulation. The leaf area equation (Figs. 9, 10)
added to this could possibly cancel the 21% completely,
or add completely to it. Obviously, the cumulative

88
error must be followed, but no cause effect
relationship can be assessed to the cumulative error.
The final plant-portion dry-matter ratios from Cobb
and Bragg soybean cultivars (Table 16) were similar to
the ratios obtained from plants used in model
verification (Table 17). In view of this evidence,
using ratios, updated daily, to produce growth of stems,
seeds, and pods in the model is a reasonable approach.
The seedistem dry-matter ratio for Cobb and Bragg
soybean cultivars (Table 18) was very similar to the
ratios obtained for a different soybean cultivar grown
under different conditions (Table 16), and also similar
to published ratios of totally different soybean
cultivars (28). The seed:pod ratio from the Cobb and
Bragg soybean cultivars (Table 18) were much higher than
published ratios (22, 28) or the ratios from another
soybean cultivar (Table 16) grown under a less intensive
water management scheme. Again, the pod dry-matter
accumulation, as discussed earlier, may be more
sensitive to environmental changes, which includes
water, than are the seeds or the stems.
The slopes from the linear equations describing the
seed dry-matter accumulated (Table 16) for the
simulation and published data (28) were similar (0.42,
0.41), but the Y-intercepts were not (0.43, 1.61). I
interpret the Y-intercept to be location dependent,

89
Table 18. Final plant dry-matter ratios for two soybean
cultivars, 1981.
Dry-matter rato
Soybean cultivar2
Bragg Cobb
Seed:stem
Seed:pod
1.57:1 1.59:1
3.43:1 4.08:1
z
Mean of three plants.

90
variety dependent, maturity group dependent, or perhaps,
planting date dependent. The slope, in grams per day
(after day 86), of the seed dry-matter accumulation is
not influenced by, for instance, location, as much as
the Y-intercept. Soybeans grown in northern United
States would not be expected to initiate seed dry-matter
accumulation, measured by the Y-intercept, at the same
time as soybeans grown in the southern United States.
Similarly, soybeans planted in northern United States
are included in different maturity groups than those
planted in the southern United States. The soybeans
included in northern maturity groups would be expected
to initiate dry-matter accumulation at a different
number of days from planting, which is again measured by
the Y-intercept. Weather would also be expected to
influence the seed dry-matter accumulation. I
hypothesize that weather would influence the slope of
the dry-matter accumulation curve, but not the
Y-intercept. Only drastic differences in
photosynthetica1ly-active radiation, water availability,
or ambient temperatures would cause notable changes in
the seed dry-matter accumulation slope to occur. The
linear relationship between seed dry-matter acculumation
and time (after flowering) has also been previously
reported (8, 20, 21).

91
The slope of pod dry-matter accumulation from this
study (0.11) was different from a previously
reported(28) slope of pod dry-matter accumulation
(0.19). My Y-intercept (-1.21) for pod dry-matter
accumulation was also different from the value I
calculated from published data (-2.92). I expect pod
dry-matter accumulation to be influenced by the same
factors that influenced seed dry-matter accumulation.
Had Hanway and Weber (28) included data points between
70 and 75 days from planting in regression (which were
omitted), the slope for the pod dry-matter accumulation
curve would be lower than 0.19, perhaps even close to
0.11. The Y-intercepts also may be closer to the ones I
found with these data points included in the regression.
The coefficient of determination for the published pod
dry-matter accumulation curve (28) is 0.92; including
data points between days 70 and 75 in the regression
analysis will lower the coefficient of determination as
well as the slope. Any damage to the pods by insects or
plant pathogens, which was present in published studies
and was different from what was experienced in my
studies, would account for some variation between the
slopes of the pod dry-matter accumulation.

92
The linearity of the entire plant (sum, Fig. 7) has
also been previously reported (31, 71).
The 1980 final dry-matter ratio for seeds :pods was
similar to published values (28), but the 1981 ratio was
not. Weather conditions much different from those in
1980 prevailed during 1981; there was more water and
more photosynthetica1ly-active radiation during the 1980
growing season than during the 1981 growing season
(51-61). The environmental conditions which prevailed
in 1980 more closely resembled the long-time averages
than did the 1981 environmental conditions. The 1980
environmental conditions can then be considered more
"normal," or closer to "normal" than the 1981
environmental conditions. As expected in the seed:stem
dry-mat ter
ratios,
the
1980
data were similar to
published
data, and
the
1981
data are not. Again,
environmental conditions were different during the two
seasons.
The seeds were the same proportion of the total dry
matter for both the 1980 and the 1981 growing season.
This further supports the rate of seed dry-matter
accumulation being relatively unaffected by
environmental changes. Had the 1980 to 1981
environmental variation been more pronounced, the seed
proportion of the final plant dry-matter ratio may have
been lower. Environmental conditions responsible for

93
lowering the seed proportion of final plant dry-matter
ratio would probably also cause the slope of the seed
dry-matter accumulation curve (from day 86 through
harvest) to be different from 0.42. The increased
proportion of final ratio of pods during 1981 (3%
increase over 1980) may account for the decreased slope
and increased Y-intercepts over the published values.

VI. APPLICATIONS FOR THE MODEL
A.) Introduction
A model is a simplified representation of a system.
The primary purpose of a model is to be applied to the
system, to interpret changes, be they growth, abiotic
pressures, or biotic pressures. The models can then be
used to predict the effect these changes have on final
plant yield or final level of biotic stress. The actual
parameters that are predicted, and the influences which
these parameters have
on
the
system,
are dependent
on
the intended purpose
of
the
model,
the choice
of
modeling techniques,
and
the
individual modeler.
The
intended purpose of this model of soybean growth was to
be a disease intensity yield loss model. The ex post
facto approach coupled with regression analysis was
ideally suited to the development of a basic model. The
separation of plants into pods, stems, seeds, and leaves
permitted the flexibility for stress to be directed to
individual plant portions, or to the entire plant. The
accumulation of leaf dry-matter (related to leaf area,
Fig. 1) drove the model, with the reasoning that the
leaves supply the plant with carbohydrates. The
94

95
reduction in leaf area by foliar diseases or by
foliage-feeding insects (velvetbean ca11erpi1 lar ,
Anticarsia gemmatalis Hubner ; green cloverworm,
Plathypena scabra Fabricus; soybean looper, Pseudoplusia
includens Walker) would result in directly reducing the
product ion
of carbohydrates.
The
reduction
in
carbohydrat e
production would
cause
reduction
in
dry-matter
accumulation in stems,
seeds,
and pods.
The
southern green stink bug (Nezara viridula L.) pierces
the soybean pod and destroys the seed within the pod. A
specific equation to reduce the seed dry-matter
accumulation dependent upon the numbers of southern
green stink bugs could be developed and incorporated
into the seed dry-matter accumulation equation.
Subtraction of damaged seed would give a resultant yield
loss associated with various levels of this insect.
Similarly, the intensity of non-foliar diseases such as
pod and stem blight or anthracnose could be incorporated
into the model. The disruption of the normal growth
process in the stem, pod, and seed could be quantitated,
and the resultant terms introduced into the equations
for dry-matter accumulation. Mathematical separation of
dry-matter accumulation for seeds, stems, and pods
permitted each individual plant portion to be weighted
differently for pathogen intensity yield loss
reduction. Undoubtedly, different equations would be

96
invo1ved
for
stems, seeds,
and pods.
The pathogen
intensity
in
the
seeds could
be related to
the intensity
in the
pods
, which could,
in turn, be related to the
intensity
in
the
stems.
The following
uses for the
soybean
growth
model
are strictly
hypothetical;
pertinent
data
to verify
the uses have not been
collected

B.) Uses For The Model
1.) Foliar Pathogens
In
the
model, attack
by
foliar
pathogens can be
simulat ed
by
removal of
leaf
area
representative of
pathogen
damage. Since
leaf
area
drives the model,
reduced
leaf
area would cause a
reduction in dry-matter
accumulation by seeds, stems, and pods. However, the
intensities of the foliar disease in my field
experiments over two years did not cause a decrease in
dry-matter accumulation. The presence of low levels of
disease without a statistically significant change in
yield is an example of a disease threshold phenomenon:
a specific level of disease must be present before a
significant change in yield is detected. The influence
of foliar diseases on yield could be modeled several
ways. The disease progress data could be to fit to a

97
continuous curve and the equation which described the
curve used to remove leaf area from a leaf-area
equation. A second approach would be to use the
equation which described the disease progress data to
add dry matter to the leaves. This addition would
permit calculation of the theoretical yield which may
have been produced in the absence of disease. Downy
mildew disease progress data from 1980 (37) were fitted
to a Gompertz (3) equation (Eq. 1)
Yi= Ymax exp(-b exp{-k T}) (Eq. 1)
Yi= disease at time i
Ymax= maximum disease
Yo= initial disease
b = -ln(Yo)
k= epidemic rate
T= time
using a nonlinear, least-squares estimation routine.
Epidemic rates (k) were solved with initial disease and
maximum disease severity held constant (Yo = 0.00001 ;
Ymax=0.02) {37}. The Gompertz equation was used to
mathematically remove leaf area from the plant. No
major differences in dry-matter accumulation from the
low disease levels occurred. Foliar diseases other than
downy mildew could also be handled in this way. A large
range of disease intensities, including intensities
higher than measured in this study, are necessary to

98
verify
and validate this
approach
to describe
the
disease
severity
yield
loss
relationships.
The
incorporation of
equation
1 into
the
flow chart of
the
soybean growth model is presented in Fig. 17.
2.) Above-ground Non-foliar Pathogens
Pod
and stem
blight
and anthracnose
did
not
regularly
appear
on the
leaves
, so reduction
of
dry-mat ter
accumulation by
these
pathogens
mus t
be
ac comp 1ished
in a way
other
than removing leaf
area ,
the
driving force of the model. One approach would be to
remove dry-matter accumulation of the stems, pods, and
seeds, dependent upon a visual rating of the stems and
pods at harvest. Equation 2 would accomplish the dry
matter reduction.
R= (S**3 / Smax**3) M (Eq. 2)
R= percent reduction in plant
dry-matter accumulation
S= average of stem and pod rating
(based on percent infection) at harvest
M= maximum percent dry-matter reduction
by pod and stem blight and anthracnose
Smax= maxmium pod and stem rating possible
Reduction in dry-matter accumulation (R) would be
removed from the seed, stem, and pod weight. The cube

Fig. 17. Incorporation of a fo 1iar-disease submodel into the soybean growth model
(Fig. 8).

