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Mathematical modeling of the growth and development of potatoes (Solanum tuberosum L.)

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Title:
Mathematical modeling of the growth and development of potatoes (Solanum tuberosum L.)
Added title page title:
Solanum tuberosum
Creator:
Ingram, Keith T., 1953- ( Dissertant )
McCloud, D. E. ( Thesis advisor )
Boote, K. J. ( Reviewer )
Duncan, W. G. ( Reviewer )
Norden, A. J. ( Reviewer )
Humphreys, T. E. ( Reviewer )
Fry, Jack L. ( Degree grantor )
Place of Publication:
Gainesville, Fla.
Publisher:
University of Florida
Publication Date:
Copyright Date:
1980
Language:
English
Physical Description:
xiii, 156 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Canopy ( jstor )
Crop growth ( jstor )
Crops ( jstor )
Photosynthesis ( jstor )
Planting ( jstor )
Potatoes ( jstor )
Soil science ( jstor )
Soil temperature regimes ( jstor )
Tubers ( jstor )
Vegetation canopies ( jstor )
Agronomy thesis Ph. D
Dissertations, Academic -- Agronomy -- UF
Potatoes -- Development -- Mathematical models ( lcsh )
Potatoes -- Growth -- Mathematical models ( lcsh )
City of Gainesville ( local )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Abstract:
During the 1978 growing season a growth analysis was performed on potatoes ( Solanum tuberosum L. ) planted on 2 February and 14 March. Two cultivars, Monona and Sebago, were studied. During the winter of 1979 a thermogradient analysis of Sebago growth was conducted. The objective of these studies was to provide data for the development and validation of a mathematical crop growth and development model. During the summer and fall of 1979 such a crop model was written in the GASP IV simulation language. The purpose of the crop model was to elucidate the effects of temperature on assimilate partitioning. The results of the crop growth and development model indicated that the primary effect of soil temperature was through a direct regulation of the tuber growth rate which had a 15° C temperature optimum, A high potential tuber growth rate stimulated photosynthesis; so a secondary effect of soil temperature was on net daily photosynthesis. The major effect of air temperature was its influence on the tuber initiation date. Air temperature and tuber initiation rate were inversely related. The air temperature also affected the rate of canopy senescence with warm temperatures speeding leaf drop and reducing the crop growth rate. The main weakness of the model was that light interception data were input rather than generated by the model itself.
Thesis:
Thesis--University of Florida.
Bibliography:
Bibliography: leaves 123-128.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Keith T. Ingram.

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University of Florida
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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:
022094677 ( ALEPH )
06345979 ( OCLC )
AAB7443 ( NOTIS )

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MATHEMATICAL MODELING OF THE GROWTH AND DEVELOPMENT

OF POTATOES (Solanum tuberosum L.)













BY

KEITH T. INGRAM


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

198C


U j,"j .,, r ) ," V .4 1( s ) o j ;, ,.- 6 - J I












ACKNOWLEDGEMENTS

I thank tne members of my advisory committee: Dr. K. J. Boote,

Dr. A. J. Norden, Dr. W. G. Duncan, and Dr. T. E. Humphreys, and

especially the chairman of this committee, Dr. D. E. McCloud. I

heartily appreciate the counsel and latitude the committee gave to

me during the pursuit of this degree program.

Thanks to Dr. D. Hensel ana the staff of the IFAS Potato Research

Station in Hastings, Florida, who helped me carry out the 1978 growth

analysis experiment.

Thanks to Mr. J. B. White who supervised the construction of tne

tnermogradient system which I used in 1979.

My parents, Billy G. and Suzanne G. Ingram, have given me untold

support and encouragement in all of :y educational endeacvrs. Myriad

thanks.

A final word of appreciation to all of my fellow students and

friends who have shared with me the pleasures and burdens I have

encountered during this degree program.













TABLE OF CONTENTS
Page

ACKNOWLEDGEMENTS.................... ... ..................... ..-. ii

LIST OF TABLES.................................................... v

LIST OF FIGURES................................................... viii

ABSTRACT .......................................................... xii

INTRODUCTION.................................. ................... 1

LITERATURE REVIEW .............. .................................. 2

Eco-Physiological Crop Modeling............................... 2
Crop Phenology............................................... 4
Heat......... .......................................... 5
Solar Radiation............................. ..... ............ 8
Nutrients.................................................. 13
Water..................................... ............ ....... .
Seas n ..................................................... 15
Crop Growth .................................................. 19
Heat ........................................................ 20
PAR......................................... ............... 27
Nutrients ......... ........................................ 29
Water..................................................... 34
Oensity........................................... 36
Summary...................................... ............. 37

MATERIALS AND METHODS ............................................ 39

Crop Growth Model .................. .......................... 39
Growth Analysis 1978........................................... 40
Thermogradient Analysis 1979................................... 47

RESULTS AND DISCUSSION ............................. ....... ....... 51

Growth Analysis 1973........................................... 51
Pre-Emergence............................................. 51
Emergence .... .............................................. 54
Plant Gensity..................................... . ...... 58
Canopy Development.................................. ..... 58
Flowering .................................................. 82
Tuber Initiation.......................................... 82
Rhizomes.................................................. 83
Yield Dynamics ............................ ........... ...... 84
iii








Pace
Thermogradient Analysis 1979................................... 90
Bud Dormancy.............................................. 90
Stem Growth and Elongation ................................. 94
Root Growth................................................ 94
Tuber Growth.............................................. 98
Sebago Crop Growth Model...................................... 100
Model Development..... ................................. .... 100
Model Validation............................................ 106
Temperature Sensitivity Analysis............................ 112

SUMMARY AND CONCLUSIONS........................................... 120

Growth Analysis ................................ ............. 120
Thermogradient Analysis.................. ..................... 121
Sebago Crop Growth Model....................................... 122

BIBLIOGRAPHY...................................................... 123

APPENDIX A: LISTING CF VARIABLE DEFINITIONS, MODEL PROGRAM,
COMMON BLOCK VARIABLES, INPUT TABLES, INITIAL VALUES OF STATE
VARIABLES, AND PLOT STATEMENT FILES OF THE SEBAGO GROWTH AND
DEVELOPMENT MODEL............................................... 130

APPENDIX B: TABLES OF RAW DRY WEIGHT DATA. TUBERS PER SEED-
PIECE, INFLORESCENCES PER SEED-PIECE, STEMS PER SEED-PIECE.
TOTAL BRANCH PLUS STEM LENGTH PER SEED-PIECE, PERCENT FINAL
EMERGENCE, MAXIMUM LEAF AREA INDEX, MAXIMUM PERCENT AROUND
COVER, AND THEIR RESPECTIVE ANALYSIS OF VARIANCE ................. 143

BIOGRAPHICAL SKETCH ........................................... 156












LIST OF TABLES


Table Page

1 Experiment dates, temperature ranges, and seed-
piece fresh weights for thermogradient analysis........... 48

2 Duration and cumulative heat units for Monona
and Sebago phenophases............................... 53

3 Seeding rates, maximum emergence, stems per seed-
piece, and plant density for all treatments.............. 57

4 Dry weights for various components of Monona planted
on Julian Day 33, based upon samples of two seed-
pieces per replicate................... ............. 65

5 Dry weights for various components of Monona planted
on Julian Day 73, based upon samples of two seed-
pieces per replicate ................................. 66

6 Dry weights for various components of Sebago planted
on Julian Day 33, based upon samples of two seed-
pieces per replicate ................................. 67

7 Dry weights for various components of Sebago planted
on Julian Day 73, based upon samples of two seed-
pieces per replicate ................................. 68

8 Crop and tuber growth rates during most linear growth
period, with statistics for linear model and parti-
tioning ratio ....................................... 91

9 A post-emergence comparison of dry weights of field-
grown and computer-simulated Sebago potatoes with a
Julian Day 33 planting date............................ 107

10 A post-emergence comparison of dry weights of field-
grown and computer simulated Sebago potatoes with a
Julian Day 73 planting date............................. 108

11 Simulated tuber and crop growth rates, assimilate
partitioning ratio, and tuber initiation dates
with climatic inputs of the Julian Day 33 and
73 growth analyses......................................... 11







Table Page

12 Simulated tuber and crop growth rates, mean daily net
photosynthesis, and photosynthate partitioning ratios
for various temperature inputs. All calculations
from linear tuber growth phase.......................... 113

13 Simulated tuber and crop growth rates, mean daily net
photosynthesis, and photosynthate partitioning ratios
for various temperature inputs. All calculations from
linear tuber growth phase................................. 114

14 Simulated final yields for tubers, canopy, roots, and
total and tuber initiation dates with various tempera-
ture inputs.............................................. 115

15 Simulated final yields for tubers, canopy, roots, and
total and tuber initiation dates with various tempera-
ture inputs........................................... 116

List of Tables in Appendix B

B-1 Dry weights of seed-pieces, tubers, and crop total
by replicates for the Julian Day 33 planting............. 13

B-2 Dry weights of seed-pieces, tubers, and croo total
by replicates for the Julian Day 73 planting............ 146

B-3 ANOVA for total crop yields at final harvest............. 148

B-4 ANOVA for tuber yields at final harvest.................. 143

B-5 Number of tubers per seed-piece......................... 149

B-6 ANOVA for number of tubers per seed-piece in Table B-5... 149

B-7 Number of inflorescences per seed-piece for date of
maximum flowering.................. ..................... 150

B-8 ANOVA for number of inflorescences per seed-piece in
Table B-7...................... .......................... 150

B-9 Number of stems per seed-piece........................... 15

B-10 ANOVA for number of stems per seed-piece in Table B-9.... 151

B-11 Total stem plus branch lengths per seed-piece at maxima.. 152

B-12 ANOVA for total stem olus branch lengths per seed-
piece in Table B-1 1...................... ............ 152
vi







Table Page

B-13 Percent final emergence............................... 153

B-14 ANOVA for emergence percentages in Table B-13........... 153

B-15 Maximum leaf area index ................................ 154

B-16 ANOVA for LAI's in Table B-15......................... 154

B-17 Maximum percent ground cover............................ 155

B-18 ANOVA for ground cover percent in Table B-17........... 155













LIST OF FIGURES


Figure Page

1 General cumulative heat model with no temperature
maximum................................................ 9

2 National Weather Service's Growing Degree Day heat
model................................................... 10

3 Cummulative heat model which accounts for fluctua-
tions about the base temperature (After Tyldesley,
1978).................................... ................ 11

4 Simplified Ontario Heat Unit System (After
Tyldesley, 1978)..................................... 24

5 Effect of temperature on the rate of an enzyme cata-
lyzed reaction: i) response with constant enzyme
activity; ii) thermal denaturation effect on enzyme
activity; iii) reaction rate, the product of curves
i and II (AfterConn and Stumpf, 1972).................... 25

6 Effect of temperature on: i) Photosynthesis; ii)
Respiration; and iii) Growth (After Larcher, 1975)....... 26

7 Model of light intensity effect on leaf photosyn-
thesis (After De Wit, 1959) .............................. 30

3 lModel of light intensity effect on leaf photosyn-
thesis (After Duncan et al., 1967)....................... 31

9 Net carbon exchange in potato canopy from sunrise
to sunset (After Sale, 1974)............................. 32

10 Weekly average temperature in Hastings, Florida.
Air temperatures (-- ) measured in standard shelter
at 150 cm height. Soil temperatures (----) measured
at 10 cm depth ............... .. ........................ 43

11 Total weekly precipitation (----) in Hastings,
Florida, and pan evaporation (- ) in Gainesville,
Florida................. ............... ............... a.

12 Daily photosynthetically active radiation average
over one week intervals................................ 45

viii








Figure Page

13 Soil temperature profiles under a Sebago canopy from
1615 hours on March 20, 1978 to 1205 hours on March
21, 1978 ................... ........................... 46

14 Percent seed-piece emergence and number of inflores-
cences per seed-piece for Monona and Sebago planted
on Julian day 33...................................... 55

15 Percent seed-piece emergence and number of inflores-
cences per seed-piece for Monona and Sebago planted
on Julian day 73...................................... 56

16 Leaf area index and percent ground cover for Monona
planted on Julian day 33................................ 59

17 Leaf area index and percent ground cover for Sebago
planted on Julian day 33............................... 60

18 Leaf area index and percent ground cover for Monona
planted on Julian day 73................................. 61

19 Leaf area index and percent ground cover for Monona
planted on Julian day 73............................... 62

20 Effective leaf area index for Monona and Sebago
planted on Julian day 33...... ......................... 69

21 Effective leaf area index for Monona and Sebago
planted on Julian day 73................................ 70

22 Total stem and branch length, main stem length, and
average branch length for Monona planted on Julian
day 33 ............................................. 73

23 Total stem and branch length per seed piece, main stem
length, and average branch length for Sebago planted
on Julian day 33...................................... 74

24 Total stem and branch length per seed piece, main stem
length, and average branch length for Monona planted
on Julian day 73...................................... 75

25 Total stem and branch length per seed piece, main
stem length, and average branch length for Sebago
planted on Julian day 73............................... 76

26 Dry weights of green and chlorotic leaves of Monona
planted on Julian day 33 as used to estimate leaf
duration................................................ 73

ix








Figure Page

27 Dry weights of green and chlorotic leaves of
Sebago planted on Julian day 33 as used to
estimate leaf duration................................. 79

28 Dry weights of green and chlorotic leaves of
Monona planted on Julian day 73.......................... 80

29 Dry weights of green and chlorotic leaves of
Sebago planted on Julian day 73 as used to
estimate leaf duration................................. 81

30 Growth curves for total plant, tubers and remainder
for Monona planted on Julian day 33 with sample
size from 12 to 20 seed-pieces per replicate............ 85

31 Growth curves for total plant, tubers, and remainder
for Sebago planted on Julian day 33 with sample
size from 12 to 20 seed-pieces per replicate............ 86

32 Growth curves for total plant, tubers, and remainder
for Monona planted on Julian day 73 with sample
size from 12 to 20 seed-pieces per replicate............ 87

33 Growth curves for total plant, tubers, and remainder
for Sebago planted on Julian day 73 with sample
size from 12 to 20 seed-pieces per replicate........... 88

34 Effect of temperature on stem growth for Sebago
seed-pieces with dormant buds.......................... 92

35 Temperature response for stem elongation in Sebago
seed-pieces with dormant buds.......................... 93

36 Effect of temperature on stem growth of Sebagc
potatoes with non-dormant buds................... .... 95

37 Temperature response for stem elongation in
Sebago seed-pieces with non-dormant buds................ 96

38 Root growth temperature response curves for
Sebago potatoes........................ ............ 97

39 Effect of soil temperature on tuber and total
growth rate of Sebago potatoes grown in 25 cm
plastic pots... ........................................ 99

40 Dry-matter flow diagram for Sebago growth model.......... 01

41 Relative growth rate vs. temperature for Sebago
canopy (TCAN), roots (TROOT), and tubers (TUBRGR)....... 104

x







Figure Page

42 Tuber growth rate (TTUBR) vs. temperature for Sebago.... 105

43 Simulated Sebago growth components with climatic
inputs of the Julian day 33 growth analysis............. 109

44 Simulated Sebago growth components with climatic
inputs of the Julian day 73 growth analysis............. 110












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



MATHEMATICAL MODELING OF THE GROWTH AND DEVELOPMENT
OF POTATOES (Solanum tuberosum L.)

By

Keith T. Ingram

March 1980

Chairman: Darell E. McCloud
Major Department: Agronomy

During the 1978 growing season a growth analysis was performed

on potatoes (Solanum tuberosum L.) planted on 2 February and 14

March. Two cultivars, Monona and Sebago, were studied. During the

winter of 1979 a thermogradient analysis of Sebago growth was con-

ducted. The objective of these studies was to provide data for the

development and validation of a mathematical crop growth and develop-

ment model. During the summer and fall of 1979 such a crop model was

written in the GASP IV simulation language. The purpose of the crop

model was to elucidate the effects of temperature on assimilate

partitioning.

The results of the crop growth and development model indicated

that the primary effect of soil temperature was through a direct

regulation of the tuber growth rate which had a 150 C temperature

optimum. A high potential tuber growth rate stimulated photosynthesis;

so a secondary effect of soil temperature was on net daily photosynthesis.

xii







The major effect of air temperature was its influence on the tuber

initiation date. Air temperature and tuber initiation rate were

inversely related. The air temperature also affected the rate of

canopy senescence with warm temperatures speeding leaf drop and

reducing the crop growth rate. The main weakness of the model was

that light interception data were input rather than generated by the

model itself.


xiii













INTRODUCTION

There are four factors which determine a crop's yield: 1) the

rate of crop photosynthesis; 2) the amount of assimilate which can

be mobilized and translocated to the yield component from storage in

other crop organs; 3) the portion of daily photosynthesis deposited

in the yield organ; and 4) the duration of yield organ growth. Of

these yield determining factors, the daily photosynthate partitioning

and the length of the yield organ growth period show most potential

response to manipulation for increasing yields. The mechanisms which

regulate photosynthate distribution are not clear; so it is impossible

to systematically change partitioning per se.

It is the aim of this study to elucidate the effects of tempera-

ture on photosynthate partitioning. The potato, Solanum tuberosum L.,

was chosen as the experimental subject because the yield organs and

the photosynthetic organs grow in different thermal environments.

The soil temperature of the tuber environment has smaller amplitude

of fluctuation and different times of maximum and minimum temperatures

than the aerial temperatures of the crop canopy. Further, these thermal

differences occur on both daily and seasonal bases.

In field and greenhouse stuGies many other environmental factors

confound interpretation of thermal effects. Therefore, a computer

simulation model was developed to isolate thermal effects on potato

crop growth dynamics.













LITERATURE REVIEW

Eco-Physiological Crop Modeling

Agronomists often use the terms crop ecology and crop physiology

synonymously. This confusion stems partly from the fact that ecology

and physiology are terms which originate from studies of natural

biological systems. Ecology can be defined as the study of relation-

ships between organisms and their environment. Physiology is the

study of normal functioning of organisms and their organs. When

applied to crop systems these definitions overlap. The goal of crop

physiology is to better understand the dynamics of yield development

(Evans,1975a). Crop physiology greatly depends upon environmental

factors which are the subject of ecology. Milthorpe and Moorby (1974)

use the term physiology when considering interrelationships between crop

plants and abiotic environmental factors as well as competitive

interactions between higher plants comprising the crop system. Some

authors recognize the commonalities between the two fields of study by

using the terms eco-physioiocy (Eckard,1965) or ecological physiology

(Leopold and Kriedemann, 1975).

This eclectic area is fundamental to models of crop growth and

development. Crop models attempt to mathematically describe plant

responses to environmental inputs. The models most frequently

encountered in literature tend to minimize input variables and

responses to facilitate understanding of the model. For example,

Lynch and Rowberry (1977a) tested two reciprocal polynomial models






3

to determine which best described the relationship between potato stem

density and tuber yield. They used the single input, stem density, to

predict two responses, total tuber yield and marketable tuber yield.

More complex models have been developed to describe other crop system

phenomena. Several models have been published which describe soil-

plant water relationships (Campbell et al., 1976; DeVries, 1972),

crop photosynthesis (Duncan et al., 1967; DeWit, 1959), and crop

microclimate (Goudriaan and Waggoner, 1972). In fact, any mathematical

description which relates two or more factors, such as by regression

analysis, is a model. With the advent of high speed computers the art

and science of modeling have progressed from simple statistical type

models, to multiple linear regression models, to complex systems of

equations which attempt to simulate crop growth and development through-

out a growing season and to models of entire eco-system functioning

(Stewart, 1975). Moorby and Milthorpe (1975) have published a flow

diagram for a possible potato growth model. The complete mathematical

description of potato growth and environmental relations is complicated

by the enormous range of adaptability and plasticity of the potato

crop, the multiplicity of uses to which potatoes are put, and by an

incomplete understanding of potato growth physiology.

Similar to ecology and physiology, crop growth and development

are often poorly distinguished. Growth, as used here, refers to the

increase in dry weight. Development, on the other hand, refers to the

combination of organ differentiation and growth coordination. The

growth of a croo is highly dependent upon its developmental phase or

phenophase. The eco-physiological model must be able to follow growth

and development alor:g separate but interdependent time courses.







Crop growth models generally include four primary processes:

water relations, mineral uptake and metabolism, photosynthesis, and

crop development. The major environmental inputs to these processes

are soil nutrient availability, air temperatures, solar radiation,

and precipitation or irrigation. The modeler must consider not only

the environmental inputs, but also how the particular crop responds

to these environmental factors. The purpose of this review is to

elucidate some of the more important eco-physiological interrelation-

ships affecting potato crop growth and development.



Crop Phenology

Crop phenology is the study of developmental phenomena which

respond to annually periodic environmental stimuli. These developmental

phenomena are catalogued by visible morphogenic changes such as bud

break, flower initiation, and fruit abscision. Phenology can be

contrasted with ontology. Whilephenology is the study of life cycle

changes due to annual climatic fluctuations, ontology is the study of

developmental phases through the life of an individual organism

(Larcher, 1975). For annual plants the difference between phenology

and ontology is slight. Cultivated potatoes fit best in the annual

growth habit classification. One might distinguish between potato

ontogeny and phenology. The ontogenic cycle begins when the tuber bud

is initiated and ends when the canopy produced by that bud senesces.

By contrast, the phonologic cycle runs from planting through harvest

and storage. Thus ontogenic generation; overlap during the period

from tuber initiation to harvest while phenologic cycles do not






5

overlap. Further, phenology emphasizes environmental effects on crop

development while ontology tends to focus on genetic factors.

One list of the climatically regulated phenophases in a potato

crop's development might include: a) tuber dormancy; b) bud break

and shoot elongation; c) root system, rhizome, and canopy development;

d) flowering; e) tuberization; f) tuber growth; g) canopy senescence;

and h) crop maturity. This list is little more than the organogenic

sequence through the crop season. Much more interesting than the

phenologic description are the factors which regulate the length of

the phenophases.

Heat

The relationship between crop development rates and thermal

environment has been noted for many crops. The heat unit theory by

Abbe states that plant development depends upon cumulative heat

exposure rather than time oer se (McCloud, 1979). The national

weather service provides growing degree day data in their Weekly

Weather and Crop Bulletin to help researchers and growers estimate

crop development rates. Most crop models include a subroutine which

integrates temperature inputs in order to regulate crop phenology.

In fact, for many crop models, heat accumulation alone is sufficient

to monitor the crop development rate.

For most crops, development rate and temperature are positively

related over the temperature range for normal growth. In wheat,

higher temperatures reduce the length of both vegetative and filling

phases (Spiertz, 1974). In field work supporting their cotton

morphology model Hesketh et al. (1972) found that higher temperatures

reduced days from planting to full cotyledon expansion, days between








development of successive leaves on the same branch and between

successive branches on the main stem as well as between flowers on a

branch. Their work showed that the cumulative heat concept can be

used to describe organogenesis, i.e., plastochron duration, as well as

longer term phenologic development, i.e., the canopy development phase.

Haun (1975) used multiple linear regression to analyze relationships

between daily maximum and minimum air temperatures as well as other

climatic data with development rate of potato leaves. He found the

best correlation between the leaf development rate and temperature when

a one or two day lag time for air temperature was used. Unfortunately,

since Haun used multiple linear regression analysis, it is nearly

impossible to isolate the exact temperature verses development rate

relationship.

According to Van Dobben (1962), the effect of heat on the rate of

vegetative crop development is independent from the effect of heat on

crop growth. Generalized trends of the influence of heat on potato

development are as follows: 1) The emergence rate is accelerated at

higher temperatures over the range of 12 to 240 C. 2) The optimum

temperature for tuberization is around 200 C with initiation delayed

relatively more by higher than lower temperatures. At 300 C tubers may

never form. 3) At high temperatures the canopy may continue to develop

past flowering under conditions of high nutrient availability. Extended

canopy growth at hign temperatures is likely related to delayed or

decreased tuberizaticn which makes more assimilate available for canopy

growth (Bodlaender, 1963).

in the above discussion little distinction was made between the

relative influences of air and soil temperatures. These factors are






7
highly correlated and difficult to distinguish (Nielson and Humphries,

1966; Richards, 1952). Richards reported a phase delay and amplitude

reduction in the soil temperature with increased depth. In other

words, the difference between maximum and minimum temperatures declines

with depth, and the time of these maximum and minimum temperatures is

delayed. In the root and tuber growth zone, however, the phase shift

and amplitude dampening with depth are slight.

In their research on tomatoes, Abdelhafeez et al. (1971) found

that the main effect of soil temperature on development rates occurred

during the emergence phase. Two weeks past emergence, little distinc-

tion could be made between soil temperature treatments. Furthermore,

soil temperature had no apparent effect on fruit maturity dates. Still,

the findings of Abdelhafeez et al. agreed with those of Nielson and

Humphries that soil temperature had a marked effect on root morphology

and development. At cool temperatures roots develop more slowly, have

fewer secondary roots and become thicker than at higher temperatures.

Soil temperature has an effect on corn development well beyond

emergence. Mederski and Jones (1963) found that corn plants grown on

soil heated from planting to maturity and from emergence to maturity

both reached maximum height earlier and matured earlier than unheated

control plants. If, as suggested by Van Dobben (1962), the effect of

soil temperature is positively related to the size of the crop

propagule's reserve of substrate, then we would expect significant

effects of temperature on potato development. Indeed, higher soil

temperatures have decreased the time from planting to emergence

(Moorby and Milthorpe, 1975). Further, since the tuber of the potato

develops underground we might expect that soil temperature plays a






8

greater role in determining potato crop development than in crops where

the bulk of the biomass is aerial. Higher soil temperatures seem to

shorten the tuber initiation period with fewer tubers being set.

However, the higher soil temperature does not appear to hasten canopy

senesence when air temperatures are held constant. Under these con-

ditions, the few tubers which do set at high soil temperature

generally grow to larger proportions than tubers growing in cool

soil (Bodlaender, 1963; Hagan, 1952b).

The cumulative heat models mentioned above commonly assume a

linear form (Figures 1 and 2). The rate of development increases

linearly above some base temperature. The development rate may or may

not have an upper limit. The Growing Degree Day information published

by the National Weather Service assumes zero development above 30 C

(Figure 2). The simplicity of these linear models makes them most

practical for general use. Discrepancies arise when temperatures

fluctuate about the base temperature or the maximum temperature.

Tyldesley (1978) presented a model to account for these temperature

fluctuations (Figure 3). Tyldesley smoothed the angle between the

linear model and the axis.

Solar Radiation

Isolating the effects of solar intensity on crop development is

difficult. Radiation provides energy for evapotranspiration and

temperature changes within the crop canopy (Chang, 1968). The effects

of these climatic factors are confounded in most field experiments.

Still, Haun (1975) found significant correlations between light

intensity and leaf development in potatoes. Effects of low light

intensities on plant development have been studied as well. At low












40-
HEAT
UNITS
30-


20-





BASE B+20 8*40

TEMPERATURE (OC)
Figure 1. General cumulative heat model with no temperature maximum.
















GROWING
DEGREE
DAYS


20 25


TEMPERATURE (C)


Figure 2. National Weather Service's Growing Degree Day heat model.
















40


30-
HEAT
UNITS 20





0-

BASE 1BO0 1-20 B530

TEMPERATURE (C)

Figure 3. Cummulative heat model which accounts for fluctuations
about the base temperature (After Tyldesley, 1978).





12

light intensities stem elongation is stimulated while leaf development

is inhibited (Van Dobben, 1962; Leopold and Kriedemann, 1975). Using

potatoes grown at 16 hour days with light intensities from 3,000 to

16,000 lx., Bodlaender (1963) found that the maximum stem length

was reached sooner, tubers initiated sooner, the canopy senesced

earlier, and flowering was stimulated by the high light level. The

applicability of these findings to field conditions is diminished

since the highest light intensity was approximately 30% of full

sunlight (54,000 Ix.). Sale (1973a) found no effect of 21% or 34%

shade on the development of field grown potatoes. The plants grown

under both of Sale's shade conditions received higher light inten-

sities than those grown in Bodlaender's growth chamber.

Plant breeders have severely altered the photoperiodic response

of the potato. Though potatoes were cultivated by Peruvian Indians

at least as long ago as 4000 B.C., Spanish explorers did not introduce

the potato to Europe until around 1570 A.D. At that time, potatoes

were a botanical curiosity. After only 100 years potatoes were grown

on a field scale in Ireland. In the same 100 years heavy selection

pressure appears to have converted S. tuberosum subspecies andigena,

a plant adapted to form tubers under twelve hour days of tropical

latitudes, to subspecies tuberosum which initiates tubers under long

summer days (H-ewkes, 1978). Modern potatoes are classified as either

long-day favorable, short-day favorable, or day neutral by Chang (1968).

S. tunerosum is one of few species where photoperiodicity is related

to tuber formation rather than flowering. The photoperiodic response

in potatoes shows great plasticity.

