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

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Title:
Development and validation of a growth model for Florida-grown soybeans with disease stress
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xii, 152 leaves : ill. ; 28 cm.
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English
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Johnson, Steven Boyd, 1955-
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Subjects / Keywords:
Soybean -- Growth -- Mathematical models   ( lcsh )
Soybean -- Diseases and pests -- Mathematical models   ( lcsh )
Plant Pathology thesis Ph. D
Dissertations, Academic -- Plant Pathology -- UF
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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.
Statement of Responsibility:
by Steven Boyd Johnson.
General Note:
Typescript.
General Note:
Vita.

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University of Florida
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All applicable rights reserved by the source institution and holding location.
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aleph - 028557823
oclc - 09309165
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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



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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



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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






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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






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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






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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.



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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






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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






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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.






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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.






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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.






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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.





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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.





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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,