LEAF AREA

101
of the mean plant quality rating (S) divided by the cube
of the maximum quality rating is suggested to mimic
observations from the field that the most infected
plants in a field yield the smallest amount of dry
matter, but not on a 1:1 relationship between percent
infection and reduced yield. Often, moderately infected
stems and pods yield as much plant dry matter as clean,
or nearly clean plants. The cubic-shaped curve would
remove proportionally more dry-matter accumulation at
higher percent disease than at lower percent disease.
The maximum percent dry-matter reduction (M)
attributable to pod and stem blight and anthracnose
would have to be determined experimentally. The purpose
of {M} is to place a limit on the amount of damage
attributable to these type of plant pathogens. It is
very possible that {M} may change from season to season,
dependent upon the environmental conditions. A
reasonable value for {M} would be <15%.
Similarly, seed quality (as opposed to quantity,
above) could be evaluated with equation 3.
Q= (S**2 / Smax**2) P (Eq. 3)
Q= reduction in seed quality
S= average of stem and pod rating (based
on percent infection) at harvest
P= maximum quality reduction by pod
and stem blight and anthracnose
Smax= maximum pod and stem rating possible

102
The reduction in seed quality (Q) could be a measure of
field emergence, or a combination of germination before
and after accelerated aging, field emergence, and
electrolyte conductivity. For these purposes, the
specific measure of seed quality is unimportant. The
squared mean plant quality rating (S) divided by the
maximum quality rating squared would likely yield a more
representative curve than a cubic equation for seed
quality. Any infection, evidenced by symptoms and signs
of pathogens on the stems and pods, could lead to seed
infection and reduced seed quality. However, the higher
the disease severity, the better the chance that the
infection has reached the seed, hence the squared term
to describe this type of relationship. The maximum
quality reduction (P) would have to be determined
experimentally. By whatever means used to measure {Q},
be it
on
a
scale
of 0
to 25 or
in
percent
, {P} would
also
have
to
appear
in
the same
form. An
appropriate
value
for
{P>
could
be
100% of
the
scale used, with a
much delayed harvest. Under normal conditions, 20% of
the range of the {S} scale would be a reasonable value.
The seed quality reduction from infection by pathogens
would be difficult to separate from physiological
decline, and both may have to be included in equation 3.
A factor multipled by the number of days after the

103
optimal ripeness that the seed was harvested would
accommodate this change. The incorporation of equations
2 and 3 into the flow chart of the soybean growth model
is presented in Fig. 18.
3.) Soil-borne Pathogens
Yield losses caused by soil-borne pathogens would
be difficult to incorporate into the present form of the
model. Soybean root growth was not used in the model.
Yield losses resulting from soil-borne diseases need to
be handled with a root submodel. A model of fusarium
root rot has been published (6, 7); a similar model
would be adequate for soybeans. In keeping with the ex
post facto nature of the model, root growth could be
incorporated in a way similar to the stems, pods, seeds,
and petioles. Ratios from published curves of
dry-matter accumulation for roots and leaves (50) could
be extracted, and added to the existing model. The root
model would not alone explain the pathogen root
system. In continuing this approach, attack by
soil-borne pathogens could be simulated using the Monte
Carlo method (27). Severe attack by, for instance,
Fusarium spp., kills the individual plant. The
percentage of plant-kill, determined by the severity of
soil infestation by Fusarium spp.,
could be removed from

Fig. 18. Incorporation of an above-ground, non-foliar disease submodel into the
soybean growth model (Fig. 8).

105
DRY MATTER

106
yields of a specified area. The soybean plant has the
ability to compensate for missing plants to a certain
degree (78). Compensation by the soybean plant would
have to be investigated more intensely and inoculum
density disease intensity relationships defined for an
accurate description of loss attributable to soil-borne
pathogens to become a reality. The incorporation of
soil-borne diseases into the flow chart of the soybean
growth model is presented in Fig 19.
4.) Foliage-feeding Insects
A comprehensive model which mathematically
describes the growth of the velvetbean caterpillar has
been developed and validated (48, 49). This latter
model, as any model, is not perfect, and has limitations
as noted (48). The model could be directly linked to
the soybean growth model to remove leaf area consumed by
velvetbean caterpillar. An aspect not incorporated into
the velvetbean caterpillar model (48) was insecticide
application, which could be easily handled by
introduction of an insect mortality factor for each
chemical used. The incorporation of foliage-feeding
insects into the flow chart of the soybean growth model
is presented in Fig. 20.

Fig. 19. Incorporation of a soil-borne disease submodel into the soybean growth model
(Fig. 8).

^START^
SOIL-BORNE
PATHOGENS
-K>
AAAaAAA/

foliage-feeding insect submodel into the soybean growth
Fig. 20. Incorporation of a
mode 1 (Fig. 8).

LEAF AREA
WVWV\
LEAF AREA INSECT MORTALITY

Ill
5.) Seed-feeding Insects
Southern green stink bug is the major seed-feeding
insect which annually causes damage in soybean fields.
Damage this pest causes could be described by equation
4.
D= I (T-86) 0.42 Y Z + 0.43 (Eq. 4)
D= reduced dry-matter accumulation by the seed
1= insect population per area
T= time from planting in days
Y= number of seed destroyed per insect per day
Z= dry-matter weight of one seed
Reduced dry-matter accumulation by seed (D) is removed
directly from the accumulation of any one day after 86
days from planting. Eighty-six days from planting is
suggested as a reference point because this is where a
published linear equation describes the seed dry-matter
accumulation (28), and my data (Table 15) are in good
accord. Appearing in equation 4 is a 0.42 factor which
describes the plant dry-matter accumulation per day for
the seeds after 86 days from planting, in grams. Also
appearing in equation 4 is a 0.43 factor added for the
Y-intercept value, in grams, from the linear equation
(Table 15). The number of seed destroyed per insect per
day (Y) would have to be determined experimentally. The

112
dry-matter weight of one seed (Z) is important to keep
the equation to scale. The scaling permits removal of
numbers of destroyed seed, not percentage of destroyed
seed. The insect population per area (I) can be
determined from "row shakes" a standard sampling
procedure for entomological studies. However, the
equation is such that the insect population would have
to be updated daily after day 86 from planting. Daily
sampling to describe southern green stink bug
populations is not practical, so an approach similar to
the velvetbean caterpillar model (48) could be used.
The insect growth from egg through instars to adult is
modeled for velvetbean caterpillar (48). The same
model, with modifications, could be used to update daily
the southern green stink bug populations. Modifications
would be necessary for differences in growth stages and
respective damage caused by each growth stage between
southern green stink bug and velvetbean caterpillar.
Again, an insecticide submodel could be easily
incorporated. The incorporation of equation 4 into the
flow chart of the soybean growth model is presented in
Fig. 21.

Fig. 21. Incorporation of a seed-feeding insect submodel into the soybean growth
mode 1 (Fig. 8) .

114
>
INSECT
MORTALITY

115
C.) Results
Results are described only for those applications
which appropriate data were collected from my field
experiments. Data on foliar diseases and above-ground
non-foliar plant pathogens (causing quantity and quality
losses) are included in this section.
Foliar disease levels were very low throughout the
1980 and the 1981 growing seasons. Equation 1
parameters of Ymax = 0.02, Yo = 0.00001 and k=0.0294
(actual data {37}), decreased the dry-matter
accumulation for seeds, stems, pods, petioles, or leaves
only 0.07%. When the plant seed yield was converted to
bushels per acre, there was no significant difference at
the 5% level. The maximum disease severity was 2%, and
yield differences were nonsignificant at the 5% level
(37). A threshold level of disease was not taken into
consideration per s e in equation 1, but low levels of
disease do not reflect a change in the final yield. If
all the disease parameters (Ymax, Yo, and k) were
increased, more seed yield loss would occur, which would
simulate a more severe epidemic. An adequate range of
disease severities would have to be present to calibrate
the foliar-disease submodel.
Dry matter is removed proportional to the cube of
the quality rating of the stems and pods (Eq. 2). When

116
rated on a scale of 0 to 10, the 1980 growing season
mean pod and stem quality rating was 3 for
benomy1-treated plots, and 8 (roundoff error present)
for non-benomy1-treated plots (Table 3). If the maximum
dry-matter loss to above-ground, non-foliar, plant
pathogens was 15%, there would be 7.3% more seed yield
lost in the non-benomy1-treated plots when compared to
benomy1-treated plots (7.3% = {1 ({3**3 / 10**3} *
.15)} {1 ({8**3 / 10**3} .15)}, roundoff error
present). Similarily, in 1981, there would be a 2%
increase in yield with mean pod and stem quality ratings
of 1 and 5 for benomyl-treated and non-benomy1-treated
plots (Table 9).
The quality of seed harvested is reduced,
proportional to the square of the mean pod and stem
quality rating (Eq. 3). Primarily, {Q} is a measure of
how appropriate the harvested seed would be for
planting. If the maximum quality loss from
above-ground, non-foliar, plant pathogens would be 20%,
there was a 11% reduction in quality in 1980 (11% = {1 -
({3**2 / 10**2} .20)} {1 ({8**2 / 10**2} .20)}).
Mean pod and stem ratings of 1 for benomyl-treated and 5
for non-benomy1-treated plots in 1981 (Table 9) would
reflect a 5% reduction in quality from the
non-benomy1-treated plots when compared to the
benomyl-treated plots.