Though some cultivars show more strict photoperiodic responses

(Leopold and Kreidemann, 1975), potatoes do not generally exhibit







threshold photoperiodic requirements for tuberization. Rather,

photoperiodic classification is based on the effect of photoperiod on

the development rate. For example, short-day conditions accelerate

progression from one phencphase to the next in European cultivars

which are short-day favorable. As well as earlier tuberization,

flowers initiate sooner, stem elongation ceases sooner, and plants

senesce earlier under favorable photoperiodic conditions (Bodlaender,

1963).

Nutrients

The effect of soil nutrients on potato phenology depends upon

timing of fertilizer application. Even the nutrients applied to the

seed crop may influence potato phenology. Nitrogen fertilizers applied

to the seed crop may hasten maturity in an early crop grown from the

seed (Gray,1974). High soil nitrogen levels at the time of planting

increase emergence rates (Moorby, 1978). According to Ivins (1963),

nitrogen applied during early canopy development will delay tuber

initiation and canopy senescence. On the other hand, Oyson and Watson

(1971) found that nitrogen fertilization did not delay tuber initiation

in King Edward cultivar potatoes. Only zero nitrogen fertilization

shortened the period for the car.opy to reach its maximum growth.

Rather, they found nitrogen to reduce the rate of tuber growth during

the period directly following tuber initiation.

Bremner, El Saeed, and Scott (1967) noted sharp inflection points

in the graph of tuber:foliage ratio versus total dry weight. These

inflection points indicated transition from the vegetative to tuber

growth phenophase. Low nitrogen treatments showed significantly faster

dvveiopment according to this analysis. The prolonged canopy





14

development phase under high nitrogen conditions is associated with

an increase in branching rather than main stem growth (Harris, 1978a;

Dyson and Watson, 1971).

In their studies with S. tuberosum sp. andigena, the South

American ancestor to sp. tuberosum, Ezeta and McCollum (1972) applied

three fertilizer levels: 150-160-160; 80-80-80; and 0-0-0 kg/ha of

N-P205-K205, respectively. Potatoes given the low fertilizer treatment

matured by 156 days after planting while those given higher fertilizer

treatments matured after 172 days. The flowering date was the same

for all treatments; so the only apparent effect of high fertility

appeared to be to extend the tuber development phase. All of the

nitrogen, calcium, and magnesium absorbed by sp. andigena was taken up

before tuber initiation. For the more commonly cultivated sp. tuberosum,

however, uptake may continue until the beginning of canopy senescence

(Soltanpour, 1969). Nitrogen is often taken to be the major nutrient

associated with crop development and growth. The relationship between

nitrogen level and development or growth is relatively linear over a

rather large range of nitrogen levels. Most crops exhibit a threshold

type response to levels of other plant nutrients. As long as these

nutrients are present above some threshold concentration they have

little effect on crop growth or development. Phosphorus and, to some

extent, potassium accumulate in soils which are intensively fertilized.

Thus, phosphorus and potassium are usually above the threshold.

Nitrogen reserves are quickly depleted to suboptimal concentrations

in the soil solution (Harris, 1978a).

Dyson and Watson (1971) found potassium to stimulate canopy

senescence. Potassium also stimulated the leaf growth rate. Potassium's






15

combined influences of hastening senescence and leaf growth stimulation

give a net zero effect on final yield. McCollum (1978a and 1978b) found

that phosphorus applications had opposite effects to nitrogen applica-

tions. When phosphorus was applied during canopy development, tuber

initiation and canopy senescence were both hastened.

Water

Early irrigation has some effects similar to early nitrogen appli-

cation on potato development. Both water and nitrogen tend to speed

emergence and leaf development while delaying tuber initiation (Sale,

1973b). Unlike nitrogen's effects, however, early irrigation tends to

hasten canopy senescence in some potato cultivars (Ivins, 1963;

Harris, 1978b). If irrigation is applied soon after tuber initiation

the tuber development phase is prolonged and canopy senescence is

delayed (Ivins, 1963).

Drought generally has the opposite effect of irrigation. Early

drought will cause earlier curtailment of leaf and branch development.

This drought effect reflects a reduction in numbers of Dranches and

leaves formed with relatively no change in the rate that new leaves

and branches are produced. A short drought period will decrease the

development rate of previously initiated leaves in potato plants having

tubers but not in pre-tuberous plants. In other words, the rate of

unfolding and expanding may be slowed by drought in tuber bearing

plants but not in tuberless plants. In both cases, the production of

new leaves occurs at the same rate but stops sooner under drought con-

ditions (Munns and Pearson, 1974).

During the tuber growth phase a short drought may retard or stop

tuber development. Upon relief from The wa-er stress only the






16

acropetal tuber tissues resume growth and development. Misshapen tubers

result (Moorby et al., 1975; Morby, 1973). These deformed tubers,

called second growth tubers, result from rapid maturation of the

basipetal tuber buds and adjacent tissues. Since these tissues mature

during the stress period only the acropetal buds may resume growth.

If all buds in a tuber mature as the result of a short water stress

period, the rhizome may resume growth when the stress is removed to

give a chain of tubers. Thus, there appears to be a threshold level cf

tuber and bud development. Buds beyond the threshold level of develop-

ment rapidly mature and cease growth when stressed and then unstressed.

Less well developed buds will continue more or less normal development

after the stress period. Long and Penman (1963) reported that resump-

tion of crop growth after drought relief did not occur for several

days. They postulated that new rootsneeded to grow before the recently

added soil moisture could be exploited.

Season

The preceding discussion shows that potato phenology is regulated

by a complex of environmental factors. The effect of growing season on

potato phenology results from interactions between several of the

factors. According to Moorby and Milthorpe (1975), potato growing

regions may be classified as cool-temperate or warm-subtropical. The

cool-temperate production season is limited by frost at both planting

and harvest. The warmer subtropical production areas may have two

growing seasons per year: the first from the last winter frost to high

temperatures of summer; the second after peak summer temperatures

until first frost in the fall. One might consider another ecosystem

of Dotato production, the high altitude tropical region. The andigen








subspecies is primarily grown in this region. The literature reviewed

pertains to the tuberosum subspecies so the high altitude tropical pro-

duction region is not included.

The effect of season on potato phenology begins with the soil

temperature influence on emergence. The two seasons of production in

subtropical areas are at opposite ends of this relationship. The first

crop is planted when soils are cool. Emergence is slow. Other factors

being constant, the second crop shows rapid emergence since it is

planted in warmed soils of late summer. In cool-temperate areas, crops

at later planting dates may emerge faster due to a combination of

warmer soil temperatures and the likelihood that more sprout development

has occurred on seed pieces before planting (Bremner and Radley, 1966;

Radley, 1963).

Once the crop has emerged,the length of the next phenophase will

be determined by the integrated effects of temperature, photoperiod,

nutrition, and water status. Only temperature and photopericd are

necessarily related to season since both water and nutrients may be

applied or withheld by the grower. The effects of these two environ-

mental stimuli, temperature and photoperiod, may be superimposed on

the effect of the age of the rhizome apex.

The end of the canopy development phase is marked by overlapping

commencement of tuber growth, flower initiation, and cessation of

leaf and branch growth. Moorby (1978) postulated two control

mechanisms for tuber initiation. One is hormonal. Photoperiodic

effects on tuberization are likely mediated by phytochrome. Such a

phytochrome mechanism would be an example of hormonal regulation of

tuber initiation. The other control rrchanism Moorby suggested is






18

substrate mediated. Retardation of canopy growth by low temperatures

might allow more assimilates to be translocated to rhizomes to stimu-

late tuber growth. In some cultivars the canopy growth itself may

regulate tuberization. In this case, tubers initiate when a

threshold canopy development level (as measured by LAI) is reached

(Radley, 1963).

In a cool-temperate region, Bremner and Radley (1966) found that

later planted crops had longer canopy development phases than early

planted potatoes. These observations conform to the predictions of

both of Moorby's tuberization control mechanisms since the later

planted potatoes grew in warmer weather and longer days. Sale's (1973a

and b) data from Australia's two crop periods can also be explained

in terms of the two control mechanisms. Cool temperatures and short

days during the first crop season stimulate cuberization more quickly

than the warm long days under which the second crop's canopy developed

(Moorby and Milthorpe, 1975).

Regardless of the factors which stimulate tuber initiation, the

balance of crop growth shifts from canopy to tubers at this time.

Known plant growth regulators and a hypothetical tuber forming sub-

stance have been implicated with the environmental stimuli mentioned

above. As yet, little consensus has been reached. Moorby (1978)

declared that the mass of apparently contradictory evidence illustrates

the futility at the present time of trying to give any definitive

explanation of the mechanism of tuber initiation.

By the time the tuber growth and development phase begins many

factors have possibly already contributed to canopy senescence and

crop maturity. Plants demaged by frost during early canopy development








appear to senesce earlier than unfrosted plants (Radley, 1963). Further,

the lengths of the canopy development and tuber development phases are

positively related. A long canopy development phase leads to a long

lasting canopy and a long tuber growth phase (Bremner and Radley, 1966;

Radley, 1963). According to Radley, the planting date in cool-

temperate regions had little influence on senescence time in some of

the cultivars tested. Presumably, the effect of canopy size at

tuberization on the length of the tuber growth period was overridden

by environmental factors.



Crop Growth

The definition of growth as an increase in dry weight is con-

venient to crop modelers. Dry weight increase can be easily described

mathematically as a function of physiologic and phenologic factors.

Dry weight increase, of course, is not an inclusive definition of

growth. Both popular and scientific connotations of growth include

reproduction, enlargement and cell division as well as assimilation

(Hagan, 1952a). Crop growth is the result of all of these processes.

Thus growth analysis by periodic harvest becomes a powerful instrument

for describing these growth phenomena (Radford, 1967; McKinion et al.,

1974). Combined with environmental descriptions, growth analysis is a

good test oF mathematical crop growth models (Leopold and Kriedemann,

1975).

As there are many definitions of growth, there are many ways to

label crop growth stages. Grcwth stages may be associated with the

cumulative crop growth curve. The expansion (exponential), linear,

and maturation growth stages combine to fonn a roughly sigmoidal






20

growth curve which applies to both crop and organ growth (Milthrope

and Moorby, 1974; Leopold and Kriedemann, 1975).

Combining the growth of crop organs into total crop growth is

the purview of photosynthate partitioning. For seed bearing crops,

partitioning may be defined as the division of daily assimilate

between reproductive and vegetative plant parts (Duncan et al.,

1978). For potatoes, we define partitioning with respect to tuber

versus non-tuber plant parts. This poorly understood phenomenon has

been related to source-sink strengths (Edelman, 1963), nutrient

availability (Alberda, 1962), plant growth regulators (Bruinsma,

1962), and the climatic factors discussed below: heat, PAR, nutrients,

and water (Brouwer, 1962a). No single mechanism fully explains

assimilate partitioning. Most source-sink arguments are too oolarized.

Assimilate metabolism and photosynthesis have mutually regulatory

feedback. Translocation, the means of this feedback, must be considered

in any partitioning scheme as well as the strength of source and sink

(Evans, 1975b).

In potatoes the rate of photosynthesis after tuber initiation seems

largely determined by tuber growth, the major photosynthate sink

(Nosberger and Humphries, 1965). Photosynthesis may increase seven-fold

after tuber initiation (Evans, 1975b). Thus tuber presence seems to

favor growth. Whether this effect is best explained by source-sink,

growth regulator, or nutrient balance remains to be seen.

Heat

As stated above, crop yield is determined by mutually independent

temperature effects on growth and development. Van Dooben (1962)

further stated that the temperature effect on the crop growth rate is





21
greater than the temperature effect on development. Where models

relating temperature and development are generally linear (Figures 1,

2, and 3), growth and temperature exhibit non-linear relationships

(Figures 4, 5, and 6). Crop and organ growth have minimum, optimum,

and maximum temperatures called cardinal temperatures. These cardinal

temperatures depend upon crop nutrition, solar radiation, and water

relations as well as the genotype (Bodlaender, 1963).

A common growth versus temperature model is the Q10 notion. For

maize seedlings, the Q10 was calculated to be greater than three at

low temperatures, from three to two at suboptimal intermediate

temperatures, and less than one for supraoptimal temperatures (Hagan,

1952a).

Tyldesley (1978) presented several means of modeling non-linear

temperature responses. One is a simplified account of the Ontario

Heat Unit system (Figure 4). Tyldesley's account assumed the response

rate to be parabolic with the optimum rate at 300 C and zero rates at

10 and 50 C where temperatures refer to daily maxima. This heat unit

system gives one means of modeling temperature responses which show a

definite optimum.

The derivations of two temperature response curves are shown in

Figures 5 and 6. Figure 5 is derived from biochemical studies of

enzyme catalyzed reactions (Conn and Stumpf, 1972). The three curves

represent: i) the temperature response at a constant enzyme activity;

ii) the effect of temperature denaturation on erzymatic response; and

iii) the overall temperature response of the reaction which is the

product of curves i and ii. The shape of curve iii corresponds well







with the temperature response curves published for several crops

(Rickman et al., 1975; Hagan, 1952a; Blacklow, 1972; Moorby and

Milthorpe, 1975).

Figure 6 shows the difference between the photosynthesis and

respiration temperature responses (Larcher, 1975). The dark respira-

tion rate is markedly temperature sensitive. The relationship was

found to be exponential over the 6 to 320 C temperature range

encountered by Sale (1974) in experiments with Sebago cv. potatoes.

The stimulatory effect of high temperature on respiration may be

overridden by substrate efficiency, enzyme denaturation, or by

respiratory product accumulation with negative feedback control

(Hagan, 1952a). Notice that the curves for photosynthesis and

respiration both have the shape of curve iii in Figure 5. The

similarity of these curves is expected since both photosynthesis and

respiration are enzymatic reactions, or more properly, systems of

enzymatic reactions.

Sale (1974) discovered a lack of photosynthetic temperature

response by a potato canopy. Sale's finding may merely point out that

photosynthesis is itself the result of two enzymatic systems having

different optimum temperatures, i.e., photosynthesis and photorespira-

tion. The combined effects of two such systems would yield a plateau

in the temperature response curve. Gross photosynthesis is commonly

considered to be temperature insensitive. Since the initial reactions

of gross photosynthesis are driven by PAR these steps may be better

explained as physical than enzymatic processes. Still, net photosyn-

thesis includes a respiration term to render it undoubtably temperature

sensitive.





23

Several authors have discussed the relative effects of air and

soil temperatures. Nielson and Humphries (1966) found that growth is

more inhibited by cold soil than cold air temperatures. The water

and nutrient uptake upon which canopy growth depends is greatly slowed

by cool soil temperatures (Kramer, 1940; Dalton and Gardner, 1978).

Sale (1974) could not find a relationship between soil temperature at

10 cm depth and soil respiration. Sale's inability to find a relation-

ship may be because he made his measurements over uncropped, low-organic-

matter soil. Bodlaender (1963) reported that 15 to 18 C is optimal

soil temperature for potato growth. Cool air temperature may reduce

the rate of assimilate translocation to underground plant parts (Hagan,

1952a). By reducing translocation to roots and tubers, air temperature

may affect the optimum soil temperature (Nielson and Humphries, 1966).

Heat has a strong effect on photosynthate distribution in the crop

system. Roots generally have a lower temperature optimum for growth

than do shoots. The shoot to root ratio increases with temperature

during canopy development (Van Dobben, 1962). During reproductive

growth of wheat, high temperature favors grain growth over shoot growth.

In fact, the shoot decreases in dry weight due to respiration and

translocation of stored assimilates to the growing grain (Spiertz,

1974). Heat also affects photosynthate distribution through its

influence on development. Tne longer tuber initiation is delayed in

potatoes by suboptimal temperatures, the greater canopy growth is

achieved before tuberization if nutrients and water are non-limiting

(Bodlaender, 1963). The larger the canopy at tuberization the longer

the tuber growth period and greater the final yield. Even though
















GROWTH
UNITS


10 20 30
TEMPERATURE


40 50
(C)


Figure 4. Simplified Ontario Heat Unit System (After Tyidesley,
1978).























VELOCITY








Z\


TEMPERATURE

Figure 5. Effect of temperature on the rate of an enzyme catalyzed
reaction: i) response with constant enzyme activity;
ii) thermal denaturation effect on enzyme activity;
iii) reaction rate, the product of curves i and ii
(After Conn and Stumpf, 1972).
















i)P
RATE



iii)G





TEMPERATURE


ii)R


Figure 6. Effect of temperature on: i) Photosynthesis;
ii) Respiration; and iii) Growth (After Larcher, 1975).








high temperatures delay tuber initiation, they also accelerate canopy

senescence to reduce the tuber growth duration.

Photosynthetically Active Radiation (PAR)

In the previous section, photosynthesis was stated to be rela-

tively temperature insensitive, at least in the primary photoelectric

reaction steps. PAR is the driving force for photosynthesis. De Wit

(1959) modeled gross photosynthesis as 6.7 x 10-13 g/erg for light

intensities below 8.5 ergs PAR/cm2/sec. Above this light intensity

photosynthesis was modeled as a constant 4.7 x 10-8 g/cm2 (Figure 7).

Rijtema and Endrodi (1970) accounted for light intensity effects on

growth by estimating the photosynthetic rate under clear and cloudy

sky conditions. By measuring daily duration of cloud cover and applying

a correction factor to account for canopy ground cover and moisture

status Rijtema and Endrodi were able to make fairly accurate predictions

of crop growth. Duncan et al. (1967) modeled individual leaf ohoto-

synthesis with a rectangular hyperbola. The rectangular hyperbola

was also the function derived by Michaelis and Menton to describe

enzyme kinetics (Conn and Stumpf, 1972; Thornley, 1976). Using a

rectangular hyperbola to model photosynthesis emphasizes the enzymatic

underpinnings of photosynthesis (Figure 8). The hyperbolic relation-

ship between light intensity and photosynthesis holds even better for

a croo canopy than for an individual leaf (Sale, 1974).

Even though photosynthesis and growth have a positive response to

PAR, the efficiency of light utilization declines as light intensity

increases. Sale (1973b) reported that photosynthetic efficiency

increased as shade was increased from 0 to 34%. Both models,

Figures 7 and 8, can explain this finding as both show a decreased





28
response at high light intensities, i.e., light saturation of photo-

synthesis. Gaastra (1962) reported that light saturation results when

stomata are fully opened at submaximal light intensities. Despite

higher efficiency of light utilization at low PAR intensities, yields

do increase with higher intensities. Using light levels below one-

third full sunlight (92 to 175 cal/cm2/day), Spiertz (1974) showed

that seed yield and growth rates for wheat both increased with light

intensity. In maize, Linvill et al. (1978) found highly significant

correlations between intercepted solar radiation and grain growth.

In potatoes, light intensity effects assimilate partitioning

as well as yield. Shade to 34% had no effect on leaf dry weight

although shaded plants had a greater leaf area (Sale, 1973b). The

top to tuber ratio increases at lower light intensities (Bodlaender,

1963). In other words, tuber growth, not canopy growth, was reduced

by shading. Fewer tubers grew in shaded potatoes though the numbers

of tubers initiated and stem density were the same at all light levels

tested. The decrease in tuber yield also related to a delay in

reaching the maximum tuber growth rate in shaded plants. Delaying

the maximum tuber growth rate shortened the tuber growth duration

since canopies at all light levels senesced at the same time (Sale,

1973b). Bremner et al. (1967) manipulated interplant competition for

light by varying spacing of potted potato plants. More PAR per pot

was thereby available at lower densities. The number of stems per

seed piece and leaf area per plant remained the same. The LAI was

therefore higher at higher densities.

The effect of PAR on the net carbon exchange (NCE) is evident

through a diurnal analysis. Sale (1974) reported a mesa-shaped curve






29

from sunrise to sunset for NCE (Figure 9). He also found that the

canopy was light saturated above 400 W/m2. At this light intensity NCE

was approximately 42 mg C02/dm2/hr. These PAR effects on growth are

moderated by crop age. Stem and leaf respiration declined as the

crop matured, probably because growth respiration (as opposed to

maintenance respiration) declined. Maximum photosynthesis also declined

with crop age. Thus the coefficients in the light response curve

equation must be updated through the crop season.

Nutrients

The effects of mineral supply on plant growth are by no means

clear. Brouwer (1962b) reported that increased mineral supply leads

to a greater increase of shoot than root growth. In fact, Brouwer's

data show almost no change in root dry weight over three nitrogen levels

in barley plants. 3rouwer and De Wit (1968) modeled plant and root

growth with low nitrogen supply reducing the shoot to root ratio. This

trend was confirmed by Lynch and Rowberry's (1977b) finding that potato

root growth was reduced at high fertilizer rates.

These studies considered ratios at a single point in time rather

than examining partitioning trends through crop growth. Dyson and

Watson (1971) found that even though nitrogen and phosphorus applica-

tion increased the potato crop growth rate from two to four weeks after

emergence, the major effect of the nutrients on growth was through

extending the canopy growth period rather than increasing the canopy

growth rate per se. Similarly, Ivins (1963) found nitrogen applications

to increase yield by delaying tuber initiation and extending the tuber

growth period.














LEAF
PHOTO-
SYNTHESIS
IO'-g CHO2
cm2 sec


10 20


LIGHT INTENSITY


(I)4erg cr.- 2sed' )


Figure 7. Model of light intensity effect on leaf photosynthesis (After
De Wit, 1959).












120. I
120- = I + 10,000
LEAF
PHOTO-
SYNTHE- 90-
SIS
Mg CO
dmn2hr 60-


30-


0
10 20
LIGHT INTENSITYY (lo3 f-c)
Figure 8. Model of light intensity effect on leaf photosynthesis
(After Duncan et al., 1967).














POTATO
CANOPY
NET 30
CARBON
EXCHANGE
Mg CO2 20
dm2hr

10



0800 1000 NOON 1400 1600
HOUR OF DAY


Figure 9. Net carbon exchange
(After Sale, 1974).


in potato canopy from sunrise to sunset






33

Nitrogen promotes canopy growth prior to tuber initiation thereby

decreasing the tuber to canopy ratio during the early tuber growth

period (Dyson and Watson, 1971). By maturity the tuber to canopy

ratio in high nitrogen treatments had increased. Thus the nitrogen

applications were found to ultimately have increased both tuber and

canopy growth.

The effect of nitrogen on tuber yield is limited. Kunkel et al.

(1973) found that excess nitrogen will increase canopy growth without

affecting tuber yield. Several authors have reported that nitrogen

uptake by the potato crop ceases long before tuber growth is complete

(Soltanpour, 1969; Ezeta and McCollum, 1972; Dyson and Watson, 1971).

After the crop nitrogen uptake ceases nitrogen is apparently trans-

located from the canopy to the growing tubers. Phosphorus is also

translocated from the canopy to the tubers (McCollum, 1978b).

The nutrient concentration in the tubers remains constant through

the tuber growth period. Kunkel et al. (1973) reported that the tuber

mineral composition was independent of applied nutrient levels or

cultural practices. Dyson and Watson (1971), on the other hand,

examined tuber carbon to nitrogen ratios and found them to be constant

For a given crop but varying between seasons and fertilizer treatments.

All of these findings point toward a mechanism whereby nitrogen

regulates tuber growth. Nitrogen levels did not influence the numbers

of tubers initiated. Still, Dyson and Watson postulated that nitrogen

availability may regulate the tuber sink strength. Of course, during

the tuber growth period nitrogen available for tuber growth depends

mostly upon the amount of nitrogen in the canopy which is available






34

for translocation. The more nitrogen in the canopy from increased

nitrogen application, the longer the tuber growth period.

Water

Potatoes are generally considered a drought sensitive crop.

Drought sensitivity results in part from the potato's relatively

shallow root system (Weaver, 1926; Harris, 1978b). Weaver found

potato roots to be even less extensive and more shallow when growing

under water deficient conditions. Not only do potatoes have shallow

roots, but leaf photosynthesis appears to be greatly reduced by a

fairly slight reduction in leaf water potential. Campbell et al. (1976)

found that stomatal resistance began to increase at a leaf water

potential of -0.8 bars. At this level, the effect on crop growth is

small. Indeed, Sale (1973a) found that canopy NCE remained relatively

constant to leaf water potentials as low as -8.0 bars.

Despite the potato's drought sensitivity, irrigation is net

always recommended. In some cultivars, King Edward for example,

frequent irrigation during early growth may lead to initiating growth

in more tubers. As a result, fewer tubers reach marketable size even

though the total tuber yield may increase (Harris, 1978b). Ivins

(1963) reported that the number of marketable tubers increased as

irrigation was delayed until after linear tuber growth had begun.

These reports contrast with Sale (1973a) who found that higher LAI's

were reached in potatoes maintained at high soil moisture. Furthermore,

the higher LAI's resulted in higher yields due to a longer growth

period. Still, there is no dispute that drought during tuber growth

will drastically reduce potato yields.






35
The mechanisms whereby plant water status affects potato yields

have been fairly well studied. According to Moorby et al. (1975) leaf

sugar concentrations increase in drought stressed potatoes. Drought

stress may reduce photosynthate translocation to tubers or reduce

starch synthesis within the leaf or both. Munns and Pearson (1971)

found that reduction of leaf water potential did indeed decrease trans-

location of assimilates to tubers, and did so in proportion to its

negative effect on net photosynthesis rather than a direct effect on

translocation. Thus Munns and Pearson agree with Moorby et al. in

finding that drought had no effect on starch synthesizing enzymes in

tubers. Tuber growth, or more specifically, tuber starch synthesis

appeared to be proportional to assimilate supply and assimilate supply

is decreased by drought.

In young potato plants, drought did not seem to influence photo-

synthate partitioning (Munns and Pearson, 1974). Both canopy and root

growth were equally reduced. In older plants, however, drought had

less effect on tuber growth than root and canopy growth. Thus the

percentage of assimilate partitioned to tubers increased with drought.

Drought also more drastically reduced leaf water potential than tuber

water potential (Moorby et al., 1975). A mechanism whereby drought

may influence partitioning was reported by Necas (1968). During a

drought period lower potato leaves abscise. Upon drought relief new

leaf area is generated. Since tubers are not shed while leaves are

the net effect is an apparent reduction of assimilate partitioned to

leaves.

The effect of water status on canopy NCE was also studied by Munns

and Pearson. They concluded that drought as a greater negative effect






35
on NCE of pre-tuberous than post-tuberous plants. The leaf water

potentials of young and old plants were not comparable. The young

plants had lower leaf water potentials on both stressed and unstressed

conditions than did the older plants. Evidently the tubers act as

water stores to prevent stress in older plants. Their data show better

the effect of leaf water potential on NCE than the influence of tuber

presence on NCE in drought conditions.

Density

Since potatoes are propagated vegetatively by tubers, seed

expenditures may be as great as 30 to 50% of the total growing costs

(Allen, 1978). Thus density effects are of both economic and physio-

logic importance.

The effects of density on potato crop growth are more complex

than the density relationships of most other crops. Units of potato

density are several. Allen listed eyes, seed pieces, seed surface area,

seed weight, and steris as units of potato density. All of these units

are correlated, so all need not be considered in relation to growth.

The stem is generally taken as the unit of potato plant density most

directly related to yield (Reestman and De Wit, 1959; Bleasdale, 1965;

Collins, 1977).

Many factors may influence the stem density. The numbers of stems

per seed-piece is positively correlated to the seed-piece weight. This

relationship is less notable in cultivars with inherently high stem

numbers (Bremner and El Saeed, 1963). Actually, the stem number per

seed-piece is more highly related to seed surface area than weight

(Reestman and De Wit, 1959), though the effects are difficult to separate.

Concomitant with Fewer stems in smaller seed-pieces, stems produced from






37

small seed attained a greater final weight and produced more and larger

tubers when planted at the same seed-piece density as large seed-pieces

(Bremner and El Saeed, 1963). Thus, the small seed-pieces had a lower

stem density.

Similar results were noted by Svensson (1966). He found that LAI,

tuber yields, tuber numbers, and mean tuber weights per seed-piece

were all higher at wider spacings. As with many other crops, the total

tuber yield showed an optimum plateau. Lynch and Rowberry (1977a)

measured this optimum density plateau to range from 6 to 12 stems/m2.

Bremner and Taha (1966) found density and tuber growth rate per unit

area to be positively related. At higher stem densities a smaller

portion of photosynthate is partitioned to tuber growth (Bremner and

El Saeed, 1963). Thus, density is one of the few factors which can be

easily manipulated to influence tuber growth rates.



Summary

The major dynamic environmental inputs for a potato growth and

development model are heat, moisture, nutrients (especially nitrogen),

and solar radiation. Other factors may be considered as combinations

of these four major inputs or as static, one-time inputs. For example,

season may be considered to be a combination of solar radiation and

heat effects which change predictably through the year. Crop density,

on the other hand, remains relatively constant through the growing

season so it need be input only once. The bulk of a crop model,

therefore, will describe the relationships between crop growth and the

four major inputs.





38

Prior to tuber initiation, warm temperatures (20-24o C), high

available nutrients and water, high PAR flux density, and long days

will stimulate and prolong canopy growth. Similarly, cool temperatures,

low nutrient and moisture availability, and short days favor early

tuber initiation and reduced canopy growth. After tubers have

initiated, optimum conditions are soil temperatures from 16 to 200 C,

air temperatures from 20 to 240 C, high available nutrients and

moisture, and high PAR flux density (Milthorpe, 1963).