117
D ) Discussion
Any of the proposed submodels can be linked to the
soybean growth model mathematically by either
subtraction or multiplication. This ease of application
makes the model and submodels attractive for a basic
framework. The disease severity was not high enough to
test the foliar disease submodel or to determine injury
threshold levels. There are published reports involving
defoliation levels and yield reductions (9, 13, 17, 25,
26, 34, 36, 37, 40, 41, 43, 46, 80, 81, 85, 86). Many
of the reports involve non-pathogen-induced defoliation
and consequent yield reduction (9, 25, 26, 34, 46, 80,
81). The studies on defoliation and yield reduction
lacked adequate spacing of treatments and lacked
accurate quantitation of defoliation levels (9, 25, 26,
34, 46, 80, 81). The unfortunate results of these
shortcomings in experimental design are that these data
cannot be
used to
test
or modify the foliar
disease
submode 1,
and
the
threshold level
for
defoliation-
induced
loss
cannot be extracted
. As
previously mentioned, the threshold level for loss from
disease cannot be extracted from my work, owing to
inadequate disease. As previously mentioned, a
threshold level for disease has not been considered in

118
equation 1. Incorporation of the disease threshold in
Fig. 17 would consist of: a value, where below, say 4%
disease, no yield loss would occur. The rate of yield
loss from disease may change with the amount of disease
present. For instance: yield loss may occur at rate
"a" for each increase in from 4-9%; from 10-15% disease,
yield loss may occur at rate "b" for each increase in
disease ;
from
16-24% disease
, yield
loss
may
occur at
rate "c"
for
each increase
in disease ;
and
above 25%
disease ,
yield
loss may occur at
rate
"d"
for each
increase
in
disease. In
addition
to
the
disease
threshold, there is an economic threshold (30), where
disease control would become economically feasible.
Detailed discussion of economic thresholds is beyond the
intended scope of my work, but one can easily see where
this concept could be incorporated into the foliar
disease submodel. A mortality factor for the pathogen,
specific for the type of control agent used would be
assigned, as well as a cost factor; when the cost of
yield reduction (at any assigned market price) is higher
than the cost of the control measure, then control is
economically feasible.
Another problem exists in the artificial
defoliation studies. There is no reasonable method for
extrapolating yield reduction caused by
non-pathog en-induced defoliation (insect-induced,

119
artificial, herbivor-grazing, etc.) to yield reduction
caused by pathogen-induced defoliation. The yield loss
caused by plant pathogens is greater than the loss
casued by reduction in leaf area equivalent to that
which the pathogen has destroyed. The plant pathogen is
a living system, and is invading another living system,
the plant. In destroying all or portions of a plant the
pathogen kills plant cells and consumes their contents.
The action of plant invasion by the pathogen can upset
the host physiology in localized areas, and possibily in
the entire host. This disruption of physiological
processes causes more yield loss than would the
disruption of processes which would occur from manually
defoliating a plant at the same level of foliage loss.
The low levels of disease present for my studies
did not permit evaluation of the above-ground,
non-foliar plant pathogen submodel. Statistical tests
at the 5% level can measure the 7.6% difference in seed
yield (Eq. 2). No significant differences as a result
of benomyl applications were described using a
Duncan-Waller k-ratio test (k=100) {Table 1}; however,
Duncan's new multiple range test, a less conservative
test, did separate seed yield into significantly
different classes. The more conservative test was
chosen (Table 1) because of the variation inherent in
field situations. Environmental conditions differed

12Q
between 1980 and 1981, which, in part, would explain why
in 1981, there was only a 2% difference (Eq. 2) in seed
yield. A statistical analysis at the 5% level would not
describe a difference between two numbers 2% apart under
these circumstances. The reduction in quality of seed
as a result of above-ground, non-foliar, plant pathogens
cannot be evaluated with my data. As previously
mentioned, pathogen activity would only be partially
responsible for seed quality reduction. A major portion
of the reduction in quality would be physiological
deterioration, partially or wholly independent of seed
pathogens .

VII. SUMMARY
The soybean growth model described herein allows
the researcher to test yields of soybean plants of
different sizes and growth habits, and plant response to
change in populations of pathogens. The model is
intended to be a basic framework for the development of
disease intensity yield loss relationships for
soybean.
The soybean growth model was developed from two
years of intensive field studies. Included in the
experiments was a fungicide with specific action toward
one soybean pathogen and a second fungicide with
activity against most other soybean pathogens.
Validation of the soybean growth model was
performed with data sets independent of the set used to
develop the model. Results published by other workers
were used to verify the model.
The presented soybean growth model and the disease
intensity yield loss submodels are to be considered as
initial models. The development of simplistic, but
accurate, models is always a first step in simulating a
phenomenon as complex as plant pathogen interactions.
121

122
The description and modeling of the physiology and
biochemistry of disease development, plant development,
and disease plant interactions must start with
holistic experiments designed to determine the responses
of these interactions. I consider the models for
soybean growth and for disease intensity yield loss as
an initial step toward the development of more accurate
models. It is work on these models which I have
inititaed and have described here.

APPENDIX A
FUNGICIDES USED
Fungicide
Tradename, source, chemical name
percent active ingredient
Benomy1
Benlate 50W, Biochemicals Department, E.
I. duPont De Nemours and Company, Inc.,
Wilmington, Delaware 19898. Methyl 1-
(butylcarbamoyl)-2-benzimidazole
carbamate, 50% a.i.
Metalaxy1
Ridomil 2E, Agricultural Division, CIBA-
GEIGY Corporation, Greensboro, North
Carolina 27409, N-(2,6-dimethylpheny1)-N
(methoxyacety1) alanine methyl ester
25.11% a.i.
123

APPENDIX B
EQUIPMENT USED
Equipment
Source
Hand-held,
two-row,
six-nozzle,
boom sprayer
Weed Systems, Gainesville, Florida 32604
124

APPENDIX C
LEAF-AREA DIAGRAMS, INSECT- AND DISEASE-RATING SCALES
(A-Z)

126

127

128

129


131
4

132


R)

135



190cm2
(V-W)

W)

140
225cm2 (x-z)
Y)

141
i

APPENDIX D
MATERIALS USED
Material
Source
Acidified
potato
dextrose agar
Potatoes, 200 g; dextrose, 20 g; agar,
20 g; 50% lactic acid, 3 ml; deionized
water, 1 1
Clorox
The Clorox Company, Oakland, California
94612, 5.25% sodium hypochlorite
142

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V

BIOGRAPHICAL SKETCH
Steven Boyd Johnson was born on 30 October 1955 in
Spokane, Washington. He graduated from West High School
in Madison, Wisconsin, in June of 1973. In September of
1973, he entered the University of Wisconsin-Madison; he
received a Bachelor of Science degree in plant pathology
in December of 1977. In January of 1978, he enrolled in
the Graduate School at the University of Maine at Orono
and accepted a position as a research assistant in the
Department of Botany and Plant Pathology. He received a
Master of Science degree in botany and plant pathology
from the University of Maine at Orono in December of
1979. Also in December of 1979, he married the former
Jennifer Alice Wilcox. In January of 1980, he enrolled
in the Graduate School at the University of Florida and
accepted a position as a research assistant in the
Department of Plant Pathology. On 20 April 1982, he
became a proud, first-time father of six pouund, eight
ounce Julie Renee Johnson. He is a member of The
American Phytopatholog ica1 Society and the Southern
Division of that society, The International Society of
Plant Protection, The Biometric Society and the Eastern
North American Region of that society, Florida State
151

Horticultural Society, Soil and Crop Science Society of
Florida, Alpha Zeta Agricultural Honor Society, and
Gamma Sigma Delta Agricultural Honor Society. He is a
candidate for the degree of Doctor of Philosophy in
plant pathology at the University of Florida.

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of
Philosophy.
Richard D. Berger, Chairman
Professor of Plant Pathology
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of
Philosophy.
T. Edward Freeman
Professor of Plant Pathology
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of
Philosophy.
Herbert H. Luke
Professor of Plant Pathology
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of
Philosophy.
Sherlie H. West
Professor of Agronomy

This dissertation was submitted to the Graduate Faculty
of the College of Agriculture and to the Graduate
Council, and was accepted as partial fulfillment of the
requirements for the degree of Doctor of Philosophy.
December, 1982
(/
Dean, Graduate School



LEAF AREA
WVWV\
LEAF AREA INSECT MORTALITY


86
Table 17. Harvested, above-ground, soybean plant
dry-matter proportioned into seeds, stems, and pods for
two seasons .
Season
Plant
portion
(%)
Seeds
Stems
Pods
1980y
49
32
19
1 981z
49
29
22
yMean of 200 plants,
^ean of 80 plants.


59
The described model is not intended to be an
all-encompassing
model,
as others
have attempted (50).
The regression
equations
are not
intended to
be viewed
as stimulus
-
response
situations
. The flow
chart for
this model
(Fig. 8) is
simp 1e
and readily
adaptable
compared to
SOYMOD (50)
or SIMED
(35). Changes in the
regression
coefficient s ,
or in the
regression
equations,
can describe
different
soybean
varieties ,
different
locations,
or
different
years (Figs. 9, 10). This
flexibility
is
desirable
in the
basic framework of a
model.
The time reserved for seedling emergence can be
easily changed to more or less than seven days. This
parameter would be location dependent. The seven days
for seedling emergence for northern Florida climatic
conditions was adequate. The model could be refined to
have the time required for seedling emergence linked to
soil temperature and moisture or planting date. This
refinement would be better than setting the time as a
fixed value. Plant dry weight was not permitted to be
negative, as a negative measurement of dry weight is
biologically meaningless. The regression equations were
continuous with respect to the time variable. This,
along with the equations not intending to describe a
biologic phenomenon but to explain a phenomenon, can
lead to negative values. Time was continuous in the


35
of benomyl, but the low numbers of infected seeds
precluded meaningful analyses; benomyl treatments had 4%
lower seed infection than non-benomyl treatments, but
this was considered inconsequential. Seed from plants
which received a metalaxyl treatment (with or without
benomyl) had 9% infection compared to 10% for seeds from
plants which had not received a metalaxyl treatment.
These values should be similar, because in each case,
half of the plots received benomyl and half did not.
Metalaxyl, specific-acting toward Pythiacious fungi, had
no effect on Fu sari um spp., Phomop s i s spp., or C_.
kikuchii. Metalaxy1-treated plants would not be
expected to have reduced seed infection when compared to
the untreated plants because P. manshurica will not grow
on acidified potato dextrose agar. Seed pathogens
occurred at similar ratios, irrespective of the
treatment. Pathogen escapes would be expected to occur
at similar frequencies to pathogens present in seeds
from the untreated-check plants.
2.) Field Plots. 1981
Seed yields from the meta 1axy1-1reated plots were
significantly less (k=100) than from the
benomy1-1reated, benomyl plus meta 1axy1-1reated, or the
untreated-check plots. Yields were quite low about


38
triggers drastic physiological changes in the soybean
plant. It is possible that the period of flowering is
when the pathogens, already present in the soybean
plant, proliferate throughout the stem. If this
hypothesis is correct, it would explain why the benomyl
treatments at 11 and 13 weeks significantly improved
stem and pod quality. An experiment specifically
designed to investigate the growth of systemic plant
pathogens would have to be undertaken before any
generalizations could be drawn.
The block by treatment interaction present in the
seed yields from the separate experiment can not be well
explained. No pattern of one treatment producing higher
seed yield was present. The conclusion from this study,
under the conditions of that year (57-61), would be that
benomyl treatments did not increase yield. The
recommended benomyl treatment (2) was for applications
to be made at 11 and 13 weeks from planting. This
treatment did not produce increased yields. Benomyl
applications during years unfavorable for pathogens did
not increase seed yields (Tables 1, 6, 12), but did
significantly improve stem and pod quality (Tables 3, 9,
13). It would seem logical to conclude that seed
infection would also be reduced with benomyl
applications and result in higher stem and pod quality,
but more disease than was present for these years would


DEVELOPMENT AND VALIDATION OF A GROWTH MODEL FOR
FLORIDA-GROWN SOYBEANS WITH DISEASE STRESS
BY
STEVEN BOYD JOHNSON
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE
UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1982


37
or the plant parts among treatments (Table 2).
Possibly, the sample size (four) from each of the 1981
season experimental plots was inadequate to describe the
population accurately.
Again in 1981, benomy1-treated plants, with or
without metalaxyl, had significantly (P=0.05) fewer
symptoms and signs of pathogens than plants which had
not received a benomyl treatment. Seed infection levels
were low in 1981. The extremely dry weather was
undoubtedly the reason for the unusually healthy seed.
The seed infection levels for the individually harvested
plants ranged from 2% to 4% and from 1% to 7% for the
plots (Tables 10, 11). Pathogen ratios, as occurred in
1980 (Tables 4, 5), would not be expected to occur.
Small changes in raw numbers drastically change ratios
when the values are less than 5%.
In the separate experiment, selected applications
of benomyl improved pod and stem quality over that of
the controls. Yields were low, and there were no
consistant significant differences among the treatments.
However, pod and stem quality was significantly improved
with the application of benomyl. Applications around
flowering (weeks 11 and 13) provided significantly
better protection against the presence of disease
symptoms and signs of the pathogen than application at
planting or than no application at all. Flowering


89
Table 18. Final plant dry-matter ratios for two soybean
cultivars, 1981.
Dry-matter rato
Soybean cultivar2
Bragg Cobb
Seed:stem
Seed:pod
1.57:1 1.59:1
3.43:1 4.08:1
z
Mean of three plants.


Fig. 15. Model-predicted versus actual dry-matter accumulation for stems, 1981


9
The growth model was derived from host
measurements. Disease intensity measurements over time
provide an account of disease progress, which could be
converted into a disease model. The separation of host
and disease is a useful approach for the determination
of economic threshold levels for diseases. Mathematical
separation of host and disease could be accomplished by
mathematically increasing the disease intensity in the
disease model and removing the increased amounts of
diseased tissue from the total host tissue.
B.) Materials and Methods
The soybean breeding line F76-4486 was chosen for
the experiments. The breeding line is susceptible to
some foliar diseases and is an F5 line from the cross
Centennial x (Forrest x {Cobb x D68-216}) (K. Hinson,
personal communication); the cultivar Foster (F76-8827 )
is a sibling to the chosen breeding line. The
experimental fields were located on the University of
Florida campus, Gainesville, Florida. The plots were
arranged in a randomized-comp1ete-b1ock design, with
five replications of fungicide treatments. The
fungicide treatments were benomyl, benomyl plus
metalaxyl, metalaxyl, and an untreated check (Appendix
A). The plots were four 6.1-meter long rows with


2
present (rust {Phakopsora pachyrhizi Sydow}) or not
prevalent in some portions of Florida (brown spot
{Septoria glycines Hemmi.}). The devastation of soybean
in areas of the world by diseases, some presently in
Florida, necessitates the establishment of disease
intensity-yield loss relationships.
The relationship between foliar diseases and yield
of soybeans has not been characterized. One approach to
determine
the disease
intensity-
yield loss relationship
would be
to measure
the host
growth
without stress
(diseases,
insects,
drought ,
poor
nutrition) and
concurrently subject other host plants to various levels
of stress and measure the resulting change in yield.
Both the host growth and stress components can be
described mathematically. The host growth model, with
and without the stress factors, would need validation
and verification to prove its applicability for decision
processes in soybean crop management. In the case of
this project, the controlled stress factors were
diseases. In the growth model, leaf area could be
mathematically removed to simulate stress. The
influence of disease on yield can be examined by
removing leaf area from fungicide-treated plants
equivalent to the disease levels on non-treated plants.
The approach of modeling will help field projects
become more efficient, or at least can help direct


Fig. 19. Incorporation of a soil-borne disease submodel into the soybean growth model
(Fig. 8).


106
yields of a specified area. The soybean plant has the
ability to compensate for missing plants to a certain
degree (78). Compensation by the soybean plant would
have to be investigated more intensely and inoculum
density disease intensity relationships defined for an
accurate description of loss attributable to soil-borne
pathogens to become a reality. The incorporation of
soil-borne diseases into the flow chart of the soybean
growth model is presented in Fig 19.
4.) Foliage-feeding Insects
A comprehensive model which mathematically
describes the growth of the velvetbean caterpillar has
been developed and validated (48, 49). This latter
model, as any model, is not perfect, and has limitations
as noted (48). The model could be directly linked to
the soybean growth model to remove leaf area consumed by
velvetbean caterpillar. An aspect not incorporated into
the velvetbean caterpillar model (48) was insecticide
application, which could be easily handled by
introduction of an insect mortality factor for each
chemical used. The incorporation of foliage-feeding
insects into the flow chart of the soybean growth model
is presented in Fig. 20.


85
similarly (analyzing 77 days from planting through day
123, harvest), my slope coefficient for the simulated
and the raw data was 0.11, compared to 0.19 for the
published value (28). The final ratio of seed:pod
dry-matter for 1980 was 2.56:1. Published values range
from 2.47:1 to 2.63:1 (Table 16) for commercially-grown
soybean varieties in the United States (22, 28,); the
1981 seed:pod dry-matter ratio was 2.27:1. The final
ratio of seed:stem dry-matter for 1980 was 1.50:1,
compared to published ratios of 1.53:1 to 1.59:1 for
commercially-grown soybean varieties (28); in 1981, the
ratio was 1.66:1 (Table 16). The 1980 to 1981
variations in final plant dry-matter ratios were
reflected in the proportions of plant dry-matter ratios.
For 1980 and 1981, 49% of the final-plant dry-matter by
weight was seeds, 19% was pods in 1980 compared to 22%
in 1981; 32% was stems in 1980 compared to 29% in 1981
(Table 17). The higher percentage of pods and lower
percentage of stems in 1981 were reflected in a lower
seed:pod dry-matter ratio and a higher seed:stem
dry-matter ratio.
D.) Discussion
The model predictions of final dry matter for seeds
(Figs. 11, 14), pods (Figs. 12, 15), and stems (Figs.


75. Sinclair, J. B., and Shurtleff, M. C. (eds ) 197 5 .
Compendium of soybean diseases. American
Phytopathological Society, St. Paul. 69 pp.
76. Splinter, W. E. 1974. Modelling of plant growth
for yield prediction. Agrie. Meteorol. 14:243-253.
77. Stapleton, H. N., and Meyers, R. P. 1971.
Modeling subsystems for cotton the cotton plant
simulator. Trans. ASAE 14:950-953.
78. Stivers, R. K., and Swearingin, M. L. 1980.
Soybean yield compensation with different populations
and missing plant patterns. Agron. J. 72:98-102.
79. Teigen, J. B., and Vorst, J. J. 1975. Soybean
response to stand reduction and defoliation. Agron. J.
67 :813-816 .
80. Thomas, G .D., Ignoffo, C .M., Biever, K. D., and
Smith, D. B. 1974. Influence and defoliation and
depodding on yield of soybeans. J. Econ. Ent.
67 :683-685 .
81. Thomas, G. D., Ignoffo, C. M., and Smith, D. B.
1976. Influence of defoliation and depodding on quality
of soybeans. J. Econ. Ent. 69:737:740.
81. Waggoner, P. E. and Horsfall, J. G. 1969. EPIDEM,
a simulator of plant disease written for a computer.
Conn. Agr. Exp. Sta. Bull. 698. 79 pp.
82. Waggoner, P. E., Horsfall, J. G., and Lukens, R. J.
1972. EPIMAY, a simulator of southern corn leaf blight.
Conn. Agrie. Exp. Sta. Bull. 729. 84pp.
83. Walters, H. J. 1980. Evaluation of fungicides on
soybean yields and delay of maturity, 1980. Fungicide
and Nematacide Tests 36:103.
84. Wann, M., and Raper Jr., C. D. 1979. A dynamic
model for plant growth: Adapation for vegetative growth
of soybeans. Crop Sci. 19:461-467.
85. Weber, C. R. 1955. Effects of defoliation and
topping simulating hail injury to soybeans. Agron. J.
47:262:266.
86. Weber, C. R., Dunleavy, J. M., and Fehr, W. R.
1966. Effect of bacterial pustule on closely related
soybean lines. Agron. J. 58:544-545.


30
Table 13. Soybean pod and stem quality ratings from
separate experiment, 1981.
Benomyl w
application
x
Rating
Pod Stem
Planting
Planting,
weeks 11&13
Weeks 11&13
Check
2 ayZ
1 b
1 b
3 a
5 b
2 c
2 c
7 a
Benomyl was applied at the rate of 586.5 g/ha; the
field was planted on 15 June 1981. Check plots received
no treatment.
x
Mean of 10 ratings.
y
Numbers within the same column followed by the same
letter are not significantly different according to
Duncan's new multiple range test (P=0.05).
z
Roundoff error present.


29
Table 12. Soybean seed yields from separate experiment,
1981 .
Benomy1
application^ Yield/plot (g)
Block
1
2
3
4
5
Planting
801 bZ
1243a
815
1113a
1154
Planting ,
weeks 11 & 13
1154a
999 b
877
807 b
1224
Weeks 11 & 13
798 b
836 b
956
1002ab
1083
Check
1203a
77 8 b
727
10 51ab
1242
NS NS
y
Benomyl was applied at the rate of 586.5 g/ha; the
field was planted on 15 June 1981. Check plots received
no treatment.
2
Numbers within the same column followed by the same
letter are not significantly different according to
Duncan's new multiple range test (P=0.05).