MATERIALS AND METHODS

Crop Growth Model

A model was developed to further understanding of how temperature

influences crop partitioning. The particular hypothesis to be tested

was: differences in the temperature versus growth relationships

between various potato organs may be used to predict dry matter

distribution within the crop.

The model was tested in the form of a computer program written

in GASP IV, a Fortran-based simulation language (Pritsker, 1974).

GASP IV has both continuous and discrete simulation capabilities, but

the model developed herein is entirely discrete. Features of the

GASP IV language crucial to this model are a table search function

called GTABL and the language's event filing mechanism.

GTABL calls data from a table array. For example, a table of

tuber growth versus temperature can be entered into an array. The

GTABL function will derive the tuber growth for a given temperature.

The event filing mechanism of GASP IV uses information stored in a

buffer called ATRIB(1). ATRIB(i) stores the time an event will occur.

ATRIB(2) stores the number of the event which is scheduled for that

particular time. ATRIB(3,....,n) can be used to hold any special

data required in an event.

The program includes five event subroutines:

1) Pre-tuberous growth (PRET) calculates crop growth and dry

matter distribution before the crop initiates tubers, determines when

tubers are to be initiated, and schedules canopy senescence.

39





40

2) Post-tuberous growth (POSTT) calculates growth and partitioning

after tubers are initiated. Both exponential and linear tuber growth

are calculated in POSTT.

3) Canopy decline (CANDE) causes a unit of canopy stored in

ATRIB(3) to abscize according to heat units accumulated in ATRIB(4).

4) The daily climatic data inputs are read by DAY which also

calculates potential net photosynthesis, mean air and soil tempera-

tures, and tuber respiration.

5) Every evening ENDAY is called to store the day's growth calcu-

lations for graphic and numeric output of organ dry weights and

certain program parameters.

A program listing of this model is included in Appendix A.

The model was validated by inputting actual climatic and ground

cover data and comparing the simulated crop growth and development to

the results of the growth analysis. To test the effect of temperature

on assimilate partitioning and crop growth dynamics a temperature

sensitivity analysis was performed.



Growth Analysis 1978

The major objective of the growth analysis was to provide data

for the development and validation of the computer model. Planting

date was chosen as the most practical means of manipulating tempera-

tures in the field. In keeping with the model purposes, the growth

analysis was designed to determine temperature effects on the crop

growth rate, tuber growth rate, partitioning, and phenology. Two

cultivars were grown in order to compare genetic and environmental

effects on potato growth and development.





41
During the 1978 potato growing season Sebago and Monona cultivars

were grown at the Yelvington Experimental Farm of the University of

Florida in Hastings. The soil was of the Rutlege taxajunct, now

classified as a sandy, silaceous, thermic Typic Humaquept. Crop

husbandry was as recommended by the Potato Production Guide (Montelero

and Marvel, 1971). Nematodes were controlled by Dichloropropane-

Dichloropropene applied two weeks pre-planting at 225 liters/ha. At

planting fertilizer was banded at a rate of 120 kg N/ha, 160 kg P205/ha,

and 160 kg K20/ha. Between tuber initiation and full ground cover

achievement, a sidedressing of 35 kg N/ha and 35 kg K20/ha was applied.

Weeds were controlled by a 5 kg/ha pre-emergence application of Dinoseb

and by cultivation after emergence. Carbaryl and Maneb were aoplied

together at seven to ten day intervals throughout the season as needed

for insect and late blight control, respectively. Carbaryl was applied

at 1.1 kg/ha and Maneb at 1.3 kg/ha.

Four replicates of both cultivars were planted on each of two

dates, 2 February (Julian day 33) and 14 March (Julian day 73). A

split plot design was used with planting date comprising the main plot

treatment and cultivar the subplot treatment, for a total of 16 sub-

plots. The subplots were 8 by 8.5 m each with rows oriented east-west.

The seed-piece spacing was approximately 20 cm within rows and 100 cm

between rows giving a density of 4.56 seed-pieces per square meter.

The seed-pieces were machine-cut on the first planting date and hand-

cut on the second planting date to about 55 g each, giving a seedling

rate of 250 g/'2.

Harvests were taken at seven to ten day intervals through the

growing season. Sequential harvests were taken from east to west





42

within each subplot. Twelve seed-piece clusters (hills) from each

subplot were divided into tops, tubers, and remainder which included

roots, rhizomes, below ground stems, and seed-pieces. All components

were dried at 1000 C and weighed. Two representative plants were

selected from each subplot and divided into laminae, petioles and

midribs, above and below ground stems, inflorescences, rhizomes, roots,

tubers, and seed-piece according to the crop's developmental status.

Stem length, tuber number, and inflorescence number were all recorded.

Leaf area was measured on an electronic area meter. For early samples

the entire sample was dried for weighing. At later dates, the total

fresh weight was measured and dry weight was determined by subsample.

Leaf area was also determined by subsample for later harvest dates.

Environmental data were collected by the IFAS experiment stations

in both Hastings and Gainesville, Florida. Measurements used from the

Hastings station were daily maximum and minimum air temperature in a

standard shelter at 150 cm, daily maximum and minimum soil temperature

at 10 cm depth, and precipitation (Figures 10 and 11). From the

Gainesville station about 60 miles west of Hastings measurements of

daily PAR were used (Figure 12). As well as these standard weather

readings, occasional soil temperature profile measurements were made in

the experimental plots to compare with the standard data. Diurnal

cycles and seasonal trends were observed. Measurements were made at

1. 5, 15, 25, and 40 cm soil depth, and air temperature in the shade

of the canopy (Figure 13).
















TEMPER-
ATURE
(C)


30 50 70 90


JULIAN DAY


110 130 150


1978


Figure 10. Weekly average temperatures in Hastings, Florida. Air
temperatures (--) measured in standard shelter at 150
cm height. Soil temperatures (-----) measured at 10 cm
depth.



















50-



40-



30-



20-


01
30


FFR


MAR


APR


MAY


ii
II
Ii


A
I
'I
/I
/I


II


I IL
II I





I I


I I
I \ _
/ \

/ \
; \l
'i bt
/ \ '.P~ci\


70
JULIAN


90
DAY


liO 130 1'50


Figure 11. Total weekly precipitation (-----) in Hastings, Florida,
and pan evaporation (--) in Gainesville, Florida.


ECIP


nd
7)


F M R APR


I I I


r_











FEB MAR APR MAY

50-


40-


PAR 30-
E/n2/doy

20


iO-
10



30 50 70 90 110 130 150
JULIAN DAY 1978
Figure 12. Daily photosynthetically active radiation averaged over one
week intervals.











0- 0645 0025 2130 I120 ib

SOIL 5- -5
DEPTH
(cm) 15- -15


251 -25





40j -40

12 14 16 18 20 22
TEMPERATURE (oC)
Figure 13. Soil temperature profiles under a Sebago canopy from 1615
hours on March 20, 1978 to 1205 hours on March 21, 1978.








Thermogradient Analysis 1979

The growth analysis considered only two temperature treatments.

Though two temperature levels are enough to estimate the general range

for model parameters, more temperature treatments are necessary to

derive a temperature response curve. Thermogradient analysis was used

primarily to determine the shapes for the temperature responses of

stem, root, and tuber growth.

During the winter of 1979 a series of experiments was conducted

in a thermogradient bath system located at the Biven's Arm Agronomy

greenhouse in Gainesville.. The thermogradient system, similar to

systems used by Kirkham and Ahring (1978) and Timbers and Hocking (1971),

was maintained by a water-covered steel bar with one end of the bar

emersed in hot water and the other emersed in cold water. All experi-

ments used uncut, grade B, Foundation potato seed of Sebago cultivar.

The mean seed-piece fresh weight was 67.5 gm with a standard deviation

of 21.2 gm. Table 1 lists dates, temperature ranges, and fresh weight

of seed-pieces used in the thermogradient experiments.

To study the effect of temperature on shoot elongation, seed-

pieces were planted about 20 cm deep in moist sandy soil neld by 0.95

liter paper cups. Convective currents in the gradient bath were

reduced by 20 mm polystyrene baffles. Ten baffles divided the

thermogradient perpendicularly to form 11 chambers. Each chamber was

considered to be at one temperature. Five cups, each containing one

seed-piece, were placed in each chamber and all chambers were covered

with a polyethylene sheet (6 mil) to prevent evaporation and heat

movement. The plastic sheet was covered with an opaque cloth to

prevent overheating of the chambers by solar radiation. The soil in





48



Table 1. Experiment dates, temperature ranges, and seed-piece
fresh weights for thermogradient analysis.


Date Temperature Seed Piece
Experiment Start End Range F.W.

Julian Day C g

Dormancy Break
5 days 42 47 20-30 40-60
10 days 37 47 15-30 40-60

Growth and Elongation
12 days 51 63 12-29 50-60
7 days 56 63 13-26 50-60
9 days 67 76 12-18 50-60

Tuber Growth 112 122 8-24 80-90






49

the cups was watered at three day intervals. Temperatures of the water

in the chambers and the soil next to the seed-piece of the central cup

in each chamber were measured periodically. Seed-pieces having

dormant buds were used to determine the temperature effect on

dormancy break. Seed-pieces with already elongating buds were used

to determine temperature effects on growth and elongation. After the

thermogradient treatment the plants were washed, broken into components,

measured, dried, and weighed.

To study the effect of temperature on tuber growth, 64 seed-pieces

were planted in 25 cm plastic pots on 29 January (Julian day 29). The

pots were arranged in an 8 by 8 pattern with border rows not utilized

in experiments. Each pot was filled to 8 cm with sandy soil. The soil

layer was covered with 4 mm mesh nylon net. According to Nosberger and

Humphries (1965), this mesh is large enough to allow root penetration

while small enough to keep tubers above the net. In this experiment,

this method did not work as tubers were often found to grow below the

net. One seed-piece per pot was placed directly on the net and covered

with 15 cm of vermiculite.

The pots were watered regularly to prevent stress. On nights of

predicted frost, all pots were covered with a 6 mil polyethylene sheet

to prevent cold damage. On 28 February (Julian day 59) the seeds were

checked. Fourteen pots were discarded due to seed-piece rot or

continued dormancy. Eight pots had shoots near the vermiculite surface.

These shoots were exposed to give more uniform emergence and equalize

development with the remaining pots which had healthy emergent stems.

Thus, on 28 February 100% emergence was obtained. Pots were fertilized

on days 1 and 19 post-emergence. According to visual inspection of the







experimental and surrounding areas the plants were sprayed with

Carbaryl and Captan to control Colorado potato beetle and late blight,

respectively. Irrigation frequency was increased after 20 March due

to higher temperatures and lower precipitation.

On day 19 post-emergence 58% of the pots had visible inflores-

ences. The ground cover was estimated at 95%. Tuber initials were

formed on all of the ten border pots inspected. Therefore, 19 March

(Julian day 78) was considered as the first day of flowering and the

beginning of the linear growth phase. Twenty-two days after flowering,

ten pots were placed in the thermogradient bath. The water was

stabilized with four polystyrene baffles and ethyl malic anhydride

(EMA-91). EMA-91, supplied by the Monsanto Corporation, forms a

polymer which increased the viscosity of the bath to slow thermal

transfer by convection both within and between the large chambers of

this experiment. Two pots were placed in each of the five chambers

formed by the baffles and the pots were protected from the EMA-91 by

plastic bags. Five control pots were harvested before and five after

thermogradient treatment. The control plots which were harvested

after the treatment period were kept on the greenhouse bench adjacent

to the thermogradient bath during the treatment period. All plants

were separated into tubers, leaves, and remainder which included

roots, stems, rhizomes, and inflorescences. The components were

dried at 1000 C and weighed.













RESULTS AND DISCUSSION

Growth Analysis 1978

Pre-Emergence

In the Julian day 33 planting, the seed-piece buds of both

Monona (M33) and Sebago (533) were still dormant. Bud dormancy break

occurred after Julian day 45 for both cultivars as indicated by the

stem length data in Figures 22 and 23. Bud break, the first major

phenologic event of this planting date, required about two weeks.

By the Julian day 73 planting the seed-piece buds of both Monona (M73)

and Sebago (S73) had begun to elongate. Many of the elongating shoots

were broken off during the planting operation. Significant stem growth

did not begin again until after day 80, one week after planting

(Figures 24 and 25).

Both M33 and S33 required about three weeks from the beginning

of stem elongation until emergence. The average stem length at

emergence was about 10 cm, the same as the planting depth. Therefore,

these stems elongated at the rate of approximately 0.5 cm/day. The

stems of M73 and S73 elongated nearly 0.7 cm/day, thus M73 and S73

only required two weeks from the beginning of stem elongation to

emergence.

Root growth began within days after initial shoot elongation in

alt treatments. By the time of emergence the shoot to root ratios

were 2.77 for M33, 2.69 for S33, 1.22 for M73, and i.31 for S73.





52

The differences between planting dates can be attributed to the

dormancy state of the seed-pieces at planting and edaphic factors.

The edaohic factor of primary importance is temperature since soil

nutrients and moisture were controlled by fertilization and irrigation,

respectively. After bud dormancy break we may assume that the seed-

pieces of both planting dates had similar physiologic status. There-

fore, soil temperature will be the only major independent variable

affecting stem and root growth until emergence. The average soil

temperature from planting to emergence was 16 C for the Julian day

33 planting and 200 C for the Julian day 73 planting (Figure 10).

This four degree temperature difference thus appears to be the main

factor which increased the rate of shoot elongation and decreased the

shoot to root ratio in the second planting date. The effect of

temperature on time from planting to emergence is described by calcu-

lation of soil heat unit accumulation during this period. Using a

base temperature of 90 C, both cultivars showed remarkable similarity

in pre-emergence soil heat unit accumulation (Table 2).

Even though it seems safe to conclude that increased soil tempera-

ture speeds stem elongation and decreases the shoot to root ratio

during the pre-emergence phenophase, the underlying physiological

mechanisms are not clear. The soil temperature regulates the rate

that the seed-piece makes substrate available to the growing organs.

The soil temperature may also influence the rate at which the

individual organs are capable of incorporating the available substrate.

These two mechanisms represent the classical source strength versus

sink strength controversy.












Table 2. Duration and cumulative heat units for Monona and
Sebago phenophases.


Treatment (Cultivar and Planting Date)
Phenophase Monona 33 Monona 73 Sebago 33 Sebago 73

Pre-Emergence

Julian Days 33-66 73-94 33-68 73-15

Soil Heat Units* 225.8 225.7 238.1 239.2

Emergence to Flowering

Julian Days 66-87 74-105 68-86 95-107

Air Heat Units** 117.7 108.3 107.2 112.1

Emergence to Tuber Initiation

Julian Days 66-80 94-111 68-84 95-116

Soil Heat Units* 113.7 250.6 142.9 304.1

Air Heat Units 44.2 155.5 60.6 172.9

c u14+ i-r tOr o\. *H* \i. u,.+ Il- /tr') 1 ( U


oj, 1 IeCQ L UII I l


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I \- I <-.








Emergence

The date of emergence, as used here, is the date when the percent

of seed-pieces with emergent stems reached half of its maximum value.

The percentages of seed-pieces with emergent stems are graphed through

time in Figures 14 and 15. The majority of M33 stems emerged during

the 20 day period from day 60 to day 80. S33 stem emergence encom-

passed an even longer period, about 25 days, from day 60 to day 85.

The M73 and S73 treatments emerged over a slightly shorter period,

about 15 days. In any case, emergence was not at all uniform.

The final emergence percentage for Monona was significantly1

greater than that for Sebago at both planting dates (Table 3). The

poor emergence of Sebago resulted from disease of the seed-pieces.

Furthermore, the emergence of the day 33 planting exceeded that of the

day 73 planting. The low emergence of the second planting may have been

due to improper storage conditions of the seed-pieces before planting

or injury to the seed during the planting operation. Since the buds

on the seed-pieces had already broken dormancy the seed-pieces may have

been more susceptible to injury. Another possibility is that the seed

rot became more widespread during the longer storage period of the

seed used in the second planting. However, the primary factor

responsible for the difference in emergence percentages between the two

planting dates appeared to be soil surface temperature. Skies were

clear and air temperatures high during the emergence period of the

second planting. The surface layer of the soil dried and became very

warm. On day 95 the soil temperature at 1 cm depth exceeded 30' C by


1 Statistical analyses are presented in Appendix B.


















ow Ld
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57



Table 3. Seeding rates, maximum emergence, stems per seed-piece, and
plant density for all treatments.


Planting Final Effective Stems Per Plant
Treatment Rate Emergence Seeding Rate Seed-Piece Density

seed/m2 % seed/m2 stems/m2

Monona 33 4.30 98.4 t 3.1 4.23 1.38 5.84

Sebago 33 4.30 76.5 t 13.0 3.29 2.00 6.58

Monona 73 4.84 82.2 5.38 3.98 2.00 7.96

Sebago 73 4.84 53.3 t 4.88 2.61 2.44 6.29






58

1400 hrs. During the emergence period of the day 33 planting the

temperature at 1 cm depth did not exceed 220 C on any day that the

soil temperature profiles were measured. As will be shown below, a

temperature of 300 C is high enough to inhibit shoot growth and will

likely cause injury.

Plant Density

Though the planting densities were 4.3 seed/m2 and 4.8 seed/m2

for the day 33 and day 73 plantings, respectively, the wide range of

final emergence percentage lead to effective seeding densities from

2.6 to 4.2 seed/m2 (Table 3). As stated in the literature review,

the seeding density is not the best measure of potato crop density.

Rather, the main stem is taken to be the individual plant unit. Both

cultivars compensated for low emergence by setting more stems per seed-

piece. Sebago and Monona had significantly higher stems per seed in

the day 73 planting than the day 33 planting. Sebago also had more

stems per seed than Monona in both planting dates. The ultimate plant

densities ranged from 5.8/m2 to 7.8/m2 with differences being insignif-

icant.

Canopy Development

Leaf area and ground cover. After emergence aerial environmental

factors begin to influence crop growth and development. Photosynthet-

ically active radiation (PAR) provides energy for crop metabolic

processes. The crop canopy intercepts PAR. Two parameters commonly

used to describe crop canopies with respect to PAR interception are

the leaf area index (LAI) and percent ground cover (GC). The LAI and

GC for the four treatments are graphed in Figures 16 through 19.
























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63
The curves for LAI and GC followed roughly parallel patterns for

M33. The LAI increased to a maximum of about 2.7 at day 110. The GC

also increased until day 110 when a maximum of about 80% was achieved.

Both LAI and GC decreased gradually after their peaks at day 110.

The pattern was very much different for S33; however, S33 developed

a larger canopy and maintained the canopy longer. The GC for 533

reached 80% by day 105 and maintained this GC through day 139. The

LAI exceeded 3.0 by day 110 and peaked at about 3.6 on day 120. On

day 139 the LAI of S33 was still almost 3.0 while that of M33 was

below 1.0.

A greater canopy growth for Sebago was not evident in the second

planting. Both S73 and M73 showed LAI and GC maxima at day 140 with

fairly rapid canopy deterioration after this time. The maximum GC of

573 was about 81%, slightly greater than that of M73 at 76%. Although

the peak LAI of S73 at 3.4 was much higher than that of M73, 2.0,

since this is the only date which showed such a difference between

LAI's of the two cultivars, the data point may be in error. Indeed,

the leaf dry weights for M73 and 573 were similar at this time (Tables

6 and 7).

The rapid canopy decline after day 139 for both 573 and M73 was

most likely due to high temperatures during this period. As shown

in Figure 10, the air and soil temperatures increased steadily after

day 110 with daily maxima exceeding 300 C by day 140. Thus, tempera-

tures began to exceed the thermal maximum for potatoes about the same

time as the beginning of canopy decline for the day 73 planting.

The differences between the Sebago and Monona canopies of the

first planting date may be attributed to phenologic differences. By






64

exponential regression, M33 initiated tubers around day 80, whereas S33

initiated tubers some four or five days later. Initial tuber growth

was also slower in 533 than M33 (Tables 4 and 5). The early initiation

and growth of tubers in M33 likely reduced canopy development relative

to S33. In other words, M33 partitioned a greater portion of its daily

photosynthetic products into tuber growth than did 533.

As a tool for characterizing crop canopies with respect to PAR

utilization, LAI is most useful after the crop canopy has closed. At

full ground cover the LAI estimates the number of leaf layers light

must penetrate before reaching the ground.

None of the crop canopies in this experiment reached full ground

cover. In order to estimate the number of leaf layers the light can

penetrate when entering the crop canopy,the LAI must be divided by GC.

This parameter is termed the effective leaf area index (ELAI). The

ELAI's for the treatments of this experiment are graphed in Figures 20

and 21.

M33 and S33 both reached an ELAI of 3.0 around day 93, 20 days

before the maximum LAI and GC were achieved. For M33 the ELAI remained

fairly constant near 3.2 from day 93 to day 120. The ELAI for S33

increased to about 4.0 by day 100 and plateaued at this level.

Similarly, M73 and 573 reached an ELAI plateau around day 116, about 25

days before the peak of LAI and GC for these treatments. Though the

LAI and GC were much greater in the first than the second planting,

the same is not true for ELAI. These results indicate that both the

Sebago and 'lonrna canopies grow upward before they extend horizontally.

The long period of constant ELAI suggests the GC alone can be used to

estimate light interception during this time.



















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71

In potato canopies, as with most crops, the incident PAR is almost

completely intercepted if the ELAI is 3.0 or greater. Apparently,

after passing through three layers of leaf the light intensity is very

near the light compensation point (Radley, 1963). The canopy growth

morphology was similar for all treatments of this experiment. The

canopy grew upward until the light intercepted was fully utilized,

when the ELAI reached 3.0. Then the canopy grew outward, maintaining

the ELAI at a level where PAR was fully intercepted.

One may question the efficiency of such a canopy. Higher

photosynthetic rates may result from more rapidly increasing GC than

ELAI. However, potatoes do require intense husbandry. Late blight

and Colorado potato beetle do require repeated pesticide applications.

Long stems would get killed by tractor wheels. Thus, high GC and long

stems would be disadvantageous in this cultivation system.

Stem elongation. The LAI and GC characterize the photosynthetic

system of the crop canopy. They do not, however, give much information

about the structural support of the photosynthetic surfaces. The

average main stem length, average branch length, and total branch and

stem length per square meter can be used to characterize the structural

support system (Figures 22 through 25).

The main stems of M33 and 533 lengthened until about day 100 with

a maximum main stem length of about 62 cm for S33 and 54 cm for M33.

Since the main stems terminated in inflorescences it is not surprising

that main stem elongation ceased soon after floral initiation. Floral

initiation is marked on the graphs at the point when inflorescences

were first visible. The point of maximum main stem length coincided

exactly ;ith the time of peak flowering (Figure 14), as one would expect.





72

For M73 and S73, however, the time of maximum main stem length

and maximum flowering did not coincide. For both cultivars the

average main stem reached its greatest value, about 32 cm, by day 116

(Figures 24 and 25). The maximum flowering was not reached until day

129 (Figure 15). Since the number of inflorescences per seed-piece

was greater than 1.0 for both S73 and M73 at day 116, it is likely

that the majority of the main stems would have incipient if not visible

flowers at this time. The further increase in flowering, then, might

represent either incipient main stem inflorescences or florescing

branch termini.

The average branch length was significantly greater for S33 than

M33 on all days observed. The total stem plus branch length of S33

was significantly greater than that of M33 after day 100. This result

is consistent with the findings of greater LAI, GC, and ELAI in S33 as

compared to M33. On the other hand, differences between the total,

main stem, and branch length for S73 and M73 were not significant.

The effect of planting date on stem and branch growth was marked.

The stems and branches of the day 73 planting were much shorter than

those of the day 33 planting. The difference in branch and stem

length between the two planting dates is consistent with the results

of LAI and GC measurements. Stem and branch growth is stopped by

flowering. The earlier termination of stem and branch growth in the

second planting was probably due to the warmer temperatures which

hastened flower initiation. Flowering appeared to be regulated by

heat (Table 3). With warmer temperatures in the second planting

flowering was hastened, as was the completion of stem and branch

elongation.























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77

Canopy senescence. Maturity of annual crops is accompanied by

senescence of the crop canopy. Decline of potato canopies in the

Hastings area is generally due to high temperatures late in the

growing season. As noted above, the canopy decline of M73 and 573

after day 139 can be attributed to excessive temperatures. A parameter

which can be used to characterize canopy senescence is leaf duration.

The leaf duration is the length of time a leaf remains physiologically

active in photosynthesis. Leaf senescence includes chlorophyll

degeneration and chlorosis. One method of estimating leaf duration

is to determine the temporal difference between the dry weight curves

for green and yellow leaves as in Figures 26 through 29. This method

assumes that the oldest leaves senesce first. There are two main

sources of error in this method of estimating leaf duration. First,

it is difficult to recover all senescent leaves, especially later in

the season after the senesced leaves have begun to abscise. This source

of error may be minimized by placing greater importance on early

observations of chlorotic leaves. Second, leaf duration estimations

will err if the specific leaf weight (SLW) of the chlorotic and green

leaves are greatly different. If a large portion of the leaf nutrients

and assimilates are mobilized and translocated to other crop organs,

then this method overestimates leaf duration. There was indeed a

significant drop in SLW of green leaves as the canopy aged (data not

reported). The decline in green leaf SLW with age can be explained by

both leaf expansion and translocation effects. More importantly, since

the SLW drops long before leaf abscission the difference between SLW

of green and chlcrotic leaves is lessened.





























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82

Two significant differences can be observed in this leaf duration

data. The leaf duration of Monona is longer than that of Sebago, and

the leaf duration of the day 33 planting was longer than that of the

day 73 planting. The effect of planting date can be related to both

environmental and physiological processes. The higher temperatures of

the second planting sped leaf development and, when temperatures became

excessive, injured the leaves through heat damage. More rapid develop-

ment and heat injury will both hasten chlorosis.

Flowering

The next heat regulated phenophase after emergence is florescence

(Table 3). The numbers ofinflorescences per square meter are graphed

in Figures 14 and 15. Sebago and Monona initiated flowers at about

the same time for a given planting date. There were no significant

differences between the peak numbers of inflorescences of the two

plantings. Sebago, however, produced more inflorescences than did

Monona. Furthermore, Sebago matured many fruits while Monona did not.

The dry weights of these fruits are included in the inflorescence

columns of Tables 4 through 7. As the inflorescence numbers, the

dry weights of the flowers and fruits showed that Sebago produced

heavier inflorescences than Monona while there was no significant

effect of planting date.

Tuber Initiation

Heat unit accumulation predicts the phenophase durations from

planting to emergence and from emergence to flowering (Table 3). The

mean daily soil and air temperatures are used to predict emergence and

floral initiation, respectively. On the other hand, neither soil nor

air heat accumulation predicts tuber initiation. Indeed, no reasonable






83
base temperature can be derived to predict tuber initiation. Only a

base temperature greater than ambient temperatures can be used to

equalize heat unit accumulation between the two plantings. Using such

a base, though mathematically feasible, does not make physiological

sense, since such accumulated units would have negative values. A

possible explanation for these tuber initiation results is the tempera-

ture versus carbohydrate availability mechanism described in the

literature review. Presumably, cooler temperatures inhibit canopy

growth but not photosynthesis. If canopy growth does not utilize the

photosynthate of a given day, then the available carbohydrate level

on the plant is high and may either stimulate tuber initiation or

reduce photosynthesis by feedback inhibition.

Rhizomes

Just as one must analyze the stems and branches when interpreting

the development of the crop's photosynthetic system, one must consider

the tuber support system to fully understand tuber growth and function-

ing. Rhizomes are rather small, horizontally growing underground

stems. Both M33 and S33 initiated rhizome development around day 80,

barely ten days after emergence. The rhizome dry weight increased to

a plateau near day 95 (Tables 4 and 5). M73 and S73 were slower to

initiate rhizomes. In other words, rhizome initiation and tuber

initiation had similar patterns with rhizome development slightly offset

to precede tuber initiation. Presumably, rhizome and tuber development

are regulated by the same mechanism since one grows from the other.

Yet, if tuber initiation is stimulated by high labile carbohydrate

levels in the plant associated with high photosynthesis rates and low

canopy growth rates at the linear phase of total crop growth, then





84
rhizome development requires another explanation. Rhizomes initiate

before tubers. Rhizomes in this experiment initiated before the

linear crop growth period. They began development when the canopy

appeared to be still utilizing seed-piece substrates for growth. The

present data are not sufficient to explain these phenomena, they

merely pose the question.

Yield Dynamics

The large carbohydrate reservoir in the potato's vegetative prop-

agule may give potatoes an advantage in early canopy growth over crops

with smaller propagules. The results of these experiments, however,

indicate otherwise. The total crop weight did not increase significant-

ly until 30 or more days after emergence in M33 and S33 (Figures 30

and 31). Although the canopy grew during this period, the canopy grew

by translocation from the seed-piece rather than from canopy photo-

synthesis. Just as a leguminous crop will utilize soil nitrogen

supplied before fixing atmospheric nitrogen, potato canopies deplete

the seed-piece substrate before they begin auto trophic growth. Once

positive growth did begin, presumably when the seed-piece carbohydrate

reservoir was inadequate to meet the growth needs of the canopy, crop

growth for all treatments is approximately linear and remained so

until final harvest.