96
invo1ved
for
stems, seeds,
and pods.
The pathogen
intensity
in
the
seeds could
be related to
the intensity
in the
pods
, which could,
in turn, be related to the
intensity
in
the
stems.
The following
uses for the
soybean
growth
model
are strictly
hypothetical;
pertinent
data
to verify
the uses have not been
collected

B.) Uses For The Model
1.) Foliar Pathogens
In
the
model, attack
by
foliar
pathogens can be
simulat ed
by
removal of
leaf
area
representative of
pathogen
damage. Since
leaf
area
drives the model,
reduced
leaf
area would cause a
reduction in dry-matter
accumulation by seeds, stems, and pods. However, the
intensities of the foliar disease in my field
experiments over two years did not cause a decrease in
dry-matter accumulation. The presence of low levels of
disease without a statistically significant change in
yield is an example of a disease threshold phenomenon:
a specific level of disease must be present before a
significant change in yield is detected. The influence
of foliar diseases on yield could be modeled several
ways. The disease progress data could be to fit to a




36. Johnson, S. B., and Berger, R. D. 1981. Foliar
diseases cause insignificant loss in leaf area of
Florida grown soybeans. (Abstr.) Phytopathology 71:884.
37. Johnson, S. B., and Berger, R. D. 1982. Effect of
metalaxyl fungicide on downy mildew of soybean. Proc.
Fla. Soil Crop Sci. 41:101-102.
38. Kampmeijer, P., and Zadoks, J. C. 1977. EPIMUL, a
simulator of foci and epidemics in mixtures of resistant
and susceptible plants, mosaics and multilines.
Simulation Monographs, Cent, for Agrie. Pub. and
Document., Wageningen. 50 pp.
39. Roller, H. R. 1972. Leaf area leaf weight
relationships in the soybean canopy. Crop Sci.
12:180-183 .
40. Lim, S. M. 1978. Disease severity gradient of
soybean downy mildew from a small focus of infection.
Phytopathology 68:1774-1778.
41. Lim, S. M. 1980. Brown spot severity and yield
reduction in soybean. Phytopathology 70:974-977.
42. Little, T. M., and Hills, F. J. 1978.
Agricultural Experimentation. John Wiley and Sons, New
York. 350 pp.
43. Lockwood, J. L., Percich, J. A., and Maduewesi, J.
N. C. 1977. Effect of leaf removal simulating
pathogen-induced defoliation on soybean yields. Plant
Dis. Rep. 61:458-462.
44. Madden, L. V., Pennypacker, S. P., Antle, C. E.,
and Kingsolver, C. H. 1981. A loss model for crops.
Phytopathology 71:685-689.
45. Madden, L. V., Pennypacker, S. P., and Kingsolver,
C. H. 1981. A comparison of crop loss models.
Phytopath. Z. 101:196-201.
46. McAlister, D. F., and Krober, 0. A. 1959.
Response of soybeans to leaf and pod removal. Agron. J.
51:674-677.
47. McCoy, R. E. 1976. Mycos, a computer simulator of
Ascochyta blight of chrysanthmum. Proc. Fla. State
Hort. Soc. 89:296-299.


129


Fig. 1. The dry-matter accumulation for soybean leaves of known area over time.


16. Published values, model predictions, and
1980 and 1981 raw data for the same parameters ... 84
17. Harvested, above-ground soybean-plant dry-matter
proportioned into seeds, stems, and pods
for two seasons 86
18. Final plant dry-matter ratios for two
soybean cultivars, 1981 89


36
11 quintals per hectare, or 38% of the 1980 plot seed
yield. No yield response to applications of benomyl was
present in other fungicide trials during that year (63,
70, 87).
Plants from block three were not similar to plants
from the rest of the blocks. No logical explanation for
block three being completely different from the
remaining blocks was evident from field observation.
The block did not have uneven stress of water, insect,
nutritional, or disease. It is possible that block
three accurately described the metalaxyl-treated plants
and the remainder of blocks did not. When the majority
of the block by treatment interaction was removed (Table
8), the metalaxyl-treated plants were significantly
(P=0.05) larger than all the rest of the plants. It is
my feeling that the selected individual plants from the
metalaxyl-treated plots did not reflect the true
population. Metalaxyl-treated plots produced the lowest
seed yield, but the selected plants produced the highest
yields. With the exception of the metalaxyl-treated
plants, there were no significant (P=0.05) differences
present in the entire, individually harvested plants, or
when the plants were separated into pods, seeds, and
stems. These results, with the exception of the
metalaxyl-treated plants, were similar to 1980 results
of no significant (P=0.05) differences between plants,


9


68
responsible for yield and disease differences. This
type of further refinement could take many, many growing
seasons to substantiate.
Verification must be performed on the model.
Verification assures the model properly mimics the
biological system under one set of conditions, namely,
the set of conditions under which it was developed.
Futher model verification with published data from
literature is useful. Often, published data are the
sole source for physiologically-based models. Because
of the nature of this model, published data did not aid
in the development or adjustment of the model, they only
verify that data used to develop and validate the model
were similar to published data.
B.) Materials and Methods
The soybean growth model was validated with 200
data sets from 1980 and 80 data sets from 1981; all 280
data sets were independent of the data set used to
develop the model, but were the same soybean cultivar.
The validation data sets consisted of nondestructive
leaf-area measurements throughout the growing season and
final measurements of dry weight for above-ground plant
parts. The final measurements were destructive. Leaf
area was converted to leaf dry matter (Fig. 1). Leaf


I. GENERAL INTRODUCTION
The soybean (Glycine max (L.) Merrill), an annual
plant, is included in the kingdom Planta, phylum
Tracheophyta, class Angiospermae, order Rosales, family
Leguminosae, and is one of the oldest cultivated crops.
The geographic adaptability, high oil content, and high
nutritive value of the pressed seed mash have placed the
soybean into prominence in United States agriculture.
Since 1954, the United States has been one of the
world's largest producer of soybeans.
Throughout the geographical distribution of the
soybean, diseases reduce yield quality and quantity.
The most prevalent fungal diseases of soybean in Florida
are purple stain (Cercospora kikuchii Matsumoto &
Tomoyasu), frogeye leaf spot (Cercospora so jina Hara. ) ,
downy mildew (Peronospora man shurica (Naoum.) Syd. ex
Gaum.), target spot (Corynespora cassiicola (Berk, and
Curt.) Wei.), Rhizoctonia blight (Rhizoctonia solani
Kuehn), anthracnose (Colletotrichum truncatum (Schw.)
Andrus and W. D. Moore), and pod and stem blight
(Phomo p sis so j ae L e h {Diaporthe so jae Leh.}) {10, 18,
75). Diseases which cause yield reduction and plant
defoliation in other soybean growing regions are not
1


25
Table 9. Pod and stem quality ratings from individually
harvested soybean plants, 1981.
Treatment*7 Rating3^
Pod
Stem
Benomyl +
meta 1axy1
la
1 a
Benomy1
1 a
1 a
Me talaxy1
2 b
7 b
Check
2 b
7 b
wBenomyl was applied at the rate of 586.5 g/ha at 14-day
intervals from 22 June 1981 to 16 October 1981.
Metalaxyl was applied at the rate of 1137 g/ha at 40-day
intervals from 22 June 1981 to 16 October 1981. Check
plots received no treatment.
Mean of 20 plants.
Rated on a scale of 0 to 10 and transformed with an
angular transformation (arcsine (disease
proportion)**{1/2}) where the ratings of 0, 1, 2, 3, 4,
5, 6, 7, 8, 9, 10 were equivelent to 0, 2.5 10, 21, 35,
50, 65, 79, 90, 97.5, 100%, respectively (42).
2
Numbers followed by the same letter are not
significantly different according to Duncan's New
Multiple Range Test (P=0.05).


20
Table 6. Soybean seed yields from plots, 1981.
X
Treatment
Seed
g/plot
yield ^
kg/ha
Benomyl +
metalaxyl
107 1 Z
1281
Benomy1
898
1074
Metalaxyl
771
922
Check
1002
1198
Duncan-Waller
k-ratio (k=100)
LSD
197
XBenomyl was applied at the rate of 586.5 g/ha at 14-day
intervals from 22 June 1981 to 16 October 1981.
Metalaxyl was applied at the rate of 1137 g/ha at 40-day
intervals from 22 June 1981 to 16 October 1981. Check
plots received no treatment.
y
Mean of five plots,
z
Round-off error present.


140
225cm2 (x-z)
Y)


Fig. 14. Model-predicted versus actual dry-matter accumulation for seeds, 1981.


PREDICTED DRY MATTER (g)
72
(g)


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VI. APPLICATIONS FOR THE MODEL
A.) Introduction
A model is a simplified representation of a system.
The primary purpose of a model is to be applied to the
system, to interpret changes, be they growth, abiotic
pressures, or biotic pressures. The models can then be
used to predict the effect these changes have on final
plant yield or final level of biotic stress. The actual
parameters that are predicted, and the influences which
these parameters have
on
the
system,
are dependent
on
the intended purpose
of
the
model,
the choice
of
modeling techniques,
and
the
individual modeler.
The
intended purpose of this model of soybean growth was to
be a disease intensity yield loss model. The ex post
facto approach coupled with regression analysis was
ideally suited to the development of a basic model. The
separation of plants into pods, stems, seeds, and leaves
permitted the flexibility for stress to be directed to
individual plant portions, or to the entire plant. The
accumulation of leaf dry-matter (related to leaf area,
Fig. 1) drove the model, with the reasoning that the
leaves supply the plant with carbohydrates. The
94


Abstract of Dissertation Presented to the Graduate
Council of the University of Florida in Partial
Fulfillment of the Requirements for the Degree of
Doctor of Philosophy
DEVELOPMENT AND VALIDATION OF A GROWTH MODEL FOR
FLORIDA-GROWN SOYBEANS WITH DISEASE STRESS
By
Steven Boyd Johnson
December, 1982
Chairman: Dr. Richard D. Berger
Major Department: Plant Pathology
Holistic field experiments with soybean were
conducted over two growing seasons, in which fungicides
were applied to achieve various disease intensities.
The experiments were monitored at weekly intervals from
planting through harvest. Each week, the disease
intensity of five different foliar diseases, the insect
damage, and the area of each individual leaf were
measured from representative plants. The above-ground
portion of the plants, which had been measured through
the growing season, were harvested for dry-matter
yields. The experiments continued after harvest when
the pathogen presence in the seed from the individually
monitored plants and in the seed from the plots was
de t ermined .
x


80
ACTUAL DRY MATTER
(9)


I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of
Philosophy.
Richard D. Berger, Chairman
Professor of Plant Pathology
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of
Philosophy.
T. Edward Freeman
Professor of Plant Pathology
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of
Philosophy.
Herbert H. Luke
Professor of Plant Pathology
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of
Philosophy.
Sherlie H. West
Professor of Agronomy


41
and would have wide applicability among locations.
Regression analysis is ideally suited to the ex_ post
facto approach, and large data sets can be handled
efficiently. The presence of large data sets, along
with the use of regression analysis (32) to construct a
continuous function from discrete points of a
quantitative variable, facilitated the choice of this
mathematical technique for the model.
A continuous mathematical function to describe the
biological nature of the crop or crop pest interaction
was not considered for the basic model. Holistic
experiments contain numerous uncontrolled and unmeasured
variables. Water stress, nematode infestation of soil,
soil-borne insects, and nutritional stress would be
included in the unmeasured variables. It is imperative
that these variables be included in a
biological-function model.
B.) Materials and Methods
During 1981, whole-plant samples were collected for
16 weeks, starting three weeks from the date of planting
and continuing through harvest (124 days from planting)
from a soybean field planted to breeding line F76-8846.
The disease damage and insect damage were expressed as
percent of total leaf area for each leaf. All


Theoretical submodels were developed for foliar
pathogens, above-ground non-foliar pathogens,
foliage-feeding insects, and seed-feeding insects.
Possible applications for the model are to develop
disease intensity yield loss relationships and
threshold levels of disease-induced loss.
XI1