Crop growth in the day 73 planting was similar to that in the day

33 planting (Figures 32 and 33). The crop growth rate was zero for

the first 20 days after emergence and became linear soon thereafter.

The common pattern for crop growth is an exponential growth phase,

or lag phase, which leads into a linear growth phase after the maximum

ground cover is reached. The large vegetative propagule of the



























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Full Text

PAGE 1

ayv^v. V\\c4t>i^\^ Aw^v/KK^t^. ^--^ ^ns) ' i^ooii 7^ro^:>zi^ ^MATHEMATICAL MODELING OF THE GROWTH AND DEVELOPMENT OF POTATOES (Solanum tuberosum L. ) BY KEITH T. INGRAM A DISSERTATION PRESENTED TO THE GRADUATF COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PMtiosqphv U^'^/cRS!~Y OF FLORIDA 1 98C

PAGE 2

ACKNOWLEDGEMENTS I thank the members of my advisory committee: Dr. K. J. Boote, Dr. A. J. Norden, Dr. W. G. Duncan, and Dr. T. E. Humohreys, and especially the chairman of this committee, Dr. D. E. McCloud, I heartily appreciate the counsel and latitude the committee gave ro me during the pursuit of this aegree crogram. Thanks to Dr. D. Hensel ana the staff o"^ the IFAS Potato Research Station in Hastings, Florida, who helped me carry out the 197S grov/th arvilysis experiment. Thanks to Mr. J. B. White who supervised the construciion of tne thermogradient system which I used in 1979. My parents, Billy G. and Suzanne G. Ingram, have given me untold support and encouragement in al"! of n:y educational endeavors. Myriad thanks. A final word of appreciation to all of my fellov.' students and fi^iends who have shared with me the pleasures and curaens I have encountered during this degree program. n

PAGE 3

TABLE OF CONTENTS Pa^e ACKNOWLEDGEMENTS i i LIST OF TABLES v LIST OF FIGURES viii ABSTRACT. . , , xi i INTRODUCTION i LITERATURE REVIEW 2 Eco-Physiological Crop Modeling 2 Crop Phenology 4 Heat 5 Solar Radiation. 3 Nutrients 13 Water ]a SeasDn 15 Crop Growth. 19 Heat 20 PAR. 27 Nutri ents 29 Water 34 Density 36 Summary 37 MATERIALS AND METHODS 39 Crop Growth Model 39 Growth Analysis 1978 40 Thermogradient Analysis 1979 47 RESL'LTS AND DISCUSSION 51 Growth Anal ys i s 1 973 51 Pi^e-Emergencs , 51 Emergence 54 Plant Density 58 Canopy Devel opment 58 Fl oweri ng 82 Tuber Initiation 82 Rhizomes , , 83 Yield Dynamics.. 84 i ii

PAGE 4

Pace Thermogradient Analysis 1979 90 Bud Dormancy 90 Stem Growth and El ongati on 94 Root Grov/th 94 Tuber Growth 93 Sebago Crop Growth Model 1 00 Model Development 100 Model Val idation 105 Temperature Sensitivity Analysis 112 SUMMARY AND CONCLUSIONS 120 Growth Analysis 120 Thermogradient Analysis 121 Sebago Crop Growth Model 1 22 BIBLIOGRAPHY 1 23 APPENDIX A: LISTING OF VARIABLE DEFINITIONS, MODEL PROGRAM, COMMON BLOCK VARIABLES, INPUT TABLES, INITIAL VALUES OF STATE VARIABLES, AND PLOT STATEMENT FILES OF THE SEBAGO GROWTH AfID DEVELOPMENT MODEL 130 APPENDIX B: TABLES OF RAW DRY WEIGHT DATA. TUBERS PER SEEDPIECE, INFLORESCENCES PER SEED-PIECE, STEMS PER SEED-PIECE. TOTAL BRANCH PLUS STEM LENGTH PER SEED-PIECE, PERCENT FINAL EMERGENCE, MAXIMUM LEAF AREA INDEX, MAXIMUM PERCENT GROUND COVER, AND THEIR RESPECTIVE ANALYSIS OF VARIANCE 143 BIOGRAPHICAL SKETCH 156 TV

PAGE 5

LIST OF TABLES Table Page 1 Experiment dates, temoerature ranges, and seedpiece fresh weights for thermogradient analysis 48 2 Duration and cummulative heat units for Monona and Sebago phenophases 53 3 Seeding rates, maximum emergence, stems per seedpiece, and plant density for all treatments 57 4 Dry weights for various components of Monona planted on Julian Day 33, based upon samples of two seedpieces per replicate 65 5 Dry weights for various components of Monona planted on Julian Day 73, based upon samples of two seedpieces per replicate , 66 5 Dry weights for various components of Sebago planted on Julian Day 33, based upon samples of two seedpieces per replicate 67 7 Dry weights for various components of Sebago planted on Julian Day 73, based upon samples of two seedpieces per replicate 68 8 Crop and tuber growth rates during most linear growth period, with statistics for linear model and partitioning ratio 91 9 A post-emergence comparison of dry weights of fieldgrown and computer-simulated Sebago potatoes with a Julian Day 33 planting date 107 10 A post-emergence comparison of dry weights of fieldgrcv/n and computer simulated Sebago potatoes with a Julian Day 73 planting date 108 11 Simulated tuber and crop growth rates, assimilate partitioning ratio, and tuber initiation dates with climatic inputs of the Julian Day 33 and 73 growth analyses Ill

PAGE 6

Table ^age 12 Simulated tuber and crop growth rates, mean daily net photosynthesis, and photosynthate partitioning ratios for various temperature inputs. All calculations from linear tuber growth phase 113 13 Simulated tuber and crop growth rates, mean daily net photosynthesis, and photosynthate partitioning ratios for various temperature inputs. All calculations from linear tuber growth phase 114 14 Simulated final yields for tubers, canopy, roots, and total and tuber initiation dates with various temperature inputs 115 15 Simulated final yields for tubers, canopy, roots, and total and tuber initiation dates with various temperature i nputs 115 List of Tables in Appendix B B-1 Dry weights of seed-pieces, tubers, and crop total by replicates for the Julian Day 33 planting 143 B-2 Dry weights of seed-pieces, tubers, and croo total by replicates for the Julian Day 73 planting 146 B-3 ANOVA for total crop yields at final harvest 148 B-^ ANOVA for tuber yields at final harvest , 143 B-5 Number of tubers per seed-piece 149 B-6 ANOVA for number of tubers per seed-piece in Table B-5... ]^9 B-7 Number of inflorescences per seed-piece for date of maximum flowering 150 B-3 ANOVA for number of inflorescences per seed-pieca in Table B-7 150 B-9 Number of stems per seed-piece 151 B-10 ANOVA for number of stems per seed-piece in Table 3-9.... 151 B-11 Total stem plus branch lengths per seed-piece at maxima.. 152 B-1 2 ANOVA for total stem dIus branch lengths per seedpiece in Table B-11 ".' 152 vi

PAGE 7

Table Page Percent final emergence 153 ANOVA for emergence percentages in Table B-13 153 Maximum leaf area index 154 ANOVA for LAI's in Table B-15 154 Maximum percent ground cover 1 55 ANOVA for ground cover percents in Table B-17 155 B-

PAGE 8

LIST OF FIGURES Figure Page 1 General cummulative heat model with no temperature maximum 9 2 National Weather Service's Growing Degree Day heat model 10 3 Cummulative heat model which accounts for fluctuations about the base temperature (After iyldesley, 1 978 ) n 4 Simplified Ontario Heat Unit System (After Tyldesley, 1978) 24 5 Effect of temperature on the rate of an enzyme catalyzed reaction: i) response with constant enzyme activity; ii) thermal denaturation effect on enzyme activity, iii) reaction rate, the product of curves i and II (After Conn and Stumpf, 1972) 25 6 Effect of temperature on: i) Photosynthesis; ii) Respiration; and iii) Grov.'th (After Larcher, 1975) 26 7 Model of light intensity effect on leaf photos vnthesis (After De Wit, 1959) ". 30 8 ilcdel of light intensity effect on leaf photosynthesis (After Duncan et al . , 1967) 31 9 Net carbon exchange in potato canopy from sunrise to sunset (After Sale, 1974) 32 10 Weekly average temperature in Hastings, Florida. Air temperatures ( ) measured in standard shelter at 150 cm height. Soil temperatures ( ) measured at 10 cm depth 43 11 Total weekly precipitaiion ( ) in Hastings, Florida, and pan evaporation ( ) in Gainesville, Florida -14 12 Daily photosynthetical ly active radiation average over one week intervals 45 viii

PAGE 9

Figure ll2^ 13 Soil temperature profiles under a Sebago canopy from 1615 hours on March 20, 1978 to 1205 hours on March 21, 1978 46 14 Percent seed-piece emergence and number of inflorescences per seed-piece for Monona and Sebago planted on Jul ian day 33 55 15 Percent seed-piece emergence and number of inflorescences per seed-piece for Monona and Sebago planted on Jul ian day 73 56 16 Leaf area index and percent ground cover for Monona planted on Julian day 33 59 17 Leaf area index and percent ground cover for Sebago planted on Julian day 33 50 18 Leaf area index and percent ground cover for Monona planted on Julian day 73 51 19 Leaf area index and percent ground cover for Monona planted on Julian day 73 62 20 Effective leaf area index for Monona and Sebago planted on Julian day 33 59 21 Effective leaf area index for Monona and Sebago planted on Julian day 73 70 22 Total stem and branch length, main stem length, and average branch length for Monona planted on Julian day 33 73 23 Total stem and branch length per seed piece, main stem length, and average branch length for Sebago planted on Julian day 33 74 24 Total stem and branch length per seed piece, main stem length, and average branch length for Monona planted on Julian day 73 75 25 Total stem and branch length per seed piece, main stem length, and average branch length for Sebago planted on Julian day 73 76 26 Dry weights of green and chlorotic leaves of Monona planted on Julian day 33 as used to estimate leaf duration 73 ix

PAGE 10

Figure Page 27 Dry weights of green and chlorotic leaves of Sebago planted on Julian day 33 as used to estimate leaf duration 79 28 Dry weights of green and chlorotic leaves of Monona planted on Julian day 73 30 29 Dry weights of green and chlorotic leaves of Sebago planted on Julian day 73 as used to estimate leaf duration 81 30 Growth curves for total plant, tubers and remainder for Monona planted on Julian day 33 with sample size from 12 to 20 seed-pieces per replicate 85 31 Growth curves for total plant, tubers, and remainder for Sebago planted on Julian day 33 with sample size from 12 to 20 seed-pieces per replicate. 35 32 Growth curves for total plant, tubers, and remainder for Monona planted on Julian day 73 with sample size from 12 to 20 seed-pieces per replicate 87 33 Growth curves for total plant, tubers, and remainder for Sebago planted on Julian day 73 with sample size from 12 to 20 seed-pieces per replicate 88 34 Effect of temperature on stem growth for Sebago seed-pieces with dormant buds 92 35 Temperature response for stem elongation in Sebago seed-pieces with dormant buds ". 93 36 Effect of temperature on stem growth of Sebago potatoes with non-dormant buds 95 37 Temperature response for stem elongation iti Sebago seed-pieces with non-dormant buds 96 38 Root growth temperature response curves for Sebago potatoes 97 39 Effect of soil temperature on tuber and total growth rate of Sebago potatoes grown in 25 cm plastic pots , 99 40 Dry-matter flow diagram for Sebago growth model 101 41 Relative growth rate vs. temperature for Sebago canopy (TCAN), roots (TROOT), and tubers (TUBRGR) 104 X

PAGE 11

Il^lMIi Paoe 42 Tuber growth rate (TTUBR) vs. temperature for Sebago 105 43 Simulated Sebago growth components with climatic inputs of the Julian day 33 growth analysis 109 44 Simulated Sebago growth components with climatic inputs of the Julian day 73 growth analysis 110 XT

PAGE 12

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 MATHEMATICAL MODELING OF THE GROWTH AND DEVELOPMENT OF POTATOES ( Solanum tuberosum L.) By Keith T. Ingram March 1980 Chairman: Darell E. McCloud Major Department: Agronomy During the 1978 growing season a growth analysis was performed on potatoes ( Solanum tuberosum L. ) planted on 2 February and 14 March. Two cultivars, Monona and Sebago, were studied. During the winter of 1979 a thermogradient analysis of Sebago growth was conducted. The objective of these studies was to provide data for tne development and validation of a mathematical crop growth and development model. During the summer and fall of 1979 such a crop model was written in the GASP IV simulation language. The purpose of the crop model was to elucidate the effects of temperature on assimilate partitioning. The results of the crop growth and development model indicated that the primary effect of soil temperature was tnrough a direct regulation of the tuber growth rate which had a 15° C temperature optimum, A high potential tuber growth rate stimulated photosynthesis; so a secondary effect of soil temperature was on net daily photosynthesis. xii

PAGE 13

The major effect of air temperature was its influence on the tuber initiation date. Air temperature and tuber initiation rate were inversely related. The air temperature also affected the rate of canopy senescence with warm temperatures speeding leaf drop and reducing the crop growth rata. The main weakness of the model was that light interception data were input rather than generated by the model itself. xin

PAGE 14

INTRODUCTION There are four factors which determine a crop's yield: 1) the rate of crop photosynthesis; 2) the amount of assimilate which can be mobilized and translocated to the yield component from storage in other crop organs; 3) the portion of daily photosynthesis decosited in the yield organ; and 4) the duration of yield organ growth. Of these yield determining factors, the daily photosynthate partitioning and the length of the yield organ growth period show most potential response to manipulation for increasing yields. The mechanisms which regulate photosynthate distribution are not clear; so it is impossible to systematically change partitioning per se . It is the aim of this study to elucidate the effects of temperature on photosynthate partitioning. The potato, Solanum tuberosum L., was chosen as the experimental subject because the yield organs and the photosynthetic organs grow in different thermal environments. The soil temperature of the tuber environment has smaller amplitude of fluctuation and different times of maximum and minimum temperatures than the aerial temperatures of the crop canopy. Further, these thermal di-^ferences occur on both aaily and seasonal bases. In field and greenhouse studies "any other environm.ental factors confound interpretation of thermal effects. Therefore, a computer simulation model was developed to isolate thermal effects on potato crcp growth dynamics.

PAGE 15

LITERATURE REVIEW Eco-Ph.ysio1oq1ca1 Crop Modeling Agronomists often use the terms crop ecology and crop physiology synonymously. This confusion stems partly from the fact that ecology and physiology are terms which originate from studies of natural biological systems. Ecology can be defined as the study of relationships between organisms and their environment. Physiology is the study of normal functioning of organisms and their organs. When applied to crop systems these definitions overlap. The goal of crop physiology is to better understand the dynamics of yield development (Evans, 1975a). Crop physiology greatly depends upon environmental factors which are the subject of ecology. Milthorpe and Moorby (197^) use the term physiology when considering interrelationships between croo plants and abiotic environmental factors as well as competitive interactions between higher plants comprising the crop system. Seme authors recognize the commonalities between the two fields of study by using the terms eco-physioiogy (Eckard, 1965) or ecological physiology (Leopold and Kriedemann, 1975). This eclectic area is fundamental to models of crop growth and development. Crop models attempt to mathematically describe plant responses to environmental inputs. The models most frequently encountered in literature tend to minimize input variables and responses to facilitate understanding of the model. For example. Lynch and Rowberry (1977a) tested two reciprocal polynomial models 2

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3 to determine which best described the relationship between potato stem density and tuber yield. They used the single input, stem density, to predict two responses, total tuber yield and marketable tuber yield. More complex models have been developed to describe other crop system phenomena. Several models have been published which describe soilplant water relationships (Campbell et al . , 1975; DeVries, 1972), crop photosynthesis (Duncan et al., 1967; DeWit, 1959), and crop microclimate (Goudnaan and Waggoner, 1972). In fact, any mathematical description which relates two or more factors, such as by regression analysis, is a model. With the advent of high speed computers the art and science of modeling have progressed from simple statistical type models, to multiple linear regression models, to complex systems of equations which attempt to simulate crop growth and develooment throughout a growing season and to models of entire eco-system functioning (Stewart, 1975). Moorby and Milthorpe (1975) have published a flow diagram for a possible potato growth model. The complete mathematical description of potato growth and environmental relations is complicated by the enormous range of adaptability and plasticity of the potato crop, the multiplicity of uses to which potatoes are put, and by an incomplete understanding of potato growth physiology. Similar to ecology and physiology, crop growth and development are often poorly distinguished. Growth, as used here, refers to the increase in cry weight. Development, on the other hand, refers to the combination of organ differentiafi^on and growth coordination. The growth of a croo is highly dependent upon its developmental phase or phenophase. The eco-physiological mode"! must be able to follow growth and development along separate but interdependent time courses.

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4 Crop growth models generally include four primary processes: water relations, mineral uptake and metabolism, photosynthesis, and crop development. The major environmental inputs to these processes are soil nutrient availability, air temperatures, solar radiation, and precipitation or irrigation. The modeler must consider not only the environmental inputs, but also how the particular crop responds to these environmental factors. The purpose of this review is to elucidate some of the more important eco-physiological interrelationships affecting potato crop growth and development. Crop Phenology Crop phenology is the study of developmental phenomena which respond to annually periodic environmental stimuli. These developmental phenomena are catalogued by visible morphogenic changes such as bud break, flower initiation, and fruit abscision. Phenology can be contrasted with ontology. While phenology is the study of life cycle changes due to annual climatic fluctuations, ontology is the study of developmental phases through the life of an individual organism (l.archer, 1975). For annual plants the difference between phenology and ontology is slight. Cultivated potatoes fit best in the annual growth habit classification. One might distinguish between potato ontogeny and phenology. The ontogenic cycle begins when the tuber bud is initiated and ends when the canopy produced by that bud senesces. By contrast, zhe phenologic cycle runs from planting through harvest and storage. Thus ontogenic generations overlap during the period from tuber iniiiation to harvest while phenologic cycles do not

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5 overlap. Further, phenology emphasizes environmental effects on crop development while ontology tends to focus on genetic factors. One list of the climatically regulated phenophases in a potato crop's development might include: a) tuber dormancy; b) bud break and shoot elongation; c) root system, rhizome, and canopy development; d) flowering; e) tuberization; f) tuber growth; g) canopy senescence; and h) crop maturity. This list is little more than the organogenic sequence through the crop season. Much more interesting than the phenologic description are the factors which regulate the length of the phenophases. Heat The relationship between crop development rates and thermal environment has been noted for many crops. The heat unit theory by Abbe states that plant development depends upon cummulative heat exposure rather than time per se (McCloud, 1979). The national weather service provides growing degree day data in tneir Weekly Weatner and Crop Bulletin to help researchers and growers estimate crop development rates. Most crop models include a subroutine which integrates temperature inputs in order to regulate crop phenology. In fact, for many crop models, neat accumulation alone is sufficient to monitor the crop development rats. For most crops, development rate and temperature are positively related over the temperature range for normal growth. In wheat, higher temperatures '"educe the length of both vegetative and filling phases (Spiertz, 1974). In field work supporting their cotton morphology model Hesketn et al . (1972) found that higher temperatures reduced days from planting to full cotyledon expansion, days between

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5 development of successive leaves on the same branch and between successive branches on the main stem as well as between flowers on a branch. Their work showed that the cummulative heat concept can be used to describe organogenesis, i.e., plastochron duration, as well as longer term phenologic development, i.e., the canopy development phase. Haun (1975) used multiple linear regression to analyze relationships between daily maximum and minimum air temperatures as well as other clTmatic data with development rate of potato leaves. He found the best correlation between the leaf development rate and temperature when a one or two day lag time for air temperature was used. Unfortunately, since Haun used multiple linear regression analysis, it is nearly impossible to isolate the exact temperature verses development rate relationship. According to Van Dobben (1962), the effect of heat on the rate of vegetative crop development is independent from the effect of heat on crop growth. Generalized trends of the influence of heat on potato development are as follows: 1) The emergence rate is accelerated at higher temperatures over the range of 12 to 24^ C. 2) The optimum temperature for tuberization is around 20'' C with initiation delayed relatively more by higher than lower temperatures. At 30^ C tubers may never form. 3) At high temperatures the canopy may continue to develop past flowering under conditions of high nutrient availability. Extended canopy growtn at hign temperatures is likely related to delayed or decreased to'berizaticn vvhich makes more assimilate available for canopy g'^^owtn (Bodlaender, :9c3). In the above discussion little dis~incti on was made between the relative influeices of air and soil temoeratures. These factors are

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7 highly correlated and difficult to distinguish (Nielson and Humphries, 1966; Richards, 1952). Richards reported a phase delay and amplitude reduction in the soil temperature with increased depth. In other words, the difference between maximum and minimum temperatures declines with depth, and the time of these maximum and minimum temperatures is delayed. In the root and tuber growth zone, however, the phase shift and amplitude dampening with depth are slight. In their research on tomatoes, Abdelhafeez et al . (1971) found that the main effect of soil temperature on development rates occurred during the emergence phase. Two weeks past emergence, little distinction could be made between soil temperature treatments. Furthermore, soil temperature had no apparent effect on fruit maturity dates. Sc-.ll. the findings of Abdelhafeez et al. agreed with those of Nielson and Humphries that soil temperature had a marked effect on root morohology and development. At cool temperatures roots develop more slowly, have fewer secondary roots and become thicker than at higher temperatures. Soil temperature has an effect on corn development well beyond emergence. Mederski and Jones (1963) found that corn plants grown on soil heated from planting to maturity and from emergence to maturity both reached maximum height earlier and matured earlier than unheated control plants. If, as suggested by Van Dobben (1962), the effect of soil temperature is positively related to the size of the crop propagule's reserve of substrate, then we would expect significant effects of temperature on potato development. Indeed, higher soil temperatures have decreased the time from planting to emergence (Moorby and Milthorpe, 1975). Further, since the tuber of the potato develops underground we might expect that soil temperature plays a

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greater role in determining potato crop development than in crops where the bulk of the biomass is aerial. Higher soil temperatures seem t,o shorten the tuber initiation period v/ith fev/er tubers being set. However, the higher soil temperature does not appear to hasten canopy senesence when air temperatures are held constant. Under these conditions, the few tubers which do set at high soil temperature generally grow to larger proportions than tubers growing in cool soil (Bodlaender, 1963; Hagan, 1952b). The cummulative heat models mentioned above commonly assume a linear form (Figures 1 and 2). The rate of development increases linearly above some base temperature. The development rate may or may net have an upper limit. The Growing Degree Day information published by the National Weather Service assumes zero devaloDment above 30° C (Figure 2). The simplicity of these linear models makes them most practical for general use. Discrepancies arise when temperatures fluctuate about the base temperature or the maximum temperature. Tyldesley (1978) presented a model to account for these temperature fluctuations (Figure 3). Tyldesley smoothed the angle between the linear model and the axis. Solar Radiation Isolating the effects of solar intensity on crop development is difficult. Radiation provides energy for evapotranspiration and temperature changes within the crop canopy (Chang, 1958). The effects of these climatic factors are confounded in most field experiments. Still, Haun (1975) found significant correlations between light intensity and leaf development in potatoes. Effects of low lighr intensities on plant development have been studied as well. At low

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HEAT UNITS BASE B*20 B*4C TEMPERATURE (^C) Figure 1. General cummulative heat model wiih no temperature maxi ]mum.

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10 36GROWING DEGREE DAYS 2'^18H^-T^ 10 15 20 25 30 TEMPERATURE C^^C) Figure 2. National Weather Service's Growing Degree Day heat model

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11 HEAT UNITS BASE BO B-20 8*30 TEMPERATURE (^C) Figure 3. Cummulative heat model which accounts for fluctuations about the base temperature (After Tyldesley, 1978).

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12 light intensities stem elongation is stimulated while leaf development is inhibited (Van Dobben, 1962; Leopold and Kriedemann, 1975). Using potatoes grown at 16 hour days with light intensities from 3,900 to 15,000 Ix., Bodlaender (1963) found that the maximum stem length was reached sooner, tubers initiated sooner, the canopy senesced earlier, and flowering was stimulated by the high light level. The applicability of these findings to field conditions is diminished since the highest light intensity was approximately 30?^ of full sunlight (54,000 Ix.). Sale (1973a) found no effect of 21% or 34% shade on the development of field grown potatoes. The plants grown under both of Sale's shade conditions received higher light intensities than those grown in Bodlaender' s growth chamber. Plant breeders have severely altered the photoperiodic response cf the potato. Though potatoes were cultivated by Peruvian Indians at least as long ago as 4000 B.C., Spanish explorers did not introduce the potato to Europe until around 1570 A.D. At that time, potatoes were a botanical curiosity. After only 100 years potatoes v.ere growri on a field scale in Ireland. In the same 100 years heavy selection pressure appears to have converted S_^ tuberosum subspecies andiqena , a plant adapted to form tubers under twelve hour days of tropical latitudes, to subspecies tuberosum which initiates tubers under long suminer days (Hawkes, 1978). Modern potatoes are classified as eitner long-day favorable, short-day favorable, or day neutral by Chang (1968), S. tuoe ro sum is one of -f-'ew species where photoperiodicity is related to tuber formation rather than flowering. The photoperiodic response in potatoes shows great plasticity. Though some cultivars show more strict photoperiodic responses (Leopold and Kreidemann, 1975), potatoes do net generally exhibit

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13 threshold photoperiodic requirements for tuberization. Rather, photoperiodic classification is based on the effect of photoperiod on the development rate. For example, short-day conditions accelerate progression from one phencphase to the next in European cultivars which are short-day favorable. As well as earlier tuberization, flowers initiate sooner, stem elongation ceases sooner, and plants senesce earlier under favorable photoperiodic conditions (Bodlaender, 1963). Nutrients The ef-Pect of soil nutrients on potato phenology depends upon timing of fertilizer application. Even the nutrients aoplied to the seed crop may influence potato phenology. Nitrogen fertilizers applied to the seed crop may hasten maturity in an early crop grown from the seed (Gray, 1974). High soil nitrogen levels at the time of planting increase emergence rates (Moorby, 1973). According to Ivins (1963), nitrogen aoplied during early cancpy development will delay tuber initiation and canopy senescence. On the other hand, Dyson and Watson (1971) found that nitrogen fertilization did not delay tuber initiation in King Edward cultivar potatoes. Only zero nitrogen fertilization shortened the period for the carooy to reach its maximum growth. Rather, they found nitrogen to reduce the rate of tuber growth during the period directly following tuber initiation. Bremner, El Saeed, and Scott (1967) noted sharp inflection points in the graph of tuber:fol iage ratio versus total dry weight. These inflection points indicated transition from the vegetative to tuber growth phencphase. Low nitrogen treatments showed significantly ''aster d-velopment according to this analysis. The prolonged canopy

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14 development phase under high nitrogen conditions is associated with an increase in branching rather than main stem growth (Harris, 1978a; Dyson and Watson, 1971). In their studies with S. tuberosum sp. andigena , the South American ancestor to sp. tuberosum , Ezeta and McCollum (1972) applied three fertilizer levels: 150-160-160; 80-80-80; and 0-0-0 kg/ha of N-P2O5-K2O5, respectively. Potatoes given the low fertilizer treatment matured by 156 days after planting while those given higher fertilizer treatments m.atured after 172 days. The flowering date was the same for all treatments; so the only apparent effect of high fertility appeared to be to extend the tuber development phase. All of the nitrogen, calcium, and magnesium absorbed by sp. andigena was taken up before tuber initiation. For the more commonly cultivated sp. tuberosum , however, uptake may continue until the beginning of canopy senescence (Soltanpour, 1969). Nitrogen is often taken to be the major nutrient associated with crop development and growth. The relationship between nitrogen level and development or growth is relatively linear over a rather large range of nitrogen levels. Most crops exhibit a threshold type resDonse to levels of other plant nutrients. As long as these nutrients are present above some threshold concentration they have little effect on crop growth or development. Phosphorus and, to some extent, potassium accumulate in soils which are intens'ively fertilized. Thus, phosphorus and potassium are usually above the threshold. Nitrogen reserves are quickly depleted to suboptimal concentrations in the soil solution (Harris, 1978a). Dyson and Watson (1971) found potassium to stimulate canopy senescence. Potassium also stimulated the leaf growth rate. Potassium's

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15 combined influences of hastening senescence and leaf growth stimulation give a net zero effect on final yield. McCollutn (1973a and 1978b) found that phosphorus applications had opposite effects to nitrogen applications. When phosphorus was applied during canopy development, tuber initiation and canopy senescence were both hastened. Water Early irrigation has some effects similar to early nitrogen application on potato development. Both water and nitrogen tend to speed emergence and leaf development while delaying tuber initiation (Sale, 1973b). Unlike nitrogen's effects, however, early irrigation tends to hasten canopy senescence in some potato cultivars (Ivins, 1963; Harris, 1978b). If irrigation is applied soon after tuber initiation the tuber development phase is prolonged and canopy senescence is delayed (Ivins, 1963). Drought generally has the opposite effect of irrigation. Early drought will cause earlier curtailment of leaf and branch development. This drought effect reflects a reduction in numbers of oranches and leaves formed with 'relatively no change in the rate that new leaves and branches are produced. A short drought period will decrease the development rate of previously initiated leaves in potato plants having tubet^s but net in pretuberous plants. In other words, the rate of unfolding and expanding raay be slowed by drought in tuber bearing plants but not in tuberless plants. In both cases, the production of new leaves occurs at the same rata but stops sooner under drought conditions (Munns and Pearson, 1974). During the tuber growth phase a short drought rr.ay retard or stop tuber development. Upon relief from the wa -cer stress only the

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16 acropetal tuber tissues resume growth and development. Misshapen tubers result (Moorby et al . , 1975; Morby, 1973). These deformed tubers, called second growth tubers, result from rapid maturation of the basipetal tuber buds and adjacsnt tissues. Since these tissues mature during the stress period only the acropetal buds may resume growth. If all buds in a tuber mature as the result of a short water stress period, the rhizome may resume growth when the stress is removed to give a chain of tubers. Thus, there appears to be a threshold level cf tuber and bud develocment. Buds beyond the threshold level of development rapidly mature and cease growth when stressed and then unstressed. Less well developed buds will continue more or less normal develooment after the stress period. Long and Penman (1963) reported that resumption of crop growth after drought relief did not occur for several days. They postulated that new roots needed to grow before the recently added soil moisture could be exploited. Season The preceding discussion shows that potato phenology is regulated by a complex of environmental factors. The effect of growing season on potato phenology results f»^om interactions between several of the factors. According to Moorby and Milthorpe (1975), potato growing regions may be classified as cool -temperate or warm-subtropical. The cool -temperate production season is limited by frost at both planting and harvest. The warmer subtropical production areas may have two growing seasons per year: the first from the last winter frost to high temperatures of summer; the second after peak summer tempe*"atu>"es until first frost in the fall. One night consider' another ecosystem cf ootatc production, the high altitude tropical region. The and i gen

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17 subspecies is primarily grown in this region. The literature reviewed pertains to the tuberosum subspecies so the high altitude tropical production region is not included. The effect of season on potato phenology begins with the soil temperature influence on emergence. The two seasons of production in subtropical areas are at opposite ends of this relationship. The first crop is planted when soils are cool. Emergence is slow. Other factors being constant, the second crop shows rapid emergence since it is planted in warmed soils of late summer. In cool -temperate areas, crops at later planting dates may emerge faster due to a combination of warmer soil temperatures and the likelihood that more sprout develcnment has occurred on seed pieces before planting (Bremner and Radley, 19G5; Radley, 1963). Once the crop has emerged, the length of the next phencphase will be determined by the integrated effects of temperature, photoperiod, nutrition, and water status. Only temperature and photoperiod are necessarily related to season since both water and nutrients may be applied r,r withheld by the grower. The effects of these two environmental stimuli, temperature and photoperiod, may be superimposed on the effect of the age of the rhizome apex. The end of the canopy development phase is marked by overlapping commencement of tuber growtn, flower initiation, and cessation of leaf and branch growth. Moorby (1978) postulated two control mechanisms for tuber initiation. One is hormonal. Photoperiodic effects on tubenzation are likely mediated by phytoch>^ome. Such a phytochrome mechanism would be an example of hormonal regulation of tuber initiation. The other control rri-chanism Moorby suggested is

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18 substrate mediated. Retardation of canopy growth by low temperatures might allow more assimilates to be translocated to rhizomes to stimulate tuber growth. In some cultivars the canopy growth itself may regulate tuberization. In this case, tubers initiate when a threshold canopy development level (as measured by LAI) is reached (Radley, 1953). In a cool -temperate region, Bremner and Radley (1966) found that later planted crops had longer canopy development phases than early planted potatoes. These observations conform to the predictions of both of Moorby's tuberization control mechanisms since the later planted potatoes grew in warmer weather and longer days. Sale's (1973a and b) data from Australia's two crop periods can also be explained in terms of the two control mechanisms. Cool temperatures and short days during the first crop season stimulate luberization more quicKly than the warm long days under which the second crop's canopy developed (Moorby and Milthorpe, 1975). Regardless of the factors which stimulate tuber initiation, the balance of crop growth shifts from canopy to tubers at this time. Known plant growth regulators and a hypothetical tuber forming substance have been implicated with the environmental stimuli mentioned above. As yet, little consensus has been reached. Moorby (1978) declared that the mass of apparently contradictory evidence illustrates the futil'^ty at the present time of trying to give any definitive explanation of the mechanism of tuber initiation. By the time tne tjoer growth and development phase begins many factors have possioly already contributed to canopy senescence and crop maturity. Plants demaged by frost during early canopy development

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19 appaar to senesce earlier than unfrosted plants (Radley, 1963). Further, the lengths of the canopy development and tuber development phases are positively related. A long canopy development phase leads to a long lasting canopy and a long tuber growth phase (Bremner and Radley, 1966; Radley, 1963). According to Radley, the planting date in cooltemperate regions had little influence on senescence time in some of the cultivars tested. Presumably, the effect of canopy size at tuberization on the length of the tuber growth period was overridden by environmental factors. Crop Growth The definition of growth as an increase in dry weight is convenient to crop modelers. Dry weight increase can be easily described mathematically as a function of physiologic and phenologic factors. Dry weight increase, of course, is not an inclusive definition of growth. Both popular and scientific connotations of growth include reproduction, enlargement and cell division as well as assimilation (Hagan, 1952a). Crop growth is the result of all of these processes. Thus growth analysis by periodic harvest becomes a powerful instrument foi^ describing these growth phenomena (Radford, 1967; McKinion et al., 1974). Combined with environmental descriptions, growth analysis is a good test of mathematical crop growth models (Leopold and Kriedemann, 1975). As there are many definitions of growth, there are many ways to Isbel crop growth stages. Growth stages may be associated with the curnmulative crop growth curve. The expansion (exponential), linear, and maturation growth stages combine to form a roughly sigmoidal

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20 growth curve which applies to both crop and organ growth (Milthrope and Moorby, 1974; Leopold and Kriedemann, 1975). Combining the growth of crop organs into total crop growth is the purview of photosynthate partitioning. For seed bearing crops, partitioning may be defined as the division of daily assimilate between reproductive and vegetative plant parts (Duncan et al . . 1978). For potatoes, we define partitioning with respect to tuber versus non-tuber plant parts. This poorly understood phenomenon has been related to source-sink strengths (Edelman, 1963), nutrient availability (Alberda, 1962), plant growth regulators (Bruinsma, 1962), and the climatic factors discussed below: heat, PAR, nutrients, and water (Brouwer, 1962a). No single mechanism fully explains assimilate partitioning. Most source-sink arguments are too oolarized. Assimilate metabolism and photosynthesis have mutually regulatory feedback. Translocation, the means of this feedback, must be considered in any partitioning scheme as well as the strength of source and sink (Evans, 1975b). In potatoes the rate of photosynthesis after tuber initiation seems largely determined by tuber growth, the major photosynthate sink (NosDerger and Humphries, 1965). Photosynthesis may increase seven-fold after tuber initiation (Evens, 1975b). Thus tuber presence seems to favor growth. Whether this effect is best explained by source-sink, grov/th regulator, or nutrient balance remains to be seen. Heat As stated above, c>^op yield is determined by mutually independent temperature e-^^fects on growth and development. Van Dooben (1962) further stc-.ted that the temperature effect on the crop growth rate is

PAGE 34

21 greater than the temperature effect on development. Where models relating temperature and development are generally linear (Figures 1, 2, and 3), growth and temperature exhibit non-linear relationships (Figures 4, 5, and 6). Crop and organ grovyth have minimum, optimum, and maximum temperatures called cardinal temperatures. These cardinal temperatures depend upon crop nutrition, solar radiation, and water relations as well as the genotype (Bodlaender, 1953). A common growth versus temperature model is the Qio notion. For maize seedlings, the Q]o was calculated to be greater than three at low temperatures, from three to two at suboptimal intermediate temperatures, and less than one for supraoptimal temperatures (Hagan, 1952a). Tyldesley (1978) presented several means of modeling non-linear temperature responses. One is a simplified account of the Ontario Keat Unit system (Figure 4). Tyldesley' s account assumed the response rate to be parabolic with the optimum rate at 30° C and zero rates at 10 and 50"^ C where temperatures refer to daily maxima. This heat unit system gives one means of modeling temperature responses which show a definite optimum. The derivations of tvyo temperature response curves are shown in Figures 5 and 5. Figure 5 is derived from biochemical studies of enzyme catalyzed reactions (Conn and Stumpf, 1972). The three curves represent: i) the temperature response at a constant enzyme activity, ii) the effect of temperature denaturation on enzymatic response; and iii) the overall temperature response of the reaction which is the product of curves i and ii. The shape of curve iii corresponds well

PAGE 35

22 with the temperature response curves published for several crops (Rickman et al . , 1975; Hagan, 1952a; Blacklow, 1972; Mocrby and Milthorpe, 1975). Figure 5 shov/s the difference between the photosynthesis and respiration temperature responses (Larcher, 1975). The dark respiration rate is markedly temperature sensitive. The relationship was found to be exponential over the 6 to 32'" C temperature range encountered by Sale (1974) in experiments with Sebago cv. potatoes. The stimulatory effect of high temperature on respiration may be overridden by substrate defficiency, enzyme denaturation, or by respiratory product accumulation with negative feedback ccntrcl (Hagan, 1952a). Notice that the curves for photosynthesis and respiration both have the shape of curve iii 1n Figure 5. The similarity of these curves is expected since both photosynthesis and respiration are enzymatic reactions, or more properly, systems of enzymatic reactions. Sale (1974) discovered a lack of priotosynthetic temperature response by a potato canopy. Sale's finding may merely point out that Dhoiosynthesis is itself the result of two enzymatic systems having different optimum temperatures, i.e., photosynthesis and photorespiration. The combined effects of two such systems would yield a plateau in the temperature response curve. Gross photosynthesis is commonly considered to be temperature insensitive. Since the initial reactions of gross photosynthesis are driven by PAR these steps may be better explained as physical than enzymatic processes. Still, net photosynthesis includes a respiration term to render it undoubtably temperature sensitive.

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Several authors have discussed the relative effects of air and soil temperatures. Nielson and Humphries (1965) found that growth is more inhibited by cold soil than cold air temperatures. The water and nutrient uptake upon which canopy growth depends is greatly slowed by cool soil temperatures (Kramer, 1940; Dalton and Gardner, 1978). Sale (1974) could not find a relationship between soil temperature at 10 cm depth and soil respiration. Sale's inability to find a relationship may be because he made his measurements over uncropped, low-organicmatter soil. Bodlaender (1963) reported that 1 5 to 18° C is optimal soil temperature for potato growth. Cool air temperature may reduce the rate of assimilate translocation to underground plant parts (Hagan, 1952a). By reducing translocation to roots and tubers, air temperature may affect the optimum soil temperature (Nielson and Humphries, 1966). Heat has a strong effect on photosynthate distribution in the crop system. Roots generally have a lower temperature optimum for growth than do shoots. The shoot to root ratio increases with temperature during canopy development (Van Dobben, 1952). During reproductive growth of wheat, high temperature favors grain growth over shoot growth. In fact, the shoot decreases in dry weight due to respiration and translocation of stored assimilates to the growing grain (Spiertz, 1974). Heat also affects photosynthate distribution through its influence on development. Tne longer tuber initiation is delayed in potatoes by suboptimal temperatures, the greater canopy growth is achieved before tuberization if nutrients and water are non-limiting (Bodlaender, 1963). The larger the canopy at tuberization the longer the tuber growth period and greater the final yield. Even though

PAGE 37

24 GROWTH UNITS 20 30 40 TEMPERATURE (°C) 50 Figure 4. Simplified Ontario Heat Unit System (After Tvld'-slpy 1978). J -J y

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VELOCITY TEMPERATURE Figure 5. Effect of temperaiure on the rate of an enzyme catalyzed reaction: i) response with constant enzyme activity; ii) thermal denaturation effect on enzyme activity; iii) reaction rate, the product of curves i and ii (After Conn and Stumpf, 1972^

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26 RATE TEMPERATURE Figure 6. Effect of temperature on: i) Photosynthesis; nj Respiration; and iii) Growth (After Larcher, 1975).

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27 high temperatures delay tuber initiation, they also accelerate canopy senescence to reduce the tuber growth duration. Photosynthetically Active Radiation (PAR) In the previous section, photosynthesis was stated to be relatively temperature insensitive, at least in the primary photoelectric reaction steps. PAR is the driving force for photosynthesis. De Wit (1959) modeled gross photosynthesis as 6.7 x 10"''-^ g/erg for light intensities below 8.5 ergs PAR/cm2/sec. Above this light intensity photosynthesis was modeled as a constant 4.7 x 10-8 g/cm2 (Figure 7). Rijtema and Endrodi (1970) accounted for light intensity effects on growth by estimating the photosynthetic rate under clear and cloudy sky conditions. By measuring daily duration of cloud cover and applying a correction factor to account for canopy ground cover and moisture status Rijtema and Endrodi were able to make fairly accurate predictions of crop growth. Duncan et al. (1967) modeled individual leaf ohotosynthesis with a rectangular hyperbola. The rectangular hyperbola was also the function derived by Michael is and Menton to describe enzyme kinetics (Conn and Stumpf, 1972; Thornley, 1976). Using a rectangular hyoerbola to model photosynthesis emphasizes the enz>'matic underpinnings of photosynthesis (Figure 8). The hyperbolic relationship between light intensity and photosynthesis holds even better for a croD canopy than for an individual leaf (Sale, 1974). Even though photosynthesis and growth have a positive response to PAR, the efficiency of light utilization declines as light intensity increases. Sale (1973b) reported that photosynthetic efficiency increased as shade was increased from to 34". Both models, Fi^'ures 7 and 8, can explain this finding as both show a decreased

PAGE 41

28 response at high light intensities, i.e., light saturation of photosynthesis. Gaastra (1962) reported that light saturation results when stomata are fully opened at submaximal light intensities. Despite higher efficiency of light utilization at low PAR intensities, yields do increase with higher intensities. Using light levels below onethird full sunlight (92 to 175 cal/cm2/day) , Spiertz (1974) showed that seed yield and growth rates for wheat both increased with light intensity. In maize, Linvill et al . (1978) found highly significant correlations between intercepted solar radiation and grain growth. In potatoes, light intensity effects assimilate partitioning as well as yield. Shade to 34% had no effect on leaf dry weight although shaded plants had a greater leaf area (Sale, 1973b). The top to tuber ratio increases at lower light intensities (Bodlaender, 1963). In other words, tuber growth, not canopy growth, was reduced by shading. Fewer tubers grew in shaded potatoes though the numbers of tubers initiated and stem density were the same at all light levels tested. The decrease in tuber yield also related to a delay in reaching the maximum tuber growth rate in shaded plants. Delaying the maximum tuber growth rate shortened the tuber growth duration since canopies at all light levels senesced at the same time (Sale, 1973b). Bremner et al . (1967) manipulated interplant competition for light by varying spacing of potted potato plants. More PAR per pot was thereby available at lower densities. The number of stems per seed piece and leaf area per plant remained the same. The LAI was therefore higher at higher densities. The effect of PAR on the net carbon exchange (NCE) is evident througn a diurnal analysis. Sale (1974) reported a mesa-shaped curve

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29 from sunrise to sunset for NCE (Figure 9). He also found that the canopy was light saturated above 400 W/m2. At this light intensity MCE was approximately 42 mg C02/dm2/hr. These PAR effects on growth are moderated by crop age. Stem and leaf respiration declined as the crop matured, probably because growth respiration (as opposed to maintenance respiration) declined. Maximum photosynthesis also declined with crop age. Thus the coefficients in the light response curve equation must be updated through the crop season. Nutrients The effects of mineral supply on plant growth are by no means clear. Brouwer (1962b) reported that increased mineral supply leads to a greater increase of shoot than root growth. In fact, Brouwer' s data show almost no change in root dry weight over three nitrogen levels in barley plants. Brouwer and De Wit (1968) modeled plant and root growth with low nitrogen supply reducing the shooi to root '^atio. This trend was confirmed by Lynch end Rowberry's (1977b) finding thai ootato root growth was reduced at high fertilizer rates. These studies considered ratios at a single point in time rather than examining partitioning trends through crop growth. Dyson and Watson (1971) found that even though nitrogen and phosphorus application Increased the potato crop growth rate from two to four weeks after emergence, the major effect of the nutrients on growth was througn extending the canopy growth period rather than increasing the canopy growth rate per se . Similarly, Ivins (1963) found nitrogen applications to increase yield by delaying tuber initiation and extending the tuber growth period.

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30 LEAF PHOTOSYNTHESIS IO*'g CH2O crn^ sec 10 20 LIGHT INTENSITY (10^ erg cm'^'sec' ) Figure 7. Model of light intensity effect on leaf photosynthesis (After De Wit, 1959).

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31 120-1 LEAF PHOTOSYNTHE90^ SfS Mg CO2 30120I P= I + 10,000 10 20 LIGHT INTENSITY (10' f-c) Figure 8. ^'lodel of light intensity effect on leaf photosynthesis (After Duncan et al., 1967).

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32 MgCO; dm^hr 50t 40 POTATO CANOPY NET 30 CARBON EXCHANGE 20 0800 1000 NOON 1400 HOUR OF DAY 1600 Figure 9. Net carbon exchange in potato canopy from sunrise to sunset (After Sale, 1974).

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33 Nitrogen promotes canopy growth prior to tuber initiation thereby decreasing the tuber to canopy ratio during the early tuber growth period (Dyson and Watson, 1971). By maturity the tuber to canopy ratio in high nitrogen treatments had increased. Thus the nitrogen applications were found to ultimately have increased both tuber and canopy growth. The effect of nitrogen on tuber yield is limited. Kunkel et al. (1973) found that excess nitrogen will increase canopy growth without affecting tuber yield. Several authors have reported that nitrogen uptake by the potato crop ceases long before tuber growth is complete (Soltanpour, 1969: Ezeta and McCollum, 1972; Dyson and Watson, 1971). After the crop nitrogen uptake ceases nitrogen is apparently translocated from the canopy to the growing tubers. Phosphorus is also translocated from the canopy to the tubers (McCollum, 1978b). The nutrient concentration in the tubers remains constant through the tuber growth period. Kunkel et al. (1973) reported that the tuber mineral composition was independent of applied nutrient levels or cultural practices. Dyson and Watson (1971), on the other hand, examined tuber carbon to nitrogen ratios and found them to be constant for a given crop but varying between seasons and fertilizer treatments. All of these findings point toward a mechanism whereby nitrogen regulates tuber growth. Nitrogen levels did not influence the numbers of tubers initiated. Still, Dyson and Watson postulated that nitrogen availability may regulate the tuber sink strength. Of course, during the tuber growth period nitrogen available for tuber growth depends mostly upon the amount of nitrogen in the canopy which is available

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34 for translocation. The more nitrogen in the canopy from increased nitrogen application, the longer the tuber growth period. Water Potatoes are generally considered a drought sensitive crop. Drought sensitivity results in part from the potato's relatively shallow root system (Weaver, 1926; Harris, 1978b). Weaver found potato roots to be even less extensive and more shallow when growing under water deficient conditions. Not only do potatoes have shallow roots, but leaf photosynthesis appears to be greatly reduced by a fairly slight reduction in leaf water potential. Campbell et al. (1976) found that stomatal resistance began to increase at a leaf water potential of -0.8 bars. At this level, the effect on crop growth is small. Indeed, Sale (1973a) found that canopy NCE remained relatively constant to leaf water potentials as low as -8.0 bar-s. Despite the potato's drought sensitivity, irrigation is net always recommended. In some cultivars. King Edward for example, frequent irrigation during early growth may lead to initiating growth in more tubers. As a resulc, fewer tubers reach marketable size even though the total tuber yield may increase (Harris, 1978b), Ivins (1963) reported that the number of marketable tubers increased as irrigation was delayed until after linear tuber growth had begun. These reports contrast with Sale (i973a) who found that higher LAI's were reached in potatoes maintained at high soil moisture. Furthermore, the higher LAI's resulted in higher yields due to a longer growth period. Still, there is no dispute that drought during tuber growth will drastically reduce potato yields.

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35 The mechanisms whereby plant water status affects potato yields have been fairly well studied. According to Moorby et al . (1975) leaf sugar concentrations increase in drought stressed potatoes. Drought stress may reduce photosynthate translocation to tubers or reduce starch synthesis within the leaf or both. Munns and Pearson (197^) found that reduction of leaf water potential did indeed decrease translocation of assimilates to tubers, and did so in proportion to its negative effect on net photosynthesis rather than a direct effect on translocation. Thus Munns and Pearson agree with Moorby et al . in finding that drought had no effect on starch synthesizing enzymes in tubers. Tuber growth, or more specifically, tuber starch synthesis apoeared to be proportional to assimilate supply and assimilate supply is decreased by drought. In young ootato plants, drought did not seem to influence photosynthate partitioning (Munns and Pearson, 1974). Both canopy and root growth were equally reduced. In older plants, however, drought had less effect on tuber growth than root and canopy growth. Thus the percentage of assimilate partitioned to tubers increased with drought. Drought also more drastically reduced leaf water potential than tuber water potential (Moorby et al . , 1975). A mechanism whereby drought may influence partitioning was reported by Necas (1968). During a drought period lower potato leaves abscise. Upon drought relief new leaf area is generated. Since tubers are not shed while leaves £re the net effect is an apparent reduction of assimilate partitioned to leaves. The effect of water status on canopy NCE was also studied by Munns and Pearson. They concluded that drought nas a greater negative effect

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36 on NCE cf pre-tuberous than post-tuberous plants. The leaf water potentials of young and old plants were not comparable. The young plants had lower leaf water potentials on both stressed and unstressed conditions than did the older plants. Evidently the tubers act as water stores to prevent stress in older plants. Their data show better the effect of leaf water potential on NCE than the influence of tuber presence on NCE in drought conditions. Density Since potatoes are propagated vegetatively by tubers, seed expenditures may be as great as 30 to 507, of the total growing costs (Allen, 1978). Thus density effects are of both economic and physiologic importance. The effects of density on potato crop growth are rvicre complex than the density relationships of most other crops. Units of potato density are several. Allen listed eyes, seed pieces, seed surface area, seed weight, and steins as units of potato density. All of these units are correlated, so all need not be considered in relation to growth. The stem is generally taken as the unit of potato plant aensity most directly related to yield (Reestman and De Wit, 1959; Bleasdale, 1965; Collins, 1977). Many factors may influence the stem density. The numbers of stems per seed-piece is positively correlated to the seed-piece weight. This relationship is less notable in cultivars with inherently high stem numbers (Sremner and El Saeed, 1963). Actually, the stem number per seed-piece is r:\ore highly related to seed surface area than weight (Reestman and De Wit, 1959), though the effects are difficult to separate, Concomitant with fewer stems in smaller seed-pieces, stems produced from

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37 small seed attained a greater final weight and produced more and larger tubers when planted at the same seed-piece density as large seed-pieces (Bremner and El Saeed, 1963). Thus, the small seed-pieces had a lower stem density. Similar results were noted by Svensson (1965). He found that LAI, tuber yields, tuber numbers, and mean tuber weights per seed-piece were all higher at wider spacings. As with many other crops, the total tuber yield showed an optimum plateau. Lynch and Rowberry (1977a) measured this optimum density plateau to range from 6 to 12 stems/m2, Bremner and Taha (1966) found density and tuber growth rate per unit area to be oositively related. At higher stem densities a smaller portion of photosynthate is partitioned to tuber growth (Bremner and El Saeed, 1963). Thus, density is one of the few factors which can be easily manipulated to influence tuber growth rates. Summary The major dynamic environmental inputs for a potato growth and development model are heat, moisture, nutrients (especially nitrogen), a!id solar radiation. Other factors may be considered as combinations of these four major inputs or as static, one-time inputs. For example, season may be considered to be a combination of solar radiation and heat effects which change predictably through the year. Crop density, on the other hand, remains relatively constant through the growing season so it need be input only once. The bulk of a crop model, therefore, will describe the i-elationships between crop growth and the four major inputs.

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38 Prior to tuber initiation, warm temperatures (20-24° C), high available nutrients and water, high PAR flux density, and long days will stimulate and prolong canopy growth. Similarly, cool temperatures, low nutrient and moisture availability, and short days favor early tuber initiation and reduced canopy growth. After tubers have initiated, optimum conditions are soil temperatures from 16 to 20° C, air temperatures from 20 to 24° C, high available nutrients and moisture, and high PAR flux density (Milthorpe, 1963).

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MATERIALS AND METHODS Crop Growth Model A model was developed to further understanding of how temperature influences crop partitioning. The particular hypothesis to be tested was: differences in the temperature versus growth relationships between various potato organs may be used to predict dry matter distribution within the crop. The model was tested in the form of a computer program written in GASP IV, a Fortran-based simulation language (Pritsker, 1974). GASP IV has both continuous and discrete simulation capabilities, but the model developed herein is entirely discrete. Features of the GASP IV language crucial to this model are a table search function called GTABL and the language's event filing mechanism. GTABL calls data from a table array. For example^ a table cf tuber growth versus temperature can be entered into an array. The GTABL function will derive the tuber growth for a given temperature. The event filing mechanism of GASP IV uses information stored in a buffer called ATRIB(l). ATP\IB(i) stores the time an event will occur. ATRIB(2) stores the number of the event which is scheduled for that particular time. ATRIB(3,. . . . ,n) can be used to hold any soecial data requii^ed in an event. The program includes five event subroutines: 1) Pre-tuberous growth (PRET) calculates crop growtn and dry matter distribution before the crop initiates tubers, determines when tubers are to be initiated, and schedules canopy senescence. 39

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40 2) Post-tuberous growth (POSTT) calculates growth and partitioning after tubers are initiated. Both exponential and linear tuber growth are calculated in POSTT. 3) Canopy decline (CANDE) causes a unit of canopy stored in ATRIB(3) to abscize according to heat units accumulated in ATRIB(4). 4) The daily climatic data inputs are read by DAY which also calculates potential net photosynthesis, mean air and soil temperatures, and tuber respiration. 5) Every evening ENDAY is called to store the day's growth calculations for graphic and numeric output of organ dry weights and certain program parameters. A program listing of this model is included in Appendix A, The model was validated by inputting actual climatic and ground cover data and comparing the simulated crop growth and development to the results of the growth analysis. To test the effect of temperature on assimilate partitioning and crop growth dynamics a temperature sensitivity analysis was performed. Growth Analysis 1978 The major objective of the growth analysis was to provide data for the development and validation of the computer model. Planting date was chosen as the most practical means of manipulating temperatures in the field. In keeping with the model purposes, the growth analysis was designed to determine temperature effects on the crop growth rate, tuber growth rate, partitioning, and phenology. Two cul "Invars were grown in order to compare genetic and environmental effects on potato growth and development.

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41 During the 1978 potato growing season Sebago and Monona cultivars were grown at the Yelvington Experiinsntal Farm of the University of Florida in Hastings. The soil was of the Rutlege taxajunct, now classified as a sandy, silaceous, thermic Typic Humaquept. Crop husbandry was as recommended by the Potato Production Guide (Montelero and Marvel, 1971). Nematodes were controlled by DichloropropaneDichloropropene applied two weeks pre-planting at 225 liters/ha. At planting fertilizer was banded at a rate of 120 kg N/ha, 160 kg P205/ha, and 160 kg K20/ha. Between tuber initiation and full ground cover achievement, a sidedressing of 35 kg N/ha and 35 kg K20/ha was applied. Weeds were controlled by a 5 kg/ha pre-emergence application of Oinoseb and by cultivation after emergence. Carbaryl and Maneb were aoplied together at seven to ten day intervals throughout the season as needed for insect and late blight control, respectively. Carbaryl was applied at 1.1 kg/ha and Maneb at 1.3 kg/ha. Four replicates of both cultivars were planted on each of two dates, 2 February (Julian day 33) and 14 March (Julian day 73). A split plot design was used with planting date comprising the main plot treatment and cultivar the subplot treatment, for a total of 16 subplots. The subplots were 8 by 8.5 m each with rows oriented east-west. The seed-piece spacing was approximately 20 cm within rows and 100 cm between rows giving a density of 4.56 seed-pieces per square meter. The seed-pieces were machine-cut on the first planting date and handcut on the second planting date to aoout 55 g each, giving a seedling rate of 250 g/m2. Harvests were taken at seven to ten d&y intervals through the growing season. Sequential harvests were taken from east to west

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42 within each subplot. Twelve seed-piece clusters (hills) from each subplot were divided into tops, tubers, and remainder which included roots, rhizomes, below ground stems, and seed-pieces. All components were dried at 100° C and weighed. Two representative plants were selected from each subplot and divided into laminae, petioles and miaribs, above and below ground stems, inflorescences, rhizomes, roots, tubers, and seed-piece according to the crop's developmental status. Stem length, tuber number, and inflorescence number were all recorded. Leaf area was measured on an electronic area meter. For early samples the entire sample was dried for weighing. At later dates, the total fresh weight was measured and dry weight was determined by subsample. Leaf area was also determined by subsample for later harvest dates. Environmental data were collected by the IFAS experiment stations in both Hastings ana Gainesville, Florida. Measurements used from the Hastings station were daily maximum and minimum air temperature in a standard shelter at 150 cm, daily maximum and minimum soil temperature at 10 cm depth, and precipitation (Figures 10 and 11). From the Gainesville station about 60 miles west of Hastings measurements of daily PAR ivere used (Figure 12). As well as these standard weather readings, occasional soil temperature profile measurements were made in the experimental plots to compare with tfie standard data. Diurnal cycles and seasonal trends were observec. Measurements were made at 1, 5, 15, 25, and 40 cm soil depth, and air temperature in the snade of the canopy (Figure 13).