98
verify
and validate this
approach
to describe
the
disease
severity
yield
loss
relationships.
The
incorporation of
equation
1 into
the
flow chart of
the
soybean growth model is presented in Fig. 17.
2.) Above-ground Non-foliar Pathogens
Pod
and stem
blight
and anthracnose
did
not
regularly
appear
on the
leaves
, so reduction
of
dry-mat ter
accumulation by
these
pathogens
mus t
be
ac comp 1ished
in a way
other
than removing leaf
area ,
the
driving force of the model. One approach would be to
remove dry-matter accumulation of the stems, pods, and
seeds, dependent upon a visual rating of the stems and
pods at harvest. Equation 2 would accomplish the dry
matter reduction.
R= (S**3 / Smax**3) M (Eq. 2)
R= percent reduction in plant
dry-matter accumulation
S= average of stem and pod rating
(based on percent infection) at harvest
M= maximum percent dry-matter reduction
by pod and stem blight and anthracnose
Smax= maxmium pod and stem rating possible
Reduction in dry-matter accumulation (R) would be
removed from the seed, stem, and pod weight. The cube


11
disease and insect damage was expressed as a percent of
leaf area for that leaf. All measurements were
comparisons against leaf-area diagrams and insect- and
disease-rating scales developed for soybeans (Appendix
C). Total photosynthetic area of the leaves was
calculated by subtracting the senescent, insect-damaged,
and diseased area from total leaf area.
At maturity, each of the labeled plants was
harvested. The dry weights for pods, seeds, and stems
were measured from each plant. The disease severity on
the stems and pods from these plants was rated on a
scale from 0 to 10. The rating scale consisted of 11
evenly spaced ratings with a rating of 0 for 0% of the
pods or main stem covered with symptoms or signs of
pathogens; and a rating of 10 for 100% of the pods or
main stem covered with symptoms or signs of pathogens.
Because the visual ratings had a binomial distribution,
an angular transformation (arcsine (disease
proport ion)**{1/2}) was used where the ratings of 0, 1,
2, 3, 4, 5, 6, 7, 8, 9, 10 were equivelent to 0, 2.5 10,
21, 35, 50, 65, 79, 90, 97.5, 100%, respectively (42).
Seeds from the labeled, individually harvested plants
were surface sterilized in a 10% Clorox (Appendix D)
solution for one minute and plated onto acidified potato
dextrose agar (Appendix D) and observed within seven
days for presence of seed-borne fungal pathogens. After


Fig. 17. Incorporation of a fo 1iar-disease submodel into the soybean growth model
(Fig. 8).


PREDICTED DRY MATTER (g)
0 10 20 30 40
ACTUAL DRY MATTER
(g)


55
TIME (days)


90
variety dependent, maturity group dependent, or perhaps,
planting date dependent. The slope, in grams per day
(after day 86), of the seed dry-matter accumulation is
not influenced by, for instance, location, as much as
the Y-intercept. Soybeans grown in northern United
States would not be expected to initiate seed dry-matter
accumulation, measured by the Y-intercept, at the same
time as soybeans grown in the southern United States.
Similarly, soybeans planted in northern United States
are included in different maturity groups than those
planted in the southern United States. The soybeans
included in northern maturity groups would be expected
to initiate dry-matter accumulation at a different
number of days from planting, which is again measured by
the Y-intercept. Weather would also be expected to
influence the seed dry-matter accumulation. I
hypothesize that weather would influence the slope of
the dry-matter accumulation curve, but not the
Y-intercept. Only drastic differences in
photosynthetica1ly-active radiation, water availability,
or ambient temperatures would cause notable changes in
the seed dry-matter accumulation slope to occur. The
linear relationship between seed dry-matter acculumation
and time (after flowering) has also been previously
reported (8, 20, 21).


5
conditions. A model can be used to predict the system
response to various changes in inputs, without going to
the actual system. The usefulness of models for
research programs, whether for identification of
problems or solving problems, cannot be overstated.
Modeling of systems dates back as far as records
were kept, and yet is as current as today. Development
of maps, models of land or water masses, continuing
through the development of laws of physics, modeling the
effect of gravity, etc., to today's high-speed
digital-computer simulations of biochemical processes,
are examples of models. Likewise, soybeans are one of
the world's oldest cultivated crops, yet today are under
intensive investigation to increase yields. Soybeans,
like modeling, can be viewed as rich in tradition and
yet extremely modern.
Soybeans as a crop and modeling as a science
started to converge with the interest of agricultural
scientists in yield maximization. Early modelers of
soybean growth were concerned with production of
soybeans as a forage source, and the effect of
defoliation (cattle grazing) on leaf, stem, and seed
yield (26). The maximization of the entire soybean
plant was investigated in this work, because the soybean
was grown as a forage source. Interest shifted from
modeling the injury from grazing to modeling the injury


Fig. 10. The dry-matter accumulation for soybean leaves, converted from leaf area
(Fig. 1), from individually harvested plants over time, 1981.




131
4


^START^
SOIL-BORNE
PATHOGENS
-K>
AAAaAAA/


APPENDIX B
EQUIPMENT USED
Equipment
Source
Hand-held,
two-row,
six-nozzle,
boom sprayer
Weed Systems, Gainesville, Florida 32604
124


foliage-feeding insect submodel into the soybean growth
Fig. 20. Incorporation of a
mode 1 (Fig. 8).


7
development, new research needs surfaced. Quantitative
descriptions of dry-matter accumulation for yield
components were required for soybean models dealing with
plant growth. From the 1960's and continuing through
today, mathematical models of dry-matter accumulation
for soybean have been published. Shibles and Weber (72,
73) were pioneers in these studies, establishing that
soybean plant dry-matter accumulation was proportional
to leaf area. The early work by Shibles and Weber has
been further documented by numerous workers (8, 20, 21,
22, 28, 29, 31, 71). The linear relationship between
the dry-matter accumulation for entire soybean plants
versus time has been documented (28, 31, 71). The
linear relationship for the dry-matter accumulation for
the seed versus time (8, 20, 21, 28) has also been
described. The development of quantitative descriptions
of dry-matter accumulation for soybean yield components
provided the data for soybean modeling.
In modeling efforts, the soybean is a relatively
new crop, when compared to potatoes or cereals. To
date, soybean models, especially soybean disease models,
are lacking the sophistication and accuracy of those of
potato and cereal crops. Much progress on modeling of
the soybean has been made in the last twenty years, and
with the ever-increasing importance of the soybean as a
crop, progress toward maximization of soybean yields
will continue to be made.


Fig. 4 .
The dry-matter accumulation for soybean pods over time.


21
summed (P=0.07); a significant block by treatment
interaction was absent for the dry weight of stems
(P=0.36). Much of the block by treatment interaction
was attributable to block 3 (Table 7). With block 3
removed from the calculations (taking a mean of the
remaining four blocks), block by treatment interactions
were nonsignificant for dry-weight yields of the
labeled, individually harvested plants when separated
into seeds (P=0.19), pods (P=0.16), stems (P=0.59), or
when the dry weights of the seeds, pods, and stems were
summed (P=0.26). With blocks 1, 2, 4, and 5 summed,
there were significant differences in the labeled,
individually harvested plants when separated into stems
(P=0.02), pods (P=0.02), and seeds (P=0.03), or when
summed (P = 0.02); the nonsignificant block by treatment
interaction was used as an error term for these tests
(Table 8). The visible quality of the stems and pods
from the labeled, individually harvested plants varied
significantly in response to treatments. Block by
treatment interaction was nonsignificant for visual
ratings of quality for pods (P=0.27) and stems (P=0.81).
Treatments with benomyl (benomyl alone, and benomyl plus
metalaxyl) had significantly less (P=0.0001) symptoms
and signs of pathogens than did treatments without
benomyl (metalaxyl alone, and check), when the
nonsignificant block by treatment interaction was used


Fig 6 .
The dry-matter accumulation for soybean leaves over time.


12Q
between 1980 and 1981, which, in part, would explain why
in 1981, there was only a 2% difference (Eq. 2) in seed
yield. A statistical analysis at the 5% level would not
describe a difference between two numbers 2% apart under
these circumstances. The reduction in quality of seed
as a result of above-ground, non-foliar, plant pathogens
cannot be evaluated with my data. As previously
mentioned, pathogen activity would only be partially
responsible for seed quality reduction. A major portion
of the reduction in quality would be physiological
deterioration, partially or wholly independent of seed
pathogens .


63. Palm, E. W. 1982. Evaluation of foliar fungicides
on soybeans, 1981. Fungicide and Nematacide Tests
37:104.
64. Robinson, C. D., and Massengale, M. A. 1967. Use
of area weight relationship to estimate leaf area in
alfalfa (Medicago sativa L. cultivar 'Moapa'). Crop
Sci. 7:394-395.
65. Roy, K. W., Arnold, B., and Miller, W. A. 1982.
Effects of fungicides on diseases and yield of soybeans,
1980. Fungicide and Nematacide Tests 37:105.
66. Roy, K. W., Buehring, N. and Miller, W. A. 1982.
Effects of fungicides on diseases and yield of soybeans,
1980. Fungicide and Nematacide Tests 37:105-106.
67. Roy, K. W., and Miller, W. A. 1982. Effects of
fungicides on diseases and yield of soybeans, 1980.
Fungicide and Nematacide Tests 37:106.
68. Sail, M. A. 1980. Epidemiology of grape powdery
mildew: A model. Phytopathology 70:338-342.
69. Schaller, C. W. 1951. The effect of mildew and
scald infection on yield and quality of barley. Agron.
J. 43:183-188.
70. Scott, D. H., and Akers, D. P. 1982. Effect of
foliar fungicides on brown spot control and yield of
soybeans, 1981. Fungicide and Nematacide Tests
37:106-107 .
71. Scott, H. D., and Batchelor, J. T. 1979. Dry
weight and leaf area production rates of irrigated
determinate soybeans. Agron. J. 71:776-782.
72. Shibles, R. M., and Weber, C. R. 1965. Leaf area,
solar radiation interception and dry matter production
by soybeans. Crop Sci. 5:575-577.
73. Shibles, R. M., and Weber, C. R. 1966.
Interception of solar radiation and dry matter
production by various soybean planting patterns. Crop
Sci 6 : 55-59 .
74.Shrum, R. 1975. Simulation of wheat stripe rust
(Puccinia striiformis West.) using EPIDEMIC, a flexible
plant disease simulator. Penn. Sta. Univ. Coll. Agrie.
Progr. Rep. 347. 41 pp.