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43 35 30FEB MAR APR MAY TEMPER^^ ATURE 25 (°C) ZOOS' soil max / 30 50 70 90 110 130 150 JULIAN DAY 1978 Figure 10. Weekly average te'^peratures in Hastings, Florida. Air temperatures ( ) measured in standard shelter at 150 cm height. Soil teiiiperatures ( ) measured at 10 cm depth.

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44 FEB MAR APR MAY 30 50 70 90 JULIAN DAY 130 150 Figure 11. Total weekly precipitation ( ) in Hastings, Florida, and pan evaporation ( ) in Gainesville, Florida.

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45 FEB MAR APR MAY PAR 30 E/tnVdoy 50 70 90 JULIAN DAY 110 97S 30 150 Figure 12. Daily photosynthetically active radiation averaged over one week intervals.

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46 SOIL 5-i DEPTH (cm) J, 25-1 0645 0025 2i30 40j 12 14 16 18 20 TEMPERATURE (°C) 1615 -0 15 1-25 J" 22 Figure 13. Soil temperature profiles under a Sebago canopy from 1615 hours on March 20, 1978 to 1205 hours on March 21, 1978.

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47 Thermogradient Analysis 1979 The growth analysis considered only two temperature treatments. Though two temperature levels are enough to estimate the general range for model parameters, more temperature treatments are necessary to derive a temperature response curve. Thermogradient analysis was used primarily to determine the shapes for the temperature responses of stem, root, and tuber growth. During the winter of 1979 a series of experiments was conducted in a thermogradient bath system located at the Biven's Arm Agronomy greenhouse in Gainesville. • The thermogradient system, similar to systems used by Kirkham and Ahring (1978) and Timbers and Hocking (1971), was maintained by a water-covered steel bar with one end of the bar emersed in hot water and the other emersed in cold water. All experiments used uncut, grade B, Foundation DOtato seed of Sebago cultivar. The mean seed-piece fresh weight was 67.5 gm with a standard deviation of 21.2 gm. Table 1 lists dates, temperature ranges, and fresh weight of seed-pieces used in the thermogradient experiments. To study the effect of temperature on shoot elongation, seedpieces were planted about 20 cm deep in moist sandy soil neld by 0.95 liter paper cups. Convective currents in the gradient bath were reduced by 20 mm polystyrene baffles. Ten baffles divided the thermogradient perpendicularly to form 11 chambers. Eacn chamber was considered to be at one temperature. Five cups, each containing one seed-piece, were olaced in each chamber and all chambers were covered with a polyethylerie sheet (6 mil) to prevent evaporation and heat movement. The plastic sheet was covered with an opaque cloth to prevent overheating of the chambers by solar radiation. The soil in

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48 Table 1. Experiment dates, temperature ranges, and seed-piece fresh weights for thermogradient analysis.

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49 the cups was watered at three day intervals. Temperatures of the water in the chambers and the soil next to the seed-piece of the central cup in each chamber were measured periodically. Seed-pieces having dormant buds were used to determine the temperature effect on dormancy break. Seed-pieces with already elongating buds were used to determine temperature effects on growth and elongation. After the thermogradient treatment the plants were washed, broken into componentSj measured, dried, and weighed. To study the effect of temperature on tuber growth, 64 seed-pieces v/ere planted in 25 cm plastic pots on 29 January (Julian day 29). The pots were arranged in an 3 by 8 pattern with border rows not utilized in experiments. Each pot was filled to 8 cm with sandy soil. The soil layer was covered with 4 mm mesh nylon net. According to Nosberger and Humphries (1965), this mesh is large enough to allow root penetration while small enough to keep tubers above the net. In this experiment, this method did not work as tubers were often found to grow below the net. One seed-piece per pot was placed directly on the net and covered with 15 cm of vermiculite. The pots were watered regularly to prevent stress. On nights of predicted frost, all pots were covered with a 6 mil polyethylene sheet to prevent cold damage. On 28 February (Julian day 59) the seeds were cnecked. Fo'-^rteen pots were discarded due to seed-piece rot or continued dormancy. Eight Dots had shoots near the vermiculite surface. These shoots were exposed to give more uniform emergence and equalize development with the remaining pots which had healthy emergent stems. Thus, on 23 February 100^' emergence was obtained. Pots v;ere fertilized on days 1 and 19 post-emergence. According to visual inspection of the

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50 experimental and surrounding areas the plants were sprayed with Carbaryl and Captan to control Colorado potato beetle and late blight, respectively. Irrigation frequency was increased after 20 March due to higher temperatures and lower precipitation. On day 19 post-emergence 58% of the pots had visible infloresences. The ground cover was estimated at 95%. Tuber initials were formed on all of the ten border pots inspected. Therefore, 19 March (Julian day 78) was considered as the first day of flowering and the beginning of the linear growth phase. Twenty-two days after flowering, ten pots were placed in the thermogradient bath. The water was stabilized with four polystyrene baffles and ethyl malic anhydride (EMA-91). EMA-91, supplied by the Monsanto Corporation, forms a polymer which increased the viscosity of the bath to slow thermal transfer by convection both within and between the large chambers of this experiment. Two pots were placed in each of the five chambers formed by the baffles and the pots were protected from the EMA-91 by plastic bags. Five control pots were harvested before and five after thermogradient treatment. The control plots which were harvested after the treatment period were kept on the greenhouse bench adjacent to the thermogradient bath during the treatment oeriod. All plants were separated into tubers, leaves, and remainder which included roots, stems, rhizomes, and inflorescences. The components were dried at lOO'' C and weighed..

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RESULTS AND DISCUSSION Growth Analysis 1973 PreEmergence In the Julian day 33 planting, the seed-piece buds of both Monona (M33) and Sebago (S33) were still dormant. Bud dormancy break occurred after Julian day 45 for both cultivars as indicated by the stem length data in Figures 22 and 23. Bud break, the first major phenologic event of this planting date, required about two weeks. By the Julian day 73 planting the seed-piece buds of both Monona (M73) and Sebago (S73) had begun to elongate. Many of the elongating shooLS were broken off during the planting operation. Significant stem growth did not begin again until after day 80, one week after planting (F^"gures 24 and 25). Both M33 and S33 required about three weeks from the beginning of stem elongation until emergence. The average stem length at emergence was about 10 cm, the same as the planting depth. Therefore, these stems elongated at the rate of approximately 0.5 cm/day. The stems of M73 and S73 elongated nearly 0.7 cm/day, thus M73 and S73 only required two weeks from the beginning of stem elongation to emergence. Root growth began within days after initial shoot elongation in all treatments. By the time of emergence the shoot to root ratios were 2.77 for M33, 2.69 for S33, 1.22 for M73, and 1.31 ^or S73. 51

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52 The differences between planting dates can be attributed to the dormancy state of the seed-pieces at planting and edaphic factors. The edaohic factor of primary importance is temperature since soil nutrients and moisture were controlled by fertilization and irrigation, respectively. After bud dormancy break we may assume that the seedpieces of both planting dates had similar physiologic status. Therefore, soil temperature will be the only major independent variable affecting stem and root growth until emergence. The average soil temperature from planting to emergence was 16° C for the Julian day 33 planting and 20° C for the Julian day 73 planting (Figure 10). This four degree temperature difference thus appears to be the main factor which increased the rate of shoot elongation and decreased the shoot to root ratio in the second planting date. The effect of temperature on time from planting to emergence is described by calculation of soil heat unit accumulation during this period. Using a base temperatu)^e of 9° C, both cultivars showed remarkable similarity in pre-emergence soil heat unit accumulation (Table 2). Even though ii seems safe to conclude that increased soil temperature speeds stem elongation and decreases the shoot to root ratio during the pre-emergence phenophase, the underlying physiological mechanisms are not clear. The soil temperature regulates the rate that the seed-piece makes substrate available to the growing organs. The soil temperature may also influence the rate at which the individual organs are capable of incorporating the available substrate. These two mechanisms represent the classical source strength versus sink strength controversy.

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53 Table 2. Duration and cummulative heat units for Monona and Sebago phenophases. Treatment (Cultivar and Planting Date) Phenophase Monona 33 Monona 73 Sebago 33 Sebago 73 Pre-Emergence Julian Days 33-65 73-94 33-68 73-15 Soil Heat Units* 225.3 225.7 238.1 239.2 Emergence to Flowering Julian Days 55-37 74-105 53-85 95-107 Air Heat Units** 117.7 108.3 107.2 112.1 Emergence to Tuber Initiation Julian Days 66-80 Soil Heat Units* 113.7 Air Heat Units 44.2 * Soil Heat Units = (°C-9); ** Air Heat Units = ("C-12.6) 94-111

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54 Emergence The date of emergence, as used here, is the date when the percent of seed-pieces with emergent stems reached half of its maximum value. The percentages of seed-pieces with emergent stems are graphed through time in Figures 14 and 15. The majority of M33 stems emerged during the 20 day period from day 50 to day 80. S33 stem emergence encompassed an even longer period, about 25 days, from day 60 to day 85. The M73 and S73 treatments emerged over a slightly shorter period, about 15 days. In any case, emergence was not at all uniform. The final emergence percentage for Monona was significantly' greater than that for Sebago at both planting dates (Table 3). The poor emergence of Sebago resulted from disease of the seed-pieces. Furthermore, the emergence of the day 33 planting exceeded that of the day 73 planting. The low emergence of the second planting may have been due to improper storage conditions of the seed-pieces before planting or injury to the seed durir.g the planting operation. Since the buds on the seed-pieces had already broken dormancy the seed-pieces may have been more susceptible to injury. Another possibility is that the seed rot became more widespread during the longer storage period of the seed used in the second planting. However, the primary factor responsible for the difference in emergence percentages between the two planting dates appeared to be soil surface temperature. Skies were clear and air temperatures high during the emergence period of the second planting. The surface layer of the soil dried and became very wann. On day S5 the soil temperature at 1 cm depth exceeded 3C^ C by ' Statistical analyses are presented in Appendix B.

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55 cnp, ^OOUJloJ o C12 o rcM o -v_-/

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56

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57 Table 3. Seeding rates, maximum emergence, stems per seed-piece, and plant density for all treatments. Treatment

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58 1400 hrs. During the emergence period of the day 33 planting the temperature at 1 cm depth did not exceed 22° C on any day that the soil temperature profiles were measured. As will be shown below, a temperature of 30° C is high enough to inhibit shoot growth and will 1 ikely cause injury. Plant Density Though the planting densities were 4.3 seed/m^ and 4.3 seed/m2 for the day 33 and day 73 plantings, respectively, the wide range of final emergence percentage lead to effective seeding densities from 2.6 to 4.2 seed/m2 (Table 3). As stated in the literature review, the seeding density is not the best measure of potato crop density. Rather, the main stem is taken to be the individual plant unit. Both cultivars compensated for low emergence by setting more stems per seedpiece. Sebago and Monona had significantly higher stems per seed in the day 73 planting than the day 33 planting. Sebago also had mora stems per seed than Monona in both planting dates. The ultimate plant densities ranged from 5.8/m2 to 7.8/m2 with differences being insignificant. Canopy Development Leaf area and ground cover . After emergence aerial environmental factors begin to influence crop growth and development. Photosynthetically active radiation (PAR) provides energy for crop metabolic processes. The crop canopy intercepts PAR. Two parameters commonly used to describe crop canopies with respect to PAR interception are the leaf area index (LAI) ana percent ground cover (GC). The LAI and GC for the four treatments are graphed in Figures 15 through 19.

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59

PAGE 73

50

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61 $-5 O o Q o 00 o < 11.1
PAGE 75

62 ^ CD o in

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63 The curves for LAI and GC followed roughly parallel patterns for M33. The LAI increased to a maximum of about 2.7 at day 110. The GC also increased until day 110 when a maximum of about 80" was achieved. Both LAI and GC decreased gradually after their peaks at day 110. The pattern was very much different for S33 ; however, S33 developed a larger canopy and maintained the canopy longer. The GC for S33 reached 80?o by day 105 and maintained this GC through day 139. The LAI exceeded 3.0 by day 110 and peaked at about 3.6 on day 120. On day 139 the LAI of S33 was still almost 3.0 while that of M33. was below 1.0. A greater canopy growth for Sebago was not evident in the second planting. Both S73 and M73 showed LAI and GC maxima at day 140 with fairly rapid canopy deterioration after this time. The maximum GC of S73 was about 31%, slightly greater than that of M73 at 76%. Although the peak LAI of S73 at 3.4 was much higher than that of M73, 2.0, since this is the only date which showed such a difference between LAI's of the two cultivars, the data point may be in error. Indeed, the leaf dry weights for M73 and S73 were similar at this time (Tables 5 and 7). The rapid canopy decline after day 139 for both S73 and M73 was most likely due to high temperatures during this period. As shown in Figure 10, the air and soil temperatures increased steadily after day 110 with daily maxima exceeding 30° C by day 140. Thus, temperatures began to exceed the thermal maximum for potatoes about the same time as the beginning of canopy decline for the day 73 planting. The differences between the Sebago and Monona canopies of the first planting date may be attributed to phenologic di-f'ferences. By

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64 exponential regression, M33 initiated tubers around day 80, whereas S33 initiated tubers some four or five days later. Initial tuber growth was also slower in S33 than M33 (Tables 4 and 5). The early initiation and growth of tubers in M33 likely reduced canopy development relative to S33. In other words, M33 partitioned a greater portion of its daily photosynthetic products into tuber growth than did S33. As a tool for characterizing crop canopies with respect to PAR utilization, LAI is most useful after the crop canopy has closed. At full ground cover the LAI estimates the number of leaf layers light must penetrate before reaching the ground. None of the crop canopies in this experiment reached full ground cover. In order to estimate the number of leaf layers the light can penetrate when entering the crop canopy, the LAI must be divided by GC. This parameter is termed the effective leaf area index (ELAI). The ELAI's for the treatments of this experiment are graphed in Figures 20 and 21. M33 and S33 both reached an ELAI of 3.0 around day 93, 20 days before the maximum LAI and GC were achieved. For M33 the ELAI remained fairly constant near 3.2 from day 93 to day 120. The ELAI for S33 increased to about 4.0 by day 100 and plateaued at this level. Similarly, M73 and S73 reached an ELAI plateau around day 115, about 25 days before the peak of LAI and GC for these treatments. Though the LAI and GC were n.uch greater in the first than the second planting, the same is not true for ELAI. These results indicate that both the Sebago and 'loncna canopies grow upward before they extend horizontally. The long period of constant ELAI suggests the GC alone can be used to estimate light interception during this time.

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c n3 c u Q r— T d o t— r— O 65 n

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66 Ol -r00 Q_ 1 — cri Lo C5 O r-^ CO o C\J I — I — I— ,— o^ o o I — I —

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o CO I — C\J O I— I — IT! r^ d CD .— 67 Q O 1O 1+1 O 0) -a u a; -t3 Q

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68 r— CO o o O) i) 0) -rI — m 3 Q 1X3 r— O <3^ CO "^ O r-^ C\J I — f —

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69 ELAI MAR APR MAY 140 JULIAN DAY Figure 20. Effective leaf area index for Monona and Sebago planted on Julian aay 33. ELAI = LAI/GC.

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70 APR MAY 10 120 130 JULIAN DAY 140 150 Figure 21. Effective leaf area index for rionono, and Sebago planted on Julian day 73. ELAI = LAI/GC.

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71 In potato canopies, as with most crops, the incident PAR is almost completely intercepted if the ELAI is 3.0 or greater. Apparently, after passing through three layers of leaf the light intensity is very near the light compensation point (Radley, 1963). The canopy growth morphology was similar for all treatments of this experiment. The canopy grew upward until the light intercepted was fully utilized, when the ELAI reached 3.0. Then the canopy grew outv/ard, maintaining the ELAI at a level where PAR was fully intercepted. One may question the efficiency of such a canopy. Higher photosynthetic rates may result from more rapidly increasing GC than ELAI. However, potatoes do require intense husbandry. Late blight and Colorado potato beetle do require repeated pesticide applications. Long stems would get killed by tractor wheels. Thus, high GC and long stems would be disadvantageous in this cultivation system. Stem elongation . The LAI and GC characterize the photosynthetic system of the crop canopy. They do not, however, give much information about the structural support of the photosynthetic surfaces. The average main stem length, average branch length, and total branch and stem length per square meter can be used to characterize the structural support system (Figures 22 through 25). The main stems of M33 and S33 lengthened until about day 100 with a maximum main stem length of about 62 cm for S33 and 54 cm for M33. Since the main stems terminated in inflorescences it is not surprising that main stem elongation ceased soon after floral initiation. Floral initiation is marked on the graphs at the point when inflorescences were first visible. The point of maximum main stem length coincided exactly ,;ith the time of peak flowering (Figure 14), as one would expect,

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72 For M73 and S73, however, the time of maximum main stem length and maximum flowering did not coincide. For both cultivars the average main stem reached its greatest value, about 32 cm, by day 116 (Figures 24 and 25). The maximum flowering was not reached until day 129 (Figure 15). Since the number of inflorescences per seed-piece was greater than 1.0 for both S73 and M73 at day 115, it is likely that the majority of the main stems would have incipient if not visible flowers at this time. The further increase in flowering, then, might represent either incipient main stem inflorescences or florescing branch termini . The average branch length was significantly greater for S33 than M33 on all days observed. The total stem plus branch length of S33 was significantly greater than that of M33 after day 100. This result is consistent with the findings of greater LAI, GC, and ELAI in S33 as compared to M33. On the other hand, differences between the total, main stem, and branch length for S73 and M73 were not significant. The effect of planting date on stem and branch growth was marked. The stems and branches of the day 73 planting were much shorter than those of the day 33 planting. The difference in branch and stem length between the two planting dates is consistent with the results of LAI and GC measurements. Stem and branch growth is stopped by flowering. The earlier termination of stem and branch growth in the second planting was probably due to the warmer temperatures which hastened flower initiation. Flowering appeared to be regulated by heat (Table 3). With warmer temperatures in the second planting flowering was hastened, as was the completion of stem and branch elongation.

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77 Canopy senescence . Maturity of annual crops is accompanied by senescence of the crop canopy. Decline of potato canopies in the Hastings area is generally due to high temperatures late in the growing season. As noted above, the canopy decline of M73 and S73 after day 139 can be attributed to excessive temperatures. A parameter which can be used to characterize canopy senescence is leaf duration. The leaf duration is the length of time a leaf remains physiologically active in photosynthesis. Leaf senescence includes chlorophyll degeneration and chlorosis. One method of estimating leaf duration is to determine the temporal difference between the dry weight curves for green and yellow leaves as in Figures 26 through 29. This method assumes that the oldest leaves senesce first. There are two main sources of error in this method of estimating leaf duration. Pirst, it is difficult to recover all senescent leaves, especially later in the season after the senesced leaves have begun to abscise. This source of error may be minimized by placing greater importance on early observations of chlorotic leaves. Second, leaf duration estimations will err if the specific leaf weight (SLW) of the chlorotic and green leaves are greatly different. If a large portion of the leaf nutrients ana assimilates are mobilized and translocated to other crop organs, then this method overestimates leaf duration. There was indeed a significant drop in SLW of green leaves as the canopy aged (data not reported). The decline in green leaf SLW with age can be explained by both leaf expansion and translocation effects. More importantly, since the SLW drops long before leaf abscission the difference between SLW O'!'' green and chlcroiic leaves is lessened.

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32 Two significant aifferences can be observed in this leaf duration data. The leaf duration of Monona is longer than that of Sebago, and the leaf duration of the day 33 planting was longer than that of the day 73 planting. The effect of planting date can be related to both environmental and physiological processes. The higher temperatures of the second planting sped leaf development and, when temperatures became excessive, injured the leaves through heat damage. More rapid development and heat injury will both hasten chlorosis. Flowering The next heat regulated phenophase after emergence is florescence (Table 3}. The numbers of inflorescences per square meter are graphed in Figures 14 and 15. Sebago and Monona initiated flowers at about the same time for a given planting date. There were no significant differences between the peak numbers of inflorescences of the two plantings. Sebago, however, oroduced more inflorescences than did Monona. Furihei'more, Sebago matured many fruits while Monona did not. The dry weights of these fruits are included in the inflorescence columns of Tables 4 through 7. As the inflorescence numbers, the dry weights of the flowers and fruits showed thai Sebago produced heavier inflorescences than Monona while there was no significant effect of planting date. Tuber Initiation Heat unit accumulation predicts the phenophase durations from planting to emergence and from emergence to flowering (Table 3). The mean daily soil and air temperatures are used to pi^edict emergence and floral initiation, respectively. On the other hand, neitl.er soil nor air heat accumulation predicts tuber initiation. Indeed, no reasonable

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83 base temperature can be derived to predict tuber initiation. Only a base temperature greater than ambient temperatures can be used to equalize heat unit accumulation betv/een the two plantings. Using such a base, though mathematically feasible, does not make physiological sense, since such accumulated units would have negative values. A possible explanation for these tuber initiation results is the temperature versus carbohydrate availability mechanism described in the literature review. Presumably, cooler temperatures inhibit canopy growth but not photosynthesis. If canopy growth does not utilize the photosynthate of a given day, then the available carbohydrate level on the plant is high and may either stimulate tuber initiation or reduce photosynthesis by feedback inhibition. Rhizomes Just as one must analyze the stems and branches when interpreting the development of the crop's photosynthetic system, one must consider the tuber support system to fully understand tuber growth and -functioning. Rhizomes are rather small, horizontally growing underground stems. Both M33 and S33 initiated rhizome development around day 80, barely ten days after emergence. The rhizome dry weight increased to a plateau near day 95 (Tables 4 and 5). M73 and S73 were slower to initiate rhizomes. In other words, rhizome initiation ana tuber initiation had similar patterns with rhizome development slightly offset to precede tuber initiation. Presumably, rhizome and tuber development are regulated by the same mechanism since one grows from the other. Yet, if tuber initiation is stimulated by high labile carbohydrate levels in the plant associated with high photosynthesis rates and low canopy growth rates at the linear phase of total crop growth, then

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84 rhizome development requires another explanation. Rhizomes initiate before tubers. Rhizomes in this experiment initiated before the linear crop growth period. They began development when the canooy appeared to be still utilizing seed-piece substrates for growth. The present data are not sufficient to explain these phenomena, they merely pose the question. Yield Dynamics The large carbohydrate reservoir in the potato's vegetative propagule may give potatoes an advantage in early canopy growth over crops with smaller propagules. The results of these experiments, however, indicate otherwise. The total croo weight did not increase significantly until 30 or more days after emergence in M33 and S33 (Figures 30 and 31). Although the canopy grew during this period, the canopy grew tiy translocation from the seed-piece rather than from canopy photosynthesis. Just as a leguminous crop will utilize soil nitrogen supplied before fixing atmospheric nitrogen, potato canopies deplete the seed-piece substrate before they begin auto trophic growth. Once positive growth did begin, presumably when the seed-pi eca carbohydrate reservoir was inadequate to meet the growth needs of the canopy, crop growth for all treatments is approximately linear and remained so until final harvest. Crop growth in the day 73 planting was similar to that in the day 33 planting (Figures 32 and 33). The crop growth rate v/as zero for the first 20 days after emergence and became linear soon thereafter. The common pattern for crop growth is an exponential growth phase, or lag phase, whicn leads into a linear growth phase after the maximum ground cover is reached. The large vegetative propagule of the

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89 potato reduces or eliminates the exponential phase. Unfortunately, the long zero growth phase of the potato crop during initial canopy growth has the same net result as an equally long lag phase for a crop propagated by units with smaller substrate reservoirs. In all treatments, tuber initiation occurred at about the same time as commencement of linear growth. If high labile carbohydrate pool levels stimulate tuber initiation, as suggested above, it is logical that tuber initiation should closely follow the onset of autotrophic growth. The crop and tuber growth rates with their respective periods of estimation are given in Table 8. All linear models are significant as indicated by the high r2 values. Both the crop and tuber growth rates were faster in the day 33 than the day 73 plantings. This difference between the growth rates of the uvo plantings is likely related to differences in ultimate canopy size. The day 33 planting achieved higher ground cover percentages and LAI's than the day 73 planting. The maximum growth rate fc^ most crops is from 20 to 22 g/m2/day. The crop growth rates in all treatments of this experiment were significantly below this rate. However, when the low crop growth rates of M33 and S33 are divided by their respective maximum ground covers, the results are both around 21.5 g/m^/day. Although the growth rates were not significantly different between cultivars, the tuber growth rate was slightly higher for Monona than Sebago. Furthermore, both the crop and tuber growth rates became linear sooner in Monona than Sebago. The tuber growth rate showed a short lag phase, about one week, for all treatments. The combination of no exponential crop growth phase and a short exponential phase for tuber growth not only simplifies

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90 partitioning analysis, but also makes such analysis more meaningful since it compares simultaneous growth rates. The percentage of daily photosynthate partitioned to tuber growth can be estimated by the ratio of tuber and crop growth rates (Table 8). Partitioning to tubers was greater in the first than the second planting and slightly higher for Monona than Sebago as one would expect from the tuber growth rates. The Monona cultivar outyielded Sebago in tubers for both plantings. The total biomass yield did not differ between the cultivars. The higher tuber yields of Monona can be attributed to two factors: 1) Monona reached the linear tuber growth phase sooner than Sebago, thus it had a longer filling or bulking period; 2) Monona partitioned a greater portion of its daily photosynthetic products into tuber growth. Thermoqradient Analysis 1979 Bud Dormancy The length of tuber bud dormancy is influenced by several factors including length of storage, wounding, moisture, nutritional level of the crop which produced the seed-pieces, and the soil tei^perature. The only factor of interest here is soil temperature. Figures 34 and 35 show the growth and elongation of buds which were dormant at sowing. According to both growth and elongation results, soil temperatures from IS to 24° C are optimum for dormancy break. No buds had broken dormancy after five days at 27° C or after ten days at 29° C. Although temperatures below 15° C were not tested, the degree of dormancy break after ten days at 15° C was less than doi^mancy break at warmer temperatures.

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94 Both the growth and elongation rates used here assume a linear growth model. Since the buds were dormant at planting, estimating daily growth with a linear model will necessarily err. However, the error appears slight since the range of growth and elongation rates estimated by the linear model correspond well with the growth and elongation rates of buds which had already begun growth at sowing (Figures 36 and 37). Another possibility is that neither dormant nor elongating buds have linear growth rates. Stem Growth and Elongation The potato seed-piece stores an enormous substrate supply for a newly initiated stem or root. Thus one may assume that the substrate supply from the tuber to the stem will be as great as the shoot initial can utilize. In other words, substrate supply will not limit initial shoot or root growth. Soil temperature markedly influenced the growth and elongation of young stems (Figures 36 and 37). The optimum temperatures for stem growth ranged fv-om 20 to 22° C. The rate of stem growth increased with the experiment duration. This growth rate increase was fitted to an exponential model whose coefficient is the relative growth rate. The stem relative growth rate was used to derive the array TCAN described below (Figure 41). The 18 to 23° C optimum temperature range for stem elongation is somewhat wider than that for stem growtn. Both elongation and growth extrapolate to thermal inaxima and minima of 30 and 0° C, respectively. Root Growth The root growth curves exhibit a form similar to the stem growth curves (Figure 38). The optimum temperature ranged from 20 to 22° C

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98 with extrapolated maximum and minimum of 30 and 0° C, respectively. The root temperature relationship, however, seems to have a shoulder on the low temperature side of the optimum. The shoulder gives roots an even greater advantage over shoots at cooler temperatures. Note that the roots grew at a rate almost four times as fast as the stems at their respective optima. The nine day curve for root growth appears misplaced. Since the seven and 12 day curves were generated by simultaneously growing plants they are presumed to show a true relationship to one another. They were used to develop an exponential relationship between root growth rate and time, thereby deriving another array, TROOT (Figure 41). Tuber Growth The temperature responses of tuber and total crop growth rates dre graphed in Figure 39. These data were collected during the linear tuber growth phase. Therefore, the linear model used to calculate the growth rate is assumed to be correct and the data were used directly to derive the temperature response array TTUBR (Figure 42). The optimun' temperature for tuber growth is around 15° C, much lower than the optima of root and stem growth. The calculated growth rates are twice as high as one would expect. The maximum crop growth rate for the field grown potatoes was about 21.5 g/m^/day when corrected for incomplete ground cover. Furthermore, De Wit has shown that the potential growth rate for many crops and other plant life is about 20 g/m2/day (McCloud, 1979). So a maximum total growth rate of 29 g/m2/day is much more likely than the 40 g/m2/day calculated.

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100 Sebago Crop Growth Model Though Monona yielded higher and seemed more adapted to Florida potato cultivation practices than Sebago according to the growth analysis, Sebago was chosen to be modeled and simulated. Sebago is more widely cultivated than Monona. Also, Sebago growth and development have been studied by several other workers so there is more information available on this cultivar. Furthermore, since the planting dates chosen for the growth analysis were the early and late extremes of the suggested planting period, Monona would out yield Sebago under more optimal conditons. Model Development A dry-matter flow diagram of the Sebago crop model is presented in Figure 40. Solid lines represent material flow and dashed lines represent information flow. Rectangles hold the dry-matter components of the model. Circular bubbles are input variables and clouds are unlimited sources or sinks. The last symbol is a labeled valve ( £>< }) which represents a flow rate. The model has three yield components, roots, tubers, and canopy, whose rates of growth depend upon temperature and the amount of substrate available for growth. If there is more carbohydrate available than these components can utilize, the extra substrate can be stored cemporarily in a leaf pool which has a maximum size of ]0% of the canopy dry weight. The model uses net rates, so respiratory losses from the yield components are implicit rather than explicit. The canopy does lose dry weight by senescence according to heat unit accumulation effects on leaf duration calculated in the growth analysis.

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101 pRooT ; PTUBR I PCAN 1 PNDAY ' igure 40. Dry-matter flow diagram for Sebago growth model. Variables defined in Appendix A, pages 13®>eH«i 132...

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102 The growth substrate may come from the seed-pieces, photosynthesis, or the labile leaf carbohydrate storage pool. The carbohydrates coming from both the seed-pieces and the leaf pool show metabolic losses associated with translocation and conversion processes. The seed-pieces also lose dry weight through respiration which is governed by the soil temperature. A two-phase linear model is used to describe the net photosynthetic light response curve: f (0.04839*PAR) + 19.597 for PAR > 30 PNDAY = ( l,0.7241*PAR for PAR < 30 where PNDAY is net photosynthesis in g/m2/day and PAR is photosynthetically active radiation in E/m2/day. This model is similar to that of De Wit (1959) described above. The constants of this light response were calculated from Sale's (1974) work with Sebago potatoes grown in Australia. The two-phase linear model was chosen over a rectangular hyperbola because the two-phase linear model is simpler and because a slight change in the parameters of the rectangular hyperbola result in great changes in the estimated photosynthetic rate. The light interception input uses ground cover data from the growth analysis. As will be seen below, inputting light interception rather than generating the photosynthetic surface internally is a major weakness of the model. After tuber initiation net photosynthesis may be stimulated up to two-fold by the potential tuber growth rate. Photosynthetic enhancement by tubers was suggested in the literature and was found to be necessary for simulated growth values to approximate actual data.

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103 Several temperature response curves have already been mentioned. A temperature response curve is used to predict or describe the effect of temperature on some process. The shapes of TCAN, TROOT, and TTUBR (Figures 41 and 42) were derived from thermogradient analysis and simulation trials. Each of these tables needed to be tested in the temperature range above the level of thermogradient analysis. The original extrapolations were found to underestimate growth in the 25 to 30° C range. The scales of these tables were determined from the growth analysis rather than the thermogradient analysis. For example, root growth was four times as fast as stem growth in the thermogradient analysis. The model, on the other hand, uses a faster canopy than root growth rate as shown in the growth analysis results. The adjustment was necessary because the temperature response curves were based upon growth when carbohydrate was not a limiting factor. To model post-emergence growth new relationships must be derived as the substrate supply becomes a limit to growth. The amplitude of the TTUBR array was also reduced to corresDond with the 'esults of the growth analysis. To make these estimations ^^rom the growth analysis, the growth rate was calculated from the dry weight accumulation data and compared to the mean temperature during that period. To generate the TUBRGR temperature response curve (Figure 41) the exponential growth phase from the growth analysis was used to determine the general range of tuber relative growth rates. Since there rates were about the same for the two plantings, a optimum plateau was modeled ranging from about 14 to 18° C. All input tables are listed and defined with the friodel listing in Appendix A.

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104

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105

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106 Model Validation Models are validated by comparing simulated results with empirical observations. Tables 9 and 10 and Figures 43 and 44 compare real and simulated results of Sebago growth. For the Julian day 33 planting the simulatea and field grown potatoes agree closely except during the no and 120 day period when the model over-estimates growth. The standard errors for tuber and total dry weights are 54.4 and 46.9 g/m2, respectively. The model estimated the growth of the Julian day 73 planting more closely than the day 33 planting. The standard errors for tuber and total dry weight estimation in the day 73 planting are 18.0 and 17.2 g/m2, respectively. The standard errors of the sii^iulation are in the same range as the linear standard errors (Table 8). The simulated tuber and crop growth rates and partitioning ratios in Table 11 can be compared to the growth analysis results in Table 3, The model over-estimates the crop growth rates of both planting dates and the tuber growth rate of the Julian day 73 planting. Still, the simulated growth rates and their ratios are close to the actual data. The tuber initiation dates calculated by exponential regression from the growth analysis were Julian day 84 and 116 for the Julian day 33 and 73 plantings, respectively. The model initiates tubers within two days of these dates. At this point let me reiterate that every model, no matter how closely it estimates reality, is only a representation of reality. Too cfien, the mathematical or verbal symbols and concepts of a model are mistaken for reality because they are more easily understood than reality. Remembering that models are approximations of reality, at best, we analyze the results of this potato model.

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107 Table 9. A post-emergence comparison of dry weights of fieldgrown and computer-simulated Sebago potatoes with a Julian Day 33 planting date. Julian

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108 Table 10. A post-emergence comparison of dry weights of fieldgrown and computer simulated Sebago potatoes with a Julian Day 73 planting date. Julian

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109 DRY V^EIGHT g/tn2 •900 80 SO 100 110 JULIAN DAY 120 130 Figure 43. Simulated Sebago growth components with climatic inputs of the Julian day 33 grov^th analysis. Growth analysis data are plotted for total (O) and tubers (^).

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no DRY WEIGHT g/m^ 500i 10 120 130 JULIAN DAY Figure 44. Simulated Sebago growth components with climatic inputs of the Julian day 73 growth analysis. Growth analysis data are plotted for total (O) and tubers {Cl).

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m Table 11. Simulated tuber and crop growth rates, assimilate partitioning ratio, and tuber initiation dates v/ith climatic inputs of the Julian Day 33 and 73 grov/th analyses. Climatic TGR i s.e. CGR + s.e. TGR/CGR Tuber Inputs Initiation Julian Day g/m^/day Julian Day 68-138 13.5 t 0.082 18.7 t 0.386 0.723 86 96-150 10.2 + 0.182 15.3 + 0.542 0.669 117

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112 Temperature Sensitivity Analysis The results of a temperature sensitivity analysis of the Sebago crop growth model are presented in Tables 12 through 15. In addition to the tuber and crop growth rates and their ratio, the crop growth model allows analysis of net photosynthesis. All of the rates in Tables 12 and 13 were computed over the linear tuber growth period. The net photosynthesis rates during the linear tuber growth period are about double the rate prior to tuber initiation as one would expect from the influence of the model variable STIM, which acts to increase photosynthesis during tuber growth. The difference between daily net photosynthesis in the various temperature treatments is insignificant. The lack of temperature effect on net photosynthesis may be taken as confirmation of Sale's (1974) finding that temperature did not influence net carbon exchange in the field. However, since this model does not generate its own photosynthetic surface one would not expect great differences between treatments. Any differences in photosynthesis between the treatments are indirect reflections of the effect of soil temperature on tuber growth. The net photosynthetic rates do differ markedly from the crop growth rates. In growth analyses the crop growth rate is often considered an estimator of net canopy photosynthesis. This model, which accounts for canopy senescence throughout the season, shows the potential error of using dry-matter accumulation to estimate net photosynthesis. At cool air temperatures, when leaf duration is prolonged, the crop growth rate closely approximates net photosynthesis.

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113 CO o C r— o o >> Q4-> rc 00 S C OJ O 4-> •(-J M2 =3r— d d O rI— 2 03 OJ Q.-ti. O d "3 £O Ol (T3 S_ E fO O :;£2. S_ O) 43 -M 00 -= o -a +-> -rOJ = 4-1 -u >, ra ITS 1/1 I — r— O 3 3 -»-> (J E O r
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115 Table 14. Simulated final yields for tubers, canopy, roots, and total and tuber initiation dates with various temperature inputs. Tempe

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116 Table 15. Simulated final yields for tubers, canopy, roots, and total and tuber initiation dates with various temperature inputs. lempf

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117 At warm air temperatures canopy development is hastened and the crop growth rate is a poor estimator of net photosynthesis. When soil and air temperature inputs are equal, 15" C is optimum for tuber and total growth. The 15° C temperature regime had a high tuber growth rate and early tuber initiation which combined to give the greatest yield of all treatments. The 10° C treatment had a total yield almost equal to that of the 15° C treatment and also had early tuber initiation. The tuber growth rate of the 10° C condition was about half the rate of the 15° C treatment and the resultant yield was about half as great in the 10 as the 15° C treatment. At 25° C the warm temperature delayed tuber initiation until Julian day 115 and greatly reduced the tuber and crop growth rates. As well as being above the optimum temperatures for tuber and crop growth, the 25° C input hastened canopy senescence to reduce crop growth further. The effects of steadily increasing and decreasing temperatures on Sebago growth and development may be compared to spring and fall crops, respectively. As with the seasonal comparison of Australian potatoes by Moorby and Milthorpe (1975), the simulated increasing temperature treatment yielded greater than the decreasing temperature treatment. The higher yield in the increasing temperature treatment occurred despite lower tuber and crop growth rates. The yield advantage in the increasing temperature condition results from earlier tuber initiation. Tubers initiated 24 days sooner when temperatures were increasing than when decreasing. This result is similar to the conclusions of Moorby and Milthorpe' s analysis. The daily mean air and upper soil layer temperatures do not differ greatly. Still, by inputting different soil and air temperatures into

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118 a model one can test their relative effects on model functioning. The primary effect of air temperature appears to be on the rate of tuber initiation. At a soil temperature of 15° C, the tuber yield was about three times higher with an air temperature of 20° C than 25° C due to a 28 day delay of tuber initiation at the high air temperature. The soil temperature seems to have its major effect on the tuber growth rate. For equal air temperatures, the tuber initiation date will be the same. The soil temperature will determine yield in this case with the optimum temperature of 15° C. In the 10° C soil and 20° C air temperature condition another factor may be involved. At this soil temperature the tuber growth rate may be low enough that the stimulatory effect of tubers on photosynthesis is either diminished or delayed. The 'jery low tuber and crop growth rates and slightly lower net photosynthetic rate suggest this possibility. Still, tubers were initiated early giving a long tuber growth period and a respectable final tuber yield. The two simulations with soil temperature exceeding a-fr temperature also show the effect of tuber growth on crop growth. At high soil temperature both tuber and crop growth are reduced. Since the air temperature and therefore the canopy senescence rates are equal, the reduction of crop growth rate must be through a reduction of the photosynthetic enhancement by tubers. In potatoes, photosynthate partitioning is a dynamic process relating tuber and haulm growth. The common means of estimating assimilate partitioning to the yield organ is by the ratio of yield and crop growth rates (Duncan et al., 1978). As noted above, potatoes offer an excellent opportunity to examine assimilate partitioning

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119 because the tuber and haulm growth periods generally coincide. However, since the crop growth rate includes canopy loss through senescence, a more accurate estimation of assimilate partitioning to tubers is the ratio of the tuber growth rate to daily net photosynthesis. Both of these ratios are given in Tables 12 and 13. Even though the tuber growth rate to net photosynthesis ratio conforms to the physiologic definition of assimilate partitioning, this ratio does not aid interpretation of this potato growth and development model. Since the net photosynthesis did not differ significantly between treatments, the partitioning ratio followed the same trends with temperature as the tuber growth rate. Here again is the need for an internally generated photosynthetic surface. The tuber growth rate to crop growth rate ratio, on the other hand, does show an interesting response to temperature. Most notable is the increase of the TGR to CGR ratio with an increase in temperature where soil and air temperature inputs are equal. The simulated potato plants in the increasing temperature regime partitioned more assimilate to tubers than canopy in the decreasing temperature regime. In the increasing temperature condition, the temperatures are warm during the tuber growth period while the converse is true in the decreasing temperature condition. Thus these gradual temperature changes show a similar response with greater partitioning when tubers grow in warmer conditions.

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SUMMARY AND CONCLUSIONS Growth Analysis The wanner soil temperatures of the Julian day 73 planting speeded shoot elongation and decreased the shoot to root ratio up to the time of emergence. In both plantings, Monona achieved a higher seed-piece emergence than Sebago. The Julian day 33 seed-piece emergence was greater than that of the Julian day 73 planting for both cultivars. In both plantings Sebago flowered more profusely and pe>"sistently than Monona. The Sebago canopy developed more slowly than that of Monona in the Julian day 73 planting. Still, Sebago 's canopy resched and maintained a higher LAI and ELAI than Monona in both plantings. Sebago grow more and longer branches than Mcnona in the Julian day 33 planting while there were no differences in branching between the cultivars in the Julian day 73 planting. The canopies of both cultivars reached maximum branch length more quickly in the Julian day 73 planting and these branch lengtns were shorter in the second planting. Monona had a slightly longer leaf duration than Sebago in both plantings. The leaf duration of the Julian day 33 planting was greater for both cu"!civars than the "leaf duration of the canopies in the Julian day 73 planting. 120

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121 Days to emergence and from emergence to flowering both have a positive relationship to cummulative heat units while the time from emergence to tuber initiation is negatively related to heat unit accumulation. Both cultivars exhibited a period of zero crop growth during which dry weight was apparently transferred from the seed-pieces to the canopy. The exponential growth phase was very short. These cultivars shifted rapidly from the zero to linear growth. Monona had a higher tuber yield than Sebago in both plantings although total yields were similar for the two cultivars. Monona partitioned more photosynthate into tuber growth than did Sebago. The yield and assimilate partitioning to tubers were greater in the Julian day 33 planting than the Julian day 73 planting for both cultivars. Thermogradient Analysis The optimum temperature for Sebago bud dormancy break was from 18 to 24° C. The optimum temperature range for stem elongation was 20 to 22° C while that for stem elongation was 18 to 23° C. The optimum temperature for root growth was from 20 to 22"" C. The root growth temperature response curve showed a shoulder to 12° C below the optimum temperature while shoot growth and elongation both declined steadily above and below their thermal optima. The optimum temperature for tuber growth was from 14 to 17° C. The optirpiim remperature for total crop growth followed the pattern for tuber growth during the linear tuber growth phase.

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122 Sebago Crop Growth Model The simulation model more closely estimated the growth and development of the Julian day 73 planting than ihe Julian day 33 planting. The standard errors of estimating the two plantings were approximately 18 and 50 g/m--, respectively. There was little difference in daily net photosynthesis in the temperature regimes tested, presumably because light interception was an input variable rather than being calculated within the model. The optimum temperature regime for tuber and total yield was with both air and soil temperature equal to 15° C. The major effect of soil temperature on Sebago g'^owth was through the tuber growth rate. A secondary effect was through the effect of tuber growth rate on the photosynthetic rate. At subor supraoptimal soil temperatures both the ruber and photosynthetic rates were reduced with the tuber growth rate being the more sensitive to temperature. The major effect of air teperature was on the tuber initiation rate. Warm air temperatures delayed tuber initiation and reduced the tuber growth period. An increasing temperature environment was shown to be more favorable for potato production than a decreasing temperature environment of equal mean temperature. Tubers initiated earlier in the increasing temperature condition giving a longer tuber growth period. Vihen using the net daily photosynthetic rate to calculate the partitioning to tubers the partitioning ratio follows the same pattern 35 the tuber growth temperature response. When the crop growth rate is used to calculate the partitioning ratio the partitioning ratio increased with temcer^ture.

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BIBLIOGRAPHY Abdelhafeez, A. T. , H. Harssenia, G. Veri , and K. Verkerk. 1971. Effects of soil and air temperature on growth, development and water use of tomatoes. Neth. J. Agric. Sci. 19:67-75. Alberda, T. H. 1962. Actual and potential production of agricultural crops. Neth. J. Agric. Sci. 10:325-333. Allen, E. J. 1978. Plant density, ^n Harris, P. M. (Ed.), The Potato Crop: The Scientific Basis for Improvement. Chaoman and Hall, Ltd., London, pp. 278-326. Blacklow, W. M. 1972. Influence of temperature on germina-ion and elongation of the radicle and shoot of corn ( Zea mays L.). Crop Sci. 12:647-649. Bleasdale, J. K. A. 1965. Relationships between set characters and yield in maincrop potatoes. J. Agric. Sci. 54:361-366. Bodlaender, K. B. A. 1963. The influence of temperature, radiation, and photoperiod on development and yield. Lt_ Ivins, J. D. and F. L. Milthorpe (Ed.), The Growth of the Potato: Proceedings of the Tenth Easter School in Agricultural Sciences, Butterworths, London. pp. 211-220. Bremner, P. M. , and E. A. K. El Saeed. 1963. The significance of seed size and spacing. _In. Ivins, J. D. , and F. L. Milthorpe (Ed.), The Growth of the Potato: Proceedings of the Tenth Easter School in Agricultural Sciences. Butterworths, London, pp. 267-280. Bremner, ?. M. , E. A. K. El Saeed, and R. K. Scott. 1967. Some aspects of competition for light in potatoes and sugar beet. J. Agric. Sci., Camb. 69:283-290. Bremner, P. M. , and R. W. Radley. 1966. Studies in potato agronomy. II. The effects of variety and time of planting on growth, development, and yield. J. Agric. Sci. 65:253-262. Bremner, P. M. , and M. A. Taha. 1966. Studies in potato agronomy. I. The effects of variety, seed size, and spacing en growth, development, and yield. J. Agric. Sci. 66:241-252. Brouwer, R. 1962a. Distribution o^ dry matter in the plant. Neth. J. Agric. Sci. 10:361-375. 123

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124 Brouwer, R. 1962b. Nutritive influences on the distribution of dry matter in the plant. Neth. J. Agric. Sci. 10:399-408. Brouwer, R. , and C. T. De Wit. 1968. A simulation model of plant growth with special attention to root growth and its consequences. In W. J. Whittington (Ed.), Proceedings of the Fifteenth Easter School in Agricultural Sciences: Root Growth. Butterworths, London, pp. 224-242. Bruinsma, J. 1962. Chemical control of crop arowth and development. Neth. J. Agric. Sci. 10:409-426. Campbell, M. D. , G. S. Campbell, R. Kunkel , and R. I. Papendick. 1976. A model describing soil -pi ant-water relations for potatoes. Am. Potato J. 53:431-441. Chang, Jen~Hu. 1968. Climate and Agriculture. Aldine Publ . Co., Chicago, Illinois. Collins, W. 3. 1977. Analysis of growth in Kennebec with emphasis on the relationship between stem number and yield. Am. Potato J. 54:33-40. Conn, E. E. , and P. K. Stumpf. 1972. Outlines of Biochemistry. ]. Wiley and Sons, Inc., New York, N. Y. Dalton, F. N. , and W. R. Gardner. 1978. Temperature dependence of water uptake by plant roots. Agron. J. 70:404-406. DeVries, F. W. T. P. 1972. A model for simulating transpiration of leaves with special attention to stomatal functining. J. Add i . Ecol. 9:57-71. De Wit, C. T. 1959. Potential photosynthesis of crop surfaces. Neth. J. Agric. Sci. 7:141-149. Duncan, W. G. , R. S. Loomis, W. A. Williams, and R. Hanan. 1967. A model for simulating photosynthesis in plant communities. Hilgardia 38:181-205. Duncan, W. G. , D. E. McClcud, R. L. McGraw, and K. J. Boote. 1978. Pnysiolcgical aspects of peanut yield improvement. Crop Sci. 18:1015-1020. Dyson, P. W. , and 0. J. Watson. 1971. An analysis of the effects of nutrient supply on the arowth of potato crops. Ann. Appl . Biol. 69:47-63. Eckard, F, E. (Ed.). 1965. UNESCO Symposium on Arid Zone Research. Edelman, J. 1963. Physiological and biochemical aspects of carbohydrate metabolism during tuber growth. Jn. Ivins, J. D. , and F. L. Milthorpe (Ed.), The Growth of the Potato. Butterworths, London, pp. 135-147.

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125 Evans, L. T. 1975a. Crops and v/orld food supply, crop evolution, and tne origins of crop physiology. I_n L. T. Evans (ed). Crop Physiology: Some Case Histories, Cambridge Univ. Press, New York, N. Y. pp. 1-22. Evans, L. T. 1975b. The physiological basis of crop yield. j_n L. T, Evans (Ed.), Crop Physiology: Some Case Histories. Cambridge Univ. Press, New York, N. Y. pp. 327-355. Ezeta, F. N. , and R. E. McCollum. 1972. Dry-matter production and nutrient uptake and removal by Solanum andegina in the Peruvian Andes. Am. Potato J. 49:151-163. Gaastra, P. 1962. Photosynthesis of leaves and field crops. Neth. J. Agric. Sci. 10:311-324. Goudriaan, J., and P. E. Waggoner. 1972. Simulating both aerial microclimate and soil temperature from observations above the foliar canopy. Neth. J. Agric. Sci. 20:104-124. Gray, D. 1974. Effect of nitrogen fertilizer applied to the seed crop on the subsequent growth of early potatoes. J. Agric. Sci. Camb. 82:363-369. Hagan, R. M. 1952a. Temperature and growth processes, hi 3. T. Shaw (Ed.), Soil Physical Conditions and Plant Growth. Academy Press, Inc., New York, N. Y. pp. 336-366. Hagan, R. M. 1952b. Soil temperature and plant growth. I_n_ 3. T. Shaw fEd.), Soil Physical Conditions and Plant Growth, Academy Press, Inc., New York, N. Y. pp. 367-459. Harris, P. M. 1978a. Mineral nutrition. |n_ P. M. Harris (Ed.), The Potato Crop. Chapman and Hall, Ltd., London, pp. 196-243. Harris, P. M. 1978b. Water. ImP. M. Harris (Ed.), The Potato Crop. Chapman and Hall, Ltd., London, pp. 244-277. Maun, J. R. 1975. Potato growth-environment relationships. Ag. Met. 15:325-332. Hawkes, J. G. 1973. Bicsystematics of the potato. ln_ P. M. Harris (Ed.), The Potato C>"Op. Chapman Hall, Ltd., London, pp. 15-69. Hesketh, J. D., D. N. 3aker, and W. G. Duncan. 1972. Simulation of growth and yield in cotton. II. Environmental control of morphogenesis. Crop Sci. 12:436-439. Ivins, J. D. 1963. Agronomic management of the potato. ln_ J. 0. Ivins and F. L. Milthorpe (Ed.), The Growth of the Potato. Butterworths, London, pp. 303-310.

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125 Kirkham, M. 3., and R. M. Ahring. 1978. Leaf temperature and -iniernal water status of wheat grown at different root temperatures. Agron. J. 70:657-662. Kramer, P. J. 1940. Root resistance as a cause of decreased water absorption by plants at low temperatures. PI. Physiol. 15:63-79. Kunkel, R. , N. Holstad, and T. S. Russell. 1973. Mineral element content of potato plants and tubers vs. yields. Am. Potato J. 50:275-282. Larcher, W. 1975. Physiological Plant Ecology. Springer-Verlag, Berlin-New York. Leopold, A. C, and P. E. Kriedemann, 1975. Plant Growth and Development. McGraw-Hill, Inc., New York. Linvill, D. E. , R. F. Dale, and K. F. Hodges. 1978. Solar radiation weighting for weather and corn growth models. Agron. J. 70:257-263. Long, I. F. , and H. L. Penman. 1963. The micro-meteorology of the potato crop. h}_ Ivins, J. D. , and F. L. Milthorpe (Ed.), The Growth of the Potato. Butterv/orths, London, pp. 183-190. Lynch, D. R. , and R. G. Rowberry. 1977a. Population density studies with Russet Burbank. I. Yield/stem density models. Am. Potato J, 54:43-56. Lynch, 0. R. , and R. G. Rowberry, 1977b. Population density studies with Russet Burbank. II. The effect of fertilization and plant density on growth, development, and yield. Am. Potato J. 54:57-71. McCloud, D. E. 1979. Man's Food Crop Resources. University o"^ Florida, Gainesville, Florida. McCollum, R. £. 1978a. Analysis of potato growth under differing P regimes. II. Time by P-status interactions for growth and leaf efficiency. Agron. J. 70:58-67. McCollum, R. E. 1978b. Analysis of potato growth under differing P regimes. I. Tuber yields and allocation of dry matter and P. Agron. J. 70:51-57. McKinior;, J. M. , J. D. Hesketh, and D. N. Baker. 1974. Analysis of the exponential growth equation. Crop Sci. 14:549-551. Mederski, H. J., and J. B. Jcnes, Jr. 1963. Effect of soil temperature on corn plant development and yield. I. Studies with a corn hybrid. Soil Sci. Soc. Prcc. 27:186-188. Miltncrpe, F. L. 1963. Some aspects of plant growth. ln_3. D. Ivins and F. L. Milthorpe (Ed.), The Growth of the Potato. Butterworths, London, pp. 3-16.

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127 Milthorpe, F. L. , and J. Moorby. 1974. An Introduction to Crop Physiology. Cambridge Univ. Press, Great Britain. Montelero, J., and M. E. Marvel. 1971. Potato production guide. Cooperative Extension Service, IFAS, Univ. of Florida and USDA. i^oorby, J. 1978. The physiology of growth and tuber yield. lu_ P. M. Harris (Ed.), The Potato Crop. Chapman and Hall, Ltd., London, pp. 153-194. Moorby, J., and F. L. Milthorpe. 1975. Potato. h]_ L. T. Evans (Ed.), Crop Physiology. Cambridae Univ. Press, New York, N. Y. pp. 225-257. Moorby, J., R. Munns, and J. Walcott. 1975. Effect of water deficit on photosynthesis and tuber metabolism in potatoes. Australian J. of PI. Physiol. 2:323-333. Munns, R. , and C. P. Pearson. 1974. Effect of water deficit on translocation of carbohydrate in Solanum tuberosum . Aust. J. PI. Physiol. 1:529-537. Necas, J. 1953. Growth analytical approach to the analysis of yielding capacity of potato varieties. Photosynthetica 2:35-100. Nielson, K. F. , and E. C. Humphries. 1966. Effects of root temperatures on plant growth. Soils and Fertilizers 29:579-583. Nosberger, J., and E. C. Humphries. 1965. The influence of removing tubers on dry-matter production and net assimilation rate o^ potato Dlants. Ann. of Bot. N. S. 29:579-538. Pritsker, A. A. B. 1974. The GASP IV Simulation Language. J. UMley and Sons, New York. Radford, P. J. 1967. Growth analysis formulae-their use and abuse. Crop Sci. 7:171-175. Raaley, R. W. 1963. The effect of season on growth and development of the potato. ln_J. D. Ivins and F. L. Milthorpe (Ed.), The Growth of the Potato. Butterworths, London, po. 211-220. Reestman, A. J., and C. T. De Wit. 1959. Yield and size distribution of potatoes as influenced by seed rate. Neth. J. Agric. Sci. 7:257-263. Ricnards, 5. J. 1952. Soil temperature. InB. T. Shaw (Ed.), Soil Physical Conditions and Plant Growth. Acad. Press, Inc., Mew York, pp. 304-336. Rickman, R. W, , R. E. Ramag, and R. R. Allniaras. 1975. Modeling dry matter accumulat^'on in drvland winter wheat. Aaron. J. 67:283-289.