APPENDIX C
LEAF-AREA DIAGRAMS, INSECT- AND DISEASE-RATING SCALES
(A-Z)


22
Table 7. Dry-matter yields from individually harvested
soybean plants, 1981.
Portion Yield/plant (g)*
Block
1
2
3
4
5
Pods M7
14.6 5aZ
M
11.88a
B
4.37
M
13.55a
M
7.93
0
9.82b
0
9.25ab
C
3.92
B
5.16 b
B
6.98
C
3.61 c
B
6.30 b
M
3.91
C
4.77 b
C
4.99
B
3.53 c
C
5.76 b
0
3.32
NS
0
4.28 b
0
4.75
NS
Seeds M
32.43a
M
26.14a
B
9.86
M
29.74a
M
17 .45
0
22.79 b
0
21 .42ab
0
8.27
B
12.70 b
B
16.12
B
8.83
c B
15.85 be
C
7 .89
C
10.39 b
C
11 .94
C
8.53
c C
13.20 c
M
6 .40
NS
0
9.58 b
0
11.55
NS
Stems M
15.63a
M
13 .32a
B
5.50
M
16 .02a
M
11.14
0
11.39 b
0
12.45a
C
4.91
C
7.49 b
B
9.69
B
5.98
c B
8.37 b
M
4.70
0
6.24b
C
8.23
C
5.57
c C
8.14 b
0
4.52
NS
B
5.83 b
0
7.91
NS
Total M
62.71a
M
51.34a
B
19.73
M
59.31a
M
36.52
0
44.00 b
0
43.12ab
C
16.72
B
23 .68
b
B
32.79
B
18.34 c
B
30.52 b
0
16.11
C
22.65
b
C
25.16
C
17.70 c
C
27.10 c
M
15.00
0
20.09
b
0
24.20
NS NS
w
Roundoff error present.
Mean of four plants.
y
B=benomy1-treated plants; M=metalaxy1-treated plants;
O=benomyl plus meta1axy1-treated plants; C=check plants.
Benomyl was applied at the rate of 586.5 g/ha at 14-day
intervals from 22 June 1981 to 16 October 1981.
Metalaxyl was applied at the rate of 1137 g/ha at 40-day
intervals from 22 June 1981 to 16 October 1981. Check
plots received no treatment.
z .
Numbers in the same column, within a row, followed by
the same letter are not significantly different
according to Duncan's new multiple range test (P=0.05).


13
In a separate experiment, the soybean breeding line
F76-884b was planted on the University of Florida
campus, Gainesville, Florida. The separate experiment
was conducted to ascertain if the scheme of benomyl
application affected the disease severity or yield. The
treatments were arranged in a randomized-complete-block
design with five replications of benomyl (586.5 g/ha)
applied i) at planting, ii) at 11 and 13 weeks from
planting, iii) at planting and at 11 and 13 weeks from
planting, iv) or not at all. The plots, fungicide
applications, and harvested plant matter were treated as
described above.
C.) Results
1.) Field Plots, 1980
The block by treatment interaction was
nonsignificant (P=0.23) for all measured variables; so
the plots were treated as an entity, not as two
individual rows. The seed yields from the plots were
not significantly different among the treatments (Table
1). Dry weight yields from the labeled, individually
harvested plants were not significantly different among
treatments (Table 2) when viewed as entities (P=0.38) or
when separated into seeds (P=0.39), stems (P=0.35), and


135


88
error must be followed, but no cause effect
relationship can be assessed to the cumulative error.
The final plant-portion dry-matter ratios from Cobb
and Bragg soybean cultivars (Table 16) were similar to
the ratios obtained from plants used in model
verification (Table 17). In view of this evidence,
using ratios, updated daily, to produce growth of stems,
seeds, and pods in the model is a reasonable approach.
The seedistem dry-matter ratio for Cobb and Bragg
soybean cultivars (Table 18) was very similar to the
ratios obtained for a different soybean cultivar grown
under different conditions (Table 16), and also similar
to published ratios of totally different soybean
cultivars (28). The seed:pod ratio from the Cobb and
Bragg soybean cultivars (Table 18) were much higher than
published ratios (22, 28) or the ratios from another
soybean cultivar (Table 16) grown under a less intensive
water management scheme. Again, the pod dry-matter
accumulation, as discussed earlier, may be more
sensitive to environmental changes, which includes
water, than are the seeds or the stems.
The slopes from the linear equations describing the
seed dry-matter accumulated (Table 16) for the
simulation and published data (28) were similar (0.42,
0.41), but the Y-intercepts were not (0.43, 1.61). I
interpret the Y-intercept to be location dependent,


127


47


BIOGRAPHICAL SKETCH
Steven Boyd Johnson was born on 30 October 1955 in
Spokane, Washington. He graduated from West High School
in Madison, Wisconsin, in June of 1973. In September of
1973, he entered the University of Wisconsin-Madison; he
received a Bachelor of Science degree in plant pathology
in December of 1977. In January of 1978, he enrolled in
the Graduate School at the University of Maine at Orono
and accepted a position as a research assistant in the
Department of Botany and Plant Pathology. He received a
Master of Science degree in botany and plant pathology
from the University of Maine at Orono in December of
1979. Also in December of 1979, he married the former
Jennifer Alice Wilcox. In January of 1980, he enrolled
in the Graduate School at the University of Florida and
accepted a position as a research assistant in the
Department of Plant Pathology. On 20 April 1982, he
became a proud, first-time father of six pouund, eight
ounce Julie Renee Johnson. He is a member of The
American Phytopatholog ica1 Society and the Southern
Division of that society, The International Society of
Plant Protection, The Biometric Society and the Eastern
North American Region of that society, Florida State
151


Fig. 12. Model-predicted versus actual dry-matter accumulation for stems,
1980 .


V. VALIDATION AND VERIFICATION OF THE MODEL
A.) Introduction
Validation is a continuing process; a model is
really never finished, it can always be improved,
adjusted, and expanded. Validation is the application
of the model to conditions different from those under
which the model was developed. The different conditions
can range from different plants to different hosts,
depending on the type of model. Validation data for
this model are from different plants of the same
cultivar, different growing seasons, and different
soybean cultivars. The soybean cultivar, soil type,
general
cultural practices (fertilization, insect
control,
disease control, cultivation) remained
unchanged
between the two seasons. Host growth
differences (Figs. 9, 10; Tables 2, 7), seed yield
differences (Tables 1, 6), differences in disease
intensity
(Tables 3, 9), and incidence (Tables 4, 5, 10,
11) can
be crudely attributed to weather conditions
(51-61) .
Far more validation data than appear here are
to discern which specific parameter(s) are
needed
67


97
continuous curve and the equation which described the
curve used to remove leaf area from a leaf-area
equation. A second approach would be to use the
equation which described the disease progress data to
add dry matter to the leaves. This addition would
permit calculation of the theoretical yield which may
have been produced in the absence of disease. Downy
mildew disease progress data from 1980 (37) were fitted
to a Gompertz (3) equation (Eq. 1)
Yi= Ymax exp(-b exp{-k T}) (Eq. 1)
Yi= disease at time i
Ymax= maximum disease
Yo= initial disease
b = -ln(Yo)
k= epidemic rate
T= time
using a nonlinear, least-squares estimation routine.
Epidemic rates (k) were solved with initial disease and
maximum disease severity held constant (Yo = 0.00001 ;
Ymax=0.02) {37}. The Gompertz equation was used to
mathematically remove leaf area from the plant. No
major differences in dry-matter accumulation from the
low disease levels occurred. Foliar diseases other than
downy mildew could also be handled in this way. A large
range of disease intensities, including intensities
higher than measured in this study, are necessary to


128


10
0.91-meter row spacing and were seeded at the rate of 39
seeds/meter. The center two rows were used as multiple
observations from each experimental unit. This allowed
for
testing
of
block
by
treatment interaction. The
field
was
fertilized
and
an
insecticide
applied as
recommended
for
the
crop
(2)
. Benomyl
was applied
(586.5 g/ha) at 14-day intervals; metalaxyl was applied
(1137 g/ha) at 40-day intervals. All fungicide
applications were made over the top of the canopy with a
hand-held, two-row, six-nozzle, boom sprayer delivering
the equivalent of 396 ls/ha at 276 kilopascals (Appendix
B). Frequent fungicide applications were used to
provide optimal disease control. Metalaxyl and benomyl
were chosen because their selectivity of action would
provide a difference in disease severity and intensity
in the plots. Metalaxyl was chosen to control downy
mildew. Benomyl was chosen to control other diseases,
primarily pod and stem blight, anthracnose, frogeye leaf
spot, and purple stain.
In each of the center two rows of a plot, plants
were randomly selected and labeled. Starting three
weeks from date of sowing, weekly measurements of leaf
area and disease incidence and severity were recorded
for each leaf of the labeled plants. Leaf emergence,
leaf senescence, insect damage, and growth stage (23,
24) also were recorded weekly.
For each leaf, the


119
artificial, herbivor-grazing, etc.) to yield reduction
caused by pathogen-induced defoliation. The yield loss
caused by plant pathogens is greater than the loss
casued by reduction in leaf area equivalent to that
which the pathogen has destroyed. The plant pathogen is
a living system, and is invading another living system,
the plant. In destroying all or portions of a plant the
pathogen kills plant cells and consumes their contents.
The action of plant invasion by the pathogen can upset
the host physiology in localized areas, and possibily in
the entire host. This disruption of physiological
processes causes more yield loss than would the
disruption of processes which would occur from manually
defoliating a plant at the same level of foliage loss.
The low levels of disease present for my studies
did not permit evaluation of the above-ground,
non-foliar plant pathogen submodel. Statistical tests
at the 5% level can measure the 7.6% difference in seed
yield (Eq. 2). No significant differences as a result
of benomyl applications were described using a
Duncan-Waller k-ratio test (k=100) {Table 1}; however,
Duncan's new multiple range test, a less conservative
test, did separate seed yield into significantly
different classes. The more conservative test was
chosen (Table 1) because of the variation inherent in
field situations. Environmental conditions differed


132


ACKNOWLEDGMENTS
I wish to acknowledge the assistance of Dr. Richard
D. Berger, major advisor for the studies and for the
dissertation, who unselfishly contributed incalculable
hours in these capacities. His dedication to science,
his critical and independent thinking, and his approach
to problems have earned my deepest respect. Special
recognition for general assistance throughout the
program of study and for critically reading and offering
valuable suggestions on this dissertation is in order
for the remainder of my supervisory committee: Drs. T.
E. Freeman, H. H. Luke, and S. H. West. I would also
like to recognize all the persons, too numerous to
mention by name, that have in some way contributed to
the completion of this dissertataion. I also wish to
acknowledge my wife, Jennifer, for she was the true
sufferer through the long hours of the studies and
preparation of the dissertation. The work was supported
by funds from EPA grant no. CR-806277-020-0 and research
funds from Dr. Berger.
ii


Fig. 2.
The dry-matter accumulation for soybean stems over time.