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128 Rijtema, P. E. , and G. Endrodi. 1970. Calculation of production of potatoes. Neth. J. of Agric. Sci. 18:26-36. Sale, P. J. M. 1973a. Productivity of vegetable crops in a region of high solar input. I. Growth and development of the potato (Solanum tuberosum , L.). Aust. J. Agric. Res. 24:751-762. Sale, P. J. M. 1973b. Productivity of vegetable crops in a region of high solar input. II. Yields and efficiencies of water use and energy. Aust. J. Agric. Res. 24:763-771. Sale, P. J. M. 1974. Productivity of vegetable crops in a region of high solar input. III. Carbon balance of potato crops. Aust J PI. Physiol. 1:283-296. Soltanpour, P. N. 1969. Accumulation of dry matter and N, P. K by Russet Burbank, Oromonte, and Red McClure potatoes. Am. Potato J 46: 111-119. Spiertz, J. H. J. 1974. Grain growth and distribution of dry matter in the wheat plant as influenced by temperature, light energy and ear size. Neth. J. Agric. Sci. 22:207-220. Stewart, D. W. 1975. Modeling plant atmosphere svstems. In J Bartholic and R. E. Jensen (Ed.), Impact of Climatic Chanq"e on the Biosphere. Part 2. Climatic Effects. National Tech. Information Service, Springfield, Virginia, pp. 3-3 through 3-17. Svensson,B. 1966. Seed Tuber-Stand-Yield, Principles and Relationships. Almquist and Wilsells, Uppsala. Thornley, J. H. 'A. 1976. Mathematical Models in Plant Physioloay Academic Press, Inc., New York. Timbers, G. E. , and R. P. Hocking. 1971. A temperature gradient bar tor seed germination and cold hardiness studies. Can J PI Sc--" 51:434-437. Tyldesley, J. B. 1978. A method of evaluating the effect of temperature on an organism when the response is non-linear. Aq Met i9:137-153. Van Dobben, W. H. 1962. Influence of temperature and light conditions on ary-niatter distribution, development rate and yield in arable crops. Neth. J. Agric. Sci. 10:377-389. Weaver, J. E. 1926. Root Development of Field Crops. McGraw-Hill Book LO. , Inc., New York.

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APPENDIX A: LISTING OF VARIABLE DEFINITIONS, MODEL PROGRAM, COMMON BLOCK VARIABLES, INPUT TABLES, INITIAL VALUES OF STATE VARIABLES, AND PLOT STATEMENT FILES OF THE SEBAGO GROWTH AND DEVELOPMENT MODEL

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VARIABLE DEFINITIONS FOR POTATO GROWTH MODEL ATRIB(I): A GASP IV variable used to store information in files NSET and QSET. ATRIB(l) = event time; ATRIB(2) = event number; ATRIB(3) = DCAN (SEE); ATRIB(4) = heat unit accumulator for canopy senescence. BULK: A flag which denotes exponential tuber growth when less than 1.0 or linear when equal to 1.0. BULKMN: The minimum potential tuber growth necessary to initiate linear tuber growth. CAN (g/m2): The dry weight of the potato canopy. CANGRO (g/g/m2): Relative canopy growth rate. CHOAV (g/m2): Carbohydrate available for canopy and root growth. CHODAY (g/m2): Total amount of carbohydrate available each day. CHOSED (g/m2): Carbohydrate available from seed-piece for growth. CHOTOT (g/m2): Carbohydrate available for total crop growth. DCAN (g/m2): The amount by which the canopy is reduced after energy heat units are accumulated in ATRIB(4). EXCESS (g/'m2): Quantity of photosynthate above that which can enter a days growth or the carbohydrate pool in leaves. EXTRA (g/m2): Quantity of photosynthate above that which can enter daily growth. FILEM(I): A GASP IV function used to file events. GCI (%): The ground cover for a particular day. GCSEl : A table of ground cover for SEl . 130

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131 GCSE2: A table of ground cover for SE2. JDAY: Julian Day LFPOOL (g/m2): Amount of carbohydrate stored in the leaf pool. MNPOOL (g/m2): Minimum stored carbohydrate level which stimulates tuber initiation. MNTUBR (g/m^): Minimum tuber growth rate for linear growth (bulking), MXGRO (g/m2): Maximum growth of crop organs. MXPOOL (g/m2): Maximum size of leaf pool 10% of CAN. NCRDR: Number of the card reader for I/O. NPRNT: Number of printer for I/O. NSET(I): A GASP IV array used to store file data. PAR (E/m2): Daily photosynthetically active radiation. PCAN (g/m2): Potential canopy growth as temperature response. PDMND (g/m2): Photosynthate demand by crop organs. PLOT(I): GASP IV variables used in plotting function. PN(I) (g/m2): Daily photosynthetic production used for calculating a three day average. PNAVE (g/m2): Three day average for photosynthesis. PNDAY (g/m2): Daily photosynthate. PNMAX (g/m2): Potential daily photosynthesis as determined by PAR and GCI. POGLAV (g/m2): Space available in MXPOOL for excess daily photosynthesis. PROOT (g/m2): Potential root growth. PR00T2 (g/m2): Potential root growth when sink demand exceeds photosynthate supply. PTUBR (g/m2): Potential tuber growth. QSET(I): GASP IV array used like NSET(I).

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132 ROOT (g/m^): Root biomas dry weight. RTGRO (g/g/ni2): Relative root growth rate. SEED (g/m2): Seed biomass dry weight. SEEDMX (g/m2): Variable used to determine the amount of seed dry weight available for daily growth. Dry weight available for daily growth. STIM: A factor by which photosynthesis is stimulated by potential tuber growth. TAIR (Deg. C): Air temperature. TAMAX (Deg. F): Daily maximum air temperature. TAMIN (Deg. F): Daily minimum air temperature. TCAN: Table of canopy relative growth rate vs. temperature. TINIT: A flag indicating that tubers have not (less than 1.0) or have (1) been initiated. TOTAL (g/m2): Total crop biomass dry weight. TROOT: Table of root relative growth rate vs. temperature. TSEED: Table of seed CHO available vs. temperature. TSMAX (Deg. F): Daily maximum soil temperature. TSMIN (Deg. F): Daily minimum soil temperature. TSOIL (Deg. C): Daily average soil temperature. TTUBR: Table of tuber growth vs. temperature. TUBGR (g/m2); Daily tuber growth. TUB8R0 (g/g/m2): Relative tuber growth rate. TUBR (g/m2): Tuber biomass dry weight. TUBRGR: Table of tuber relative growth rate vs. temperature.

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133 SE3AGO GROWTH ANO DEVELOPMENT MODEL //POTATO JOB ( 100 1 . 140 1 , 5. 10) , 'KINGRAM • ,CLASS=2 /PASSWORD /ROUTE PRINT TCP // EXEC GASP IV,PARM=«NOMAP,NOSOURCE' //FORT.SYSIN DO BLOCK DATA /INCLUDE COMMON /INCLUDE TABLES ZNO /INCLUDE COMMON DIMENSION NSET(2000) COMMON QSET<2000) EQUIVALENCE ( NSET ( I ) , QSET ( 1 ) ) N
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134 SEBAGO GROWTH AND DEVELOPMENT MODEL C CULATES THE CARBOHYDRATE AVAILABLE FROM PHOTOSYNTHESIS C AND THE SEED-PIECEt AND SCHEDULES A CROP GROWTH EVENT. C NOTE THAT LIGHT INTERCEPTION IS GREATER THAN GROUND C CaVFR DURING EARLY GROWTH. THIS INCREASES PNOAY. C ALSO, THE POTENTIAL TUBER GROWTH RATE (PTU3P) IS USED C TO STIMULATE AN INCREASE IN PHOTOSYNTHESIS DURING THE C TUBER GROWTH PERIOD. C SUBROUTINE DAY /INCLUDE COMMON REA0(5, 100 )JD AY, PAR, T AM AX , TAM I N, T SMAX, TSM IN 100 FORMAT (F3.0, 1X»F3.1 , 1 X.F2.0, 1 X,F2.0, IX .F2.0, 1X,F2 .0) TSOIL= ( ( { (TSMIN+TSMAX)/2. )-32« ) *5. ) /9. TAIR = ( ( ((TAMIN + TAMAX)/2«)-32.)*5. )/'3« IF(PAR.LT.30. ) PNMAX=0.7241 *PAR •TFf TiAP /,« S.O )PNMAX=(0.0 4839*PAR) + 19.597 UT^ t f<«..aB.. ^Gci=GTAa_(GCSEl ,JDAY,68.,138.,5.) L I = GCI*( 0.75+( (100. -GC I )/100. ) ) STIM= (PTUBR/3ULKMN ) +1 . IF( STIM.GT.2. ) STIM=2. PNOAY=< (PNMAX*LI ) /lOO. ) STIM SEEDMX = GTABL(TSEED,TSOIL,0 ..2B.,2 . ) CHCSED=( ( SEED-1 0. » /40. ) *3EEDMX IF( 3EED-LE.10. ) CHOSED=0. CHOTOT=CHOSEO + PND AY ^-LFPOOL MXPOOL=CAN*0. 1 POOLAV=MXPQOL-LFPOOL 3EE0= SEED( SEED* ( ( .005 5*T30 I L )-0 .0 1 23 ) ) IF (TUBR.GT.O.) GO TO 14 ATRIr»(2) = l ATRIB( I ) =JOAY CALL FIL£M( 1 ) GO TO 1 5 14 ATRI3(2)=2 ATRIQI 1 )=JDAY CALL FILEM( 1 ) 15 CO.-4TI NUE RETURN END C C THE PRET SUBR0UTI^4E IS USED TO CALCULATE GROWTH AND C PARTITIONING DURING THE INITIAL CROP GROWTH PHASEC POTENTIAL GROWTH RATES ARE CALCULATED BASED UPON C TEMPERATURE. THESE ARE COMPARED TO THE CHO AVAILA3LE C FOR GROWTH. IF POTENTIAL GROWTH IS GREATER THAN THE C CHO AVAILABLE THE CHO IS PAPTIflONED ACCORDING TO C THE SINK DEMAND (TAKEN TO 3E RELATED TO POTENTIAL C GROWTH) AND THE MASS OF THE SINK. IF THERE IS EXCESS C CHO AVAILABLE (EXTRA) THIS IS EITHER OLACED IN A C LEAF POOL IF SPACE IS AVAILABLE IN THE POOL, OR C PHOTOSYNTHESIS IS REDUCED AS BY FEEDBACK INHIBITION. C SUBROUTINE PRET /INCLUDE COMMON ROOT = RnOT^-0. i CANGRO=GTAaL(TCAN,TAIR,0. ,30., 2.) PCAN=CAN*CANGRO CHODAY= (CHOSED*0, 7692 )+PNDAY-0.1 CHOAVL=CHODAY + (LFPOOL*0 .7692 » IF{PCAN.GT.CHOAVL )GQ TO 20

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135 SE3AG0 GROWTH AND DEVELOPMENT MODEL CAN=CAN+PCAN DCAN=PCAN IF( PCAN.GT.CHODAY )GO TO 21 E XTRA=CHOOAYPCAN IF(EXTRA-GT.POOLAV) GO TO 22 LFPOOL = LFPOOl.+EXTRA SEED=SEED-CHQSED 0£3UG=1 . GO TO 23 22 LFPOOL=LFPOOU+POOLAV £XCESS=EXTRA-POOLAV 3EED=S£ED-CH0SED+EXCESS OE3UG=2. GO TO 23 21 3EED=SEED-CH0SED LF°OOL=LFPOGL-( 1 . 3*( PCAN-CHOD A Y ) » 0E3UG=3 . GO TO 23 20 CAN=CAN+CHOAVL OCAN=CHOAVL SEED= SEED-CHOSED LFPOOL=0. 3E3UG = 4.. 23 T INIT=TINIT+GTABL ( TBIZE.TAIR, 2.,2 3. ,2. ) IF(TINlT.LT.l . >GO TO 25 TUOR=0.4. «rRITE{6.200 ) JDAY 200 FORMAT( '0« , • ***** TUBERS INITIATED ON JULIAN DAY', IX. &F5. 0» IX » •**** • ) 25 CONTINUE TOTAL=CAN+ROOT+SEEO 28 ATRIB( 1 )=JDAY-»-l . ATRIB(2 )=3 ATRIB(3)=DCAN ATRI3(4)=(0.00423*TAIR)-0.0 32 CALL FILEMC 1 ) ATRf 3( 1 )=JDAY ATRIB{2)=5 CALL FILEM{ I ) RETURN END C C THE POSTT SUBROUTINE CALCULATED GROWTH AND PARTITIONING C DURING THE TUBER GROWTH PHASES (BOTH EXPONENTIAL 'VNO C LINEAR) OF CROP DEVELOPMENT. A THREE DAY AVERAGE OF C PHOTOSYNTHESIS IS USED TO DETERMINE WHEN THE LINEAR C PHASE OF TUBER GROWTH IS REACHED. WHEN TUOER GROWTH C REACHES 70 PERCENT OF THE THREE DAY AVERAGE OF PHOTOC SYNTHESIS THE LINEAR PHENOPHASE IS INITIATED. AS IN C THE PRET SUBROUTINE, THE CHO AVAILABLE FOR GROWTH IS C COMPARED TO THE POTENTIAL JRGANS GROWTH AND THE POOL C SPACE AVAILABLE. THE TUBERS HAVE ULTIMATE PRIORITY C FOR CARBOHYDRATE AND WILL REDUCE THE CANOPY AND ROOT C DRY WEIGHTS IF NECESSARY. C SUBROUTINE POSTT /INCLUDE COMMON CANGRO=GT ABL( TCAN,TAIR,0.,30.,2.) PCAN=CAN*CANGRO PPOOT=0.1

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136 SE3AG0 GROWTH AND DEVELOPMENT MODEL MXGRO=PROOT+PCAN IF( BULK.GE. 1 >G0 TO 35 TUBGR0=GTA8L{TUBRGR.TSaiLt 0,«30..2.) PTU8R=TU8R*T'JBGP.O 3ULKMN=PNAVE*0, 7 rF(PTUBR«GT«BULKMN)GO TO 34 TUBR=TuaR*PTU8R CHQOAY=PNOAY*( CHOSED+0 • 7692 )-PTUBR C HO AVL= CHOOAY-KLF POOL *0. 7692) IF{ MXGRO.GT.CHOAVL) GO T O 30 CAN=CAN+PCAN TUBR=TU8R+PTUBR DCAN=PCAN IF(MXGRO.GT.CHODAY)GO TO 31 EXTRA=CHODAY-MXGRO IF(EXTRA.GT.POOLAV ) GO TO 32 LFPO0L=LFPO0L+EXTRA SEEO=SEED-CHOSED 0EBUG=5. GO TO 33 32 LFPQOL=LFPaOL>POOLAV 3EE0=SEED-CH0SED+ EXTRAPOOL A V DE3UG=6. GO TO 33 31 LFPaOL=LFPGOL-( 1 . 3* ( M XGRO-CHODAY ) ) 3EED=SEEO-CHOSED 0EBUG=7. GO TO 33 30 LFPOOL=0. RaOT=ROOT* ( ( PROOT/MXGRO ) *CHOAVL ) CAN = CAN+( ( PCAN/»^XGRO) *CHOAVL) SEEO=SEED-CHOSED OCAN=(PCAN/MXGRO) *CHOAVL D£BUG=8. GO TO 33 34 TU8R=TUBR+8ULKMN 3ULK=B'JLK-H CHOAVL= (PNOAY-BUL
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137 SE3AGO GROWTH AND DEVELOPMENT MODEL IFCCHOAVL.LT.O. )GO TO 39 OCAN= ( PCAN/MXGRO > *CHO AVL GO TO 301 39 OCAN=0. 301 CDNTIiNUE ROOT=RQCT+( { PROOT/MXGRO )*CHOAVL) 33 CONTINUE TOTAL=SEED+ROOT+TU8R+CAN ATRIB< 1 )=JDAY+l . ATRI3i2)=3 ATRia<3 )=OCAN ATRI3(4)={0.0 0423*TAIR)-0.032 CALL FILEM( 1 ) ATRI3(1 )=JDAY ATR IB( 2 ) = 5 CALL FILEMCl) RETURN END C C THE CANOE SUBROUTINE CALLS FOR THE REDUCTION OF C THE CROP CANOPY BASED UPON AERIAL HEAT UNITS C ACCUMULATED IN ATR 18(4). C SUBROUTINE CANOE /INCLUDE COMMON ATRI8(4)=ATRIB{4) +((0,0 0423*TAIR)-0.0 32) IF( ATRIB( 4).GT.l .2)GO TO 40 ATRIBI 1 ) = JOAY + l . ATRIB(2 )=3 CALL FILEM( 1 ) GO TO 45 40 CAN=CAN-( 0.7*ATRI B(3) ) 45 CONTINUE •RETURN END C C THE ENOAY SUBROUTINE IS CALLED AFTER EACH DAY'S C GROWTH. HEREi THE DAY SUBROUTINE 15 SCHEDULED, C THE THREE-DAY AVERAGE PHOTOSYNTHESIS IS CALCULC ATEO , AND BOTH TABULAR AND GRAPHIC OUTPUT ARE C PROGRAMMED. C SUBROUTINE ENDAY /INCLUDE COMMON ATRia { 1 ) = JOAY-H. ATRIB(2 )=4 CALL FILEM(l) PN( I )=PN( 2 ) PN(2) =PN(3) PN( 3)=PNDAY PNAVE=(PN< 1 )+PN{ 2 ) +PN( 3 ) ) /3. WRITE( 6,500) JDAY, TOTAL. TU BR . DEBUG .P ND AY , C AN , IROOT.SEED 500 FORMAT (•0«,F4.0,2(2X,F8.4),3X,F4.0,4(2X,ra.4)) /INCLUDE PLOT RETURN END //GO.SYSIN OD GEN, K.INGRAM, 1, 1,4, 1980, 1^ STA.(5) 1

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138 SE3AG0 GROWTH AND DEVELOPMENT MODEL HM.O.O .200, 4. I, 2000* PLO. 1 .J DAY. 0. 3» 0» !. VAR, l,l.T.TOTAL.l,1.0,1000«2.C. CANOPY* 1 »1, 0,1 00 0, 3, P, TUBERS, 1 , 1 , 0, 100 0* INI . 1, • ,68, 138* FIN* /INCLUDE OATAl /INCLUDE DATA2 /INCLUDE 0ATA3 / //STEP2 EXEC CARDLIST

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139 INPUT TA3LES C C GCSEl AND GCSE2 ARE TABLES CONTAINING GROUNO COVER C PERCENTAGES FOR SEBAGO PLANTINGS JOAY 33 AND 73, C RESPECTIVELY, THE OURATION FOR GCSEl IS FROM JDAY C 68 THRU 133. THE DURATION FOR GCSEZ IS FROM JOAY C 96 THRU 151. C DATA GCSEl /O.O 1 .0 .88.2-56,6.94. 17.5.34.3, 46.5. A6 4. 7.82.2. 85.5. 87,2.8 5.2. 82.2 .79. 45.7 6.7/ C DATA GCSE2/0.0 1 ,3 .37. 8 . 96 . 1 2. I . 22 . 5. 30 . 2. 45. . A57. 5. 70.. 81. 2. 78.. 70./ C C TCAN IS A TABLE CONTAINING THE RELATIVE CANOPY C GRO»»TH RATE FOR TEMPERATURES FROM TO 30 D£ G C. C DATA TCAN/0..0.01 .0.0 4,0.08.0. 12,0. 18,0. 2 5, A0.32. 0.39. 0.45, 0,5, 0.51,0. 49,0. 44, 0. 34, 0./ C C TROOT IS A TABLE WHICH CONTAINS RELATIVE ROOT GROWTH C RATE VERSUS TEMPERATUREC DATA TROOT/0.0,0.15,0.196 .0.24 1 .0 .287.0.372.0.378. A0.3 85. 0.3 89.0.392 .0.424, 0.428, 0.3 93,0. 312, 0.16,0./ C C TBIZE IS A TABLE CONTAINING THE TUBER INITIATION RATE C VERSUS TEMPERATURE. C DATA TBIZE/0.,0.0 128,0.02 56,0,0 33 4,0.05 12,0.0 64, AO.0672,0. 064, 0. 06 I, 0.05 04, 0.03 95, 0. 02 9,0. 0132. 0./ C C TUBRGR IS A TABLE OF THE TEMPERATURE RESPONSE OF THE C TUBER RELATIVE GROWTH RATE USED IMMEDIATELY AFTER . C INITIATION. C DATA TUBRGR/ 0.0.0. 02. 0.06. 0.13.0.21 ,0.34. 0.37. AO .3 75.0.3 75. 0.37, 0.36 4, 0.35,0.3 3, 0.33. 0.3. 0.2/ C C TTU3R IS A TABLE CONTAINING THE TUBER GROWTH RATE C TEMPERATURE RESPONSE. IT IS USED DURING THE LINEAR C PHASE OF TUBER GROWTH (THE BULKING PERIOD). C DATA TTUBR/0.0.0.38, 1 .237. 3.454.6.148, 1 0.43, 14. , Al 9* 7, 18. 5.17. ,16. ,15., 13. .11. ,9. ,7./ C C TSEED IS A TABLE CONTAINING THE CARBOHYDRATE AVAILA3LE C FROM THE SEED-PIECE VERSUS TEMPERATURE. C DATA TSEED/0.,0.2 ,0.3, 1. 94, 3. 22, 3. 35, 3. 42, 3. 42, A3. 35, 3. 28. 3. 22. 2. 68.1. 21.0. 27, 0./ //STEP3 EXEC CAROLIST

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140 COMMON COMMON /GCOMl/ ATR I B ( 25 ) . JEV NT MFA MFE ( 1 00 ) . ML E( 1 00 ) » IMSTOP.NCRDRt NNA P0» NNAPT . NN ATR . NNF I L . NN Q( 100) .NNTRY, 2NPRNT, PPARM(50 . 4 ) , TNO* t TTBEG . TTCLR . TTF IN,TTRI3(25). 3TTSET COMMON /GCOM2/ 00( 1 00 ) » DDL ( 1 00 ) . O TF UL . OTNO W « I SEES • 1L.FLAG< 50 ), NFLAG,NNEQO» NNEQT.SS( 1 00 ) « SSL ( 1 ) , T TNEX COMMON /GCaM3/ AAERR .OTMAX . O TM I N. 0T3AV . I IT E5 .LLERR . 1LL5AV,LLSEV» RRERRtTTLAS, TTSAV COMMON /GC0M4/ DTPLT ( I ) , HHL OW ( 25 ) , HH,rt 10 < 25 ) , I ICRO , 1 I I TAP( 10 ) JJCEL( 500) ,LLABC(25.2) .LLABH(25,2) .LLASPC H .2 ) . 2LLAaT( 25t2 ) .LLPHK 1 ) , LLPLO ( 10 ) , LLPLT. LL3UP ( 15 ) , 3LLSYM( 10) , MMPTS.NNCEH 25) , NNCL T , NNH I S. NNPLT , NNPTS( 10 ), 4NNSTA, NNVAR( 10) .PPHI ( i 0) .PPLO( 10 ) COMMON /GC0M5/ I lEVT , I I SED ( 6 ) . J JBEG . J J CLR. MMNI T . MMON , 1NNAME( 3) »NNCFI , NNOA Y . NNPT . NNSET tNNPRJ. NNPRM, NNRNS* NNRUN* 2NNSTR, NNYR.SSEED( 6 ) COMMON /GC0M6/ EENQ { 1 ) I I NN{ 1 00 ) , KKRNK ( 1 00 ) . MM AXQ ( 10 ) . 1QQTIM( 100 ) .SSOBV(25.5) ,SSTPV(25.6) , VVNQ( 100) COMMON /UCQMl/ GCSEK 1 5 ) » TCAN( 1 6 ) t TROO T ( 1 6 ) , TTUBR ( 1 6 ) I .TSEED( 1 5) .rU8RGR( 16) t JOAY , MXGRO,LFPO0L, MNPOOL . MXPOOL , 2MNTU8R ,aULKtPNOAY.PN( 3 ) . SEEO t C AN, ROOT . TUBR .TOFALtTINIT . 3CH0S ED. C HOT OT, POOLAV, TSO IL . T A IR , EX TRA, GC SE2( 12 ) .TBIZE[ 1 4) » 4PNAVE. BULKMN,PTUBR.0E3UG REAL JOAY, MX GRO. MNPOOL . MNTU BR , LF POOL . MXPOOL INTEGER BULK //STEP4 EXEC CAROL! ST

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141 INITIAL VALUES FOR THE DAY 33 PLANTING 13 FEBRUARY 1980 SEED=49.57 CAN=1.47 R00T=0.8774 TUBR=0. T0TAL=51.917 ATRIB(1)=68. ATRIB(2 =4. CALL FILEM(l) INITIAL VALUES FOR THE DAY 73 PLANTING SEED=35.53 CAN=1.49 R00T=0.981 TUBR=0. T0TAL=38. ATRIB(1)=96. ATRIB(2)=4. CALL FILEM(l) PLOT INPUTS DIMENSION PL0T(3) PL0T(1)=T0TAL PL0T(2)=CAN PL0T(3)=TUBR CALL GPLOT (PL0T,JDAY,1 )

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APPENDIX B; TABLES OF RAW DRY WEIGHT DATA, TUBERS PER SEED-PIECE, INFLORESCENCES PER SEED-PIECE, STEMS PER SEED-PIECE, TOTAL BRANCH PLUS STEM LENGTH PER SEED-PIECE, PERCENT FINAL EMERGENCE, MAXIMUM LEAF AREA INDEX, MAXIMUM PERCENT GROUND COVER, AND THEIR RESPECTIVE ANALYSES OF VARIANCE

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Table B-1. Dry weights of seed-pieces, tubers, and crop total by replicates for the Julian Day 33 planting. Julian Treatment Rep. SeedTotal Tuber Day Piece 66 M 33 S 33 73 M 33 S 33 80 M 33 S 33 88 M 33 S 33 95 M 33 1

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Table B-1 Continued, 144 95 102 m 121 130 S 33 M 33 M 33 M 33 S 33 M 33 S 33 M 33 S 3: 13.8

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145 Table B-1

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146 Table B-2. Dry weights of seed-pieces, tubers, and crop total by replicates for the Julian Day 73 planting. Julian Treatment Rep. SeedTotal Tuber Day Piece 95 M 73 S 73 100 M 73 S 73 107 M 73 S 73 115 M 73 S 73 125 M 73 S 73

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147 Table B-2 Continued. 139 M 73 S 73 153 M 73 S 73 387.0

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148 Table B-3. ANOVA for total crop yields at final harvest. bource df SS Reps Planting (A) Error (a) Whole-Unit Variety (B) A-B Error (b) Total 1 1 6 15 8498 627660 15157 651315 60 8327 22913 682614 NS 124 ** NS 2.18 Table B-4. ANOVA for tuber yields at final harvest. Source

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149 Table B-5. Number of tubers per seed-piece. Average of all harvests after the full tuber load was achieved. Planting Day Rep. Monona Sebago 33 73 1 2 3 4

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150 Table B-7. Number of inflorescences per seed-piece for date of maximum flowering. Planting Day Rep. Monona Sebago 33 1 1.0 4.7 2 1.5 7.2 3 1.5 7.8 4 1.7 8.7 73 1 0.5 2.5 2 0.5 1.0 3 1.5 2.0 4 1.0 2.5 Table B-8. ANOVA for number of inflorescences per seedpiece in Table B-7. Source df SS F Rep 3 4.24 NS Planting (A) 1 31.67 12.8 * Error (a) 3 7.4 Whole-Unit 39.07 Variety (B) 1 46.14 24.6 ** A-B 1 13.23 7.05 * Error (b) 6 1.88 Total 15 109.8 *,**: ct level equal to 0.05 and 0.01, respectively.

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151 Table B-9. Number of stems per seed-piece. Average of all harvests after full emergence. Planting Day Rep. Monona Sebago 33 1 2 3 4 73 1 2 3 4 1.00

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152 Table B-11. Total stem plus branch lengths per seed-piece at maxima. Planting Day

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153 Table B-13. Percent final emergence. Planting Day Rep. Monona Sebago 33 73 1

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154 Table B-15. Maximum leaf area index. Planting Day Rep. Monona Sebago 33 1 2 3 4 73 1 2 3 4 Table B-16. ANOVA for LAI's in Table B-15, 1.64

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155 Table B-17. Maximum percent ground cover. Planting Day Rep. Monona Sebago 33 1 75 95 2 80 90 3 85 82 4 70 70 73 1 70 75 2 65 90 3 75 75 4 85 80 Table B-13. ANOVA for ground cover percents in Table B-17. Source

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BIOGRAPHICAL SKETCH Keith T. Ingram was born 18 August 1953 in Corona, California. While his father was in the U. S. Navy, the Ingram family resided in the states of Cal ifornia, Georgia, Florida, and Hawaii. The author received the Bachelor of Arts degree in psychology from the University of California, Riverside, in June 1974. He was elected to the Phi Beta Kappa Honor Society. In June 1976 he received the Master of Science degree in plant sciences from the same university. The author enrolled in the Agronomy Department of the University of Florida in September 1976. He expects to receive the degree of Doctor of Philosophy in March 1980 from this institution. He was elected to the Gamma Sigma Delta Honor Society in Agriculture in 1979. 156

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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. Sc^^^JIi £ V> s.qG^ D. E. McCloud, Chairman Professor of Agronomy 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. K. J. S6cte Associate Professor of Agronomy 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. hm W. G. Duncan Professor of Aqronomv 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. A. J7 Norden Prorassor of Agronomy

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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. J.. C . ^-~ ' :. ;-^l24:i±^ T. E. Humphreys Professor of Botany 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. March 1980 Jl d.. d'y Dean/7College of Agrieti'l-ure Dean, Graduate School