VII. SUMMARY
The soybean growth model described herein allows
the researcher to test yields of soybean plants of
different sizes and growth habits, and plant response to
change in populations of pathogens. The model is
intended to be a basic framework for the development of
disease intensity yield loss relationships for
soybean.
The soybean growth model was developed from two
years of intensive field studies. Included in the
experiments was a fungicide with specific action toward
one soybean pathogen and a second fungicide with
activity against most other soybean pathogens.
Validation of the soybean growth model was
performed with data sets independent of the set used to
develop the model. Results published by other workers
were used to verify the model.
The presented soybean growth model and the disease
intensity yield loss submodels are to be considered as
initial models. The development of simplistic, but
accurate, models is always a first step in simulating a
phenomenon as complex as plant pathogen interactions.
121


This dissertation was submitted to the Graduate Faculty
of the College of Agriculture and to the Graduate
Council, and was accepted as partial fulfillment of the
requirements for the degree of Doctor of Philosophy.
December, 1982
(/
Dean, Graduate School


TABLE OF CONTENTS
LIST OF TABLES v
LIST OF FIGURES vii
LIST OF ABBREVIATIONS ix
ABSTRACT x
GENERAL INTRODUCTION 1
LITERATURE SURVEY 4
I. DEVELOPMENT OF THE MODEL 8
A.) Introduction 8
B.) Materials and Methods 9
1.) Field Plots, 1980 12
2 .) Field Plots 1981 12
C ) Results 13
1 .) Field Plots 1980 13
2.) Field Plots, 1981 16
D.) Discussion 28
1 .) Field Plots 1980 28
2 ) Field Plots 1981 35
II. DESCRIPTION OF THE MODEL 40
A.) Introduction 40
B.) Materials and Methods 41
C.) Results 43
D.) Discussion 58
iii


141
i


114
>
INSECT
MORTALITY


118
equation 1. Incorporation of the disease threshold in
Fig. 17 would consist of: a value, where below, say 4%
disease, no yield loss would occur. The rate of yield
loss from disease may change with the amount of disease
present. For instance: yield loss may occur at rate
"a" for each increase in from 4-9%; from 10-15% disease,
yield loss may occur at rate "b" for each increase in
disease ;
from
16-24% disease
, yield
loss
may
occur at
rate "c"
for
each increase
in disease ;
and
above 25%
disease ,
yield
loss may occur at
rate
"d"
for each
increase
in
disease. In
addition
to
the
disease
threshold, there is an economic threshold (30), where
disease control would become economically feasible.
Detailed discussion of economic thresholds is beyond the
intended scope of my work, but one can easily see where
this concept could be incorporated into the foliar
disease submodel. A mortality factor for the pathogen,
specific for the type of control agent used would be
assigned, as well as a cost factor; when the cost of
yield reduction (at any assigned market price) is higher
than the cost of the control measure, then control is
economically feasible.
Another problem exists in the artificial
defoliation studies. There is no reasonable method for
extrapolating yield reduction caused by
non-pathog en-induced defoliation (insect-induced,


58
Figures 2 through 7 represent the positive
dry-matter accumulation over time and associated
coefficients of determination for soybean plant organs.
When a mathematical equation described negative
dry-matter accumulation, the dry matter was set to zero.
The model had a flexible harvest date, determined by the
progression of leaf dry-matter accumulation, but
generally was run 123 or fewer days from sowing.
D ) Pis cus sion
To have a soybean model driven by leaf dry-matter
accumulation over time seems a reasonable approach, as
leaves produce photosynthate to fill pods and seeds and
to grow stems and petioles. Shibles and Weber (72, 73)
have reported soybean dry-matter accumulation was
proportional to leaf area. The proportionality of
dry-matter accumulation to leaf area is not unique to
soybeans. Allen and Scott (1) described a linear
relationship between dry-matter accumulation in potato
and interception of solar radiation; interception of
solar radiation was proportional to leaf area. Peanut
canopies under various disease and insect stresses had a
linear leaf area to leaf dry-weight relationship; LAI
values from the work ranged from 0.32 to 3.55 (9).


22
20
I 8
I 6
14
I 2
I 0
8
6
4
2
0
49
SEEDS
9 = -3.447 +0.2767x 0.00644x 2
+ (4.444* 10"5)x3
Rz = 0.88
20 40 60 80 100 I 20
TIME (days)


115
C.) Results
Results are described only for those applications
which appropriate data were collected from my field
experiments. Data on foliar diseases and above-ground
non-foliar plant pathogens (causing quantity and quality
losses) are included in this section.
Foliar disease levels were very low throughout the
1980 and the 1981 growing seasons. Equation 1
parameters of Ymax = 0.02, Yo = 0.00001 and k=0.0294
(actual data {37}), decreased the dry-matter
accumulation for seeds, stems, pods, petioles, or leaves
only 0.07%. When the plant seed yield was converted to
bushels per acre, there was no significant difference at
the 5% level. The maximum disease severity was 2%, and
yield differences were nonsignificant at the 5% level
(37). A threshold level of disease was not taken into
consideration per s e in equation 1, but low levels of
disease do not reflect a change in the final yield. If
all the disease parameters (Ymax, Yo, and k) were
increased, more seed yield loss would occur, which would
simulate a more severe epidemic. An adequate range of
disease severities would have to be present to calibrate
the foliar-disease submodel.
Dry matter is removed proportional to the cube of
the quality rating of the stems and pods (Eq. 2). When


83
Table 15. Harvested above-ground plant dry matter
proportioned into seeds, stems, and pods for two soybean
cultivars 1981.
Soybean cultivar
Bragg
Cobb
z
Mean of three plants.
Plant
portion
(%)Z
Seeds
Stems
Pods
52
33
15
53
34
13


51


48.Menke, W. W. 1973. A computer simulation model:
The velvetbean caterpillar in the soybean agroecosystem
Fla. Entomol. 56:92-102.
49. Menke, W. W., and Greene, G. L. 1976.
Experimental validation of a pest management model.
Fla. Entomol. 59:135-142.
50. Meyer, G. E., Curry, R. B., Streeter, J. G., and
Mederski, H. J. 1979. SOYMOD/OARDC-Dynamic simulator
of soybean growth, development, and seed yield: 1.
Theory, structure, and validation. Ohio Agrie. Res.
Dev. Centr. Res. Bull. 1113. 36 pp .
51. Mitchell,
Center. 1980.
D. B. (Director), National Climatic
Climatological data, Florida 84(6):1-15
52. Mitchel1,
Center. 1980.
D. B. (Director), National Climatic
Climatological data, Florida 84(7):116
53. Mitchel1,
Center. 1980.
D. B. (Director). National Climatic
Climatological data, Florida 84(8):1-15
54. Mitchell,
Center. 1980.
D. B. (Director). National Climatic
Climatological data, Florida 84(9):1-14
55. Mitchell,
Center. 1980 .
84(10):1-15.
D. B. (Director), National Climatic
Climatological data, Florida
56 Mitchell,
Center. 1980 .
84(11):1-14.
D. B. (Director). National Climatic
Climatological data, Florida
57. Mitchell,
Center. 1981.
D. B. (Director), National Climatic
Climatological data, Florida 85(6) :1 14
58. Mitchell,
Center. 1981.
D. B. (Director), National Climatic
Climatological data, Florida 85(7):l-22
59. Mitchell,
Center. 1981.
D. B. (Director), National Climatic
Climatological data, Florida 85(8):l-20
60. Mitchell,
Center. 1981.
D. B. (Director), National Climatic
Climatological data, Florida 85(9):1 20
61. Mitchell,
Center 1981.
85( 10): 1-20 .
D. B. (Director), National Climatic
Climatological data, Florida
62. Morse, W.
Pages 3-59 in:
Markley (ed ) .
J. 1950. History of soybean production
Soybeans and soybean production I, K. S
Interscience Publishers, Inc., New York


3
investigations toward aspects of the pathosystem which
need clarification.
Any model is the simplified representation of a
system. The soybean growth model developed with disease
stress, described here, does not cover all aspects of
plant growth, but that was not its intended purpose.
The purpose of this new model was to be a beginning
framework for a disease intensity yield loss model.
Further model refinements could incorporate pathogen
response to environmental conditions and growth of
systemic, non-foliar pathogens.
Data were analyzed on an Amdahl 470 V6 and an IBM
3033N at the facilities of the Northeast Regional Data
Center of the State University System of Florida, and on
an APPLE II Plus microcomputer (48 K memory); all
computers were located on the University of Florida
campus, Gainesville, Florida.


33
undoubtedly was not optimal, as soil tensiometers were
not used. No irrigation management scheme was followed,
so it would be improper to conclude that irrigation was
applied to produce optimal yields or favor disease
spread. The foliar disease levels ranged from less than
0.01% to 1.0% throughout most of the growing season and
the nonsignificant differences in seed yield of plots as
a result of fungicide treatments were expected.
The lack of a yield response as a result of disease
control manifested itself in soybean fungicide trials
conducted by others during the season (5, 19, 65, 66,
67, 83). In some reports, foliar disease levels were
not significantly different (P=0.05) for frogeye leaf
spot (65, 67), purple stain (66), or for pod
discoloration (66). Pod discoloration (67), purple
stain (67), and frogeye leaf spot (66) levels were
significantly different (P=0.05) for other tests. No
significant (P=0.05) yield response as a result of
fungicide treatment was present across most fungicide
trials during that year. Plots with treatments which
controlled diseases generally yielded better than those
plots which did not have a fungicide treatment, although
not always significantly (P=0.05). The general trend
observed was the highest control of foliar disease
provided the highest yield of plant mass. I also
observed the same trend of highest yield associated with


12
the labeled plants were individually harvested, the
center 4.88 meters of the center two rows were harvested
for seed yield.
1 ) Field Plots 1980
The field was planted on 27 June and harvested 125
days later on 4 November. Benomyl was first applied 4
July, and sunsequent applications were made every 14
days through harvest. Metalaxyl was first applied 30
June, and sunsequent applications were made every 40
days through harvest. Leaf area and disease intensity
data were collected from five plants in each of the
center two plot rows.
2 ) Field Plots 1981
The field was planted on 15 June and harvested 124
days
later
on 16 October. Benomyl
was
f irst applied
22
June ,
and
sunsequent
applications
were made every
14
days
through harvest
. Metalaxyl
was
first applied
22
June ,
and
sunsequent
applications
were made every
40
days
through harvest
. Leaf area
and
disease intensity
data
were
collected
f rom two plants
in each of
the
center two plot rows.