Title: 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.)
Alternate Title: Solanum tuberosum
Physical Description: xiii, 156 leaves : ill. ; 28 cm.
Language: English
Creator: Ingram, Keith T., 1953-
Copyright Date: 1980
 Subjects
Subject: Potatoes -- Growth -- Mathematical models   ( lcsh )
Potatoes -- Development -- Mathematical models   ( lcsh )
Agronomy thesis Ph. D
Dissertations, Academic -- Agronomy -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Statement of Responsibility: by Keith T. Ingram.
Thesis: Thesis--University of Florida.
Bibliography: Bibliography: leaves 123-128.
General Note: Typescript.
General Note: Vita.
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Bibliographic ID: UF00098436
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000014243
oclc - 06345979
notis - AAB7443

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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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3

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r-r









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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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Figure 20. Effective leaf area index for Monona and Sebago
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JULIAN DAY


Figure 21. Effective leaf area index for Mononoand Sebago planted
on Julian day 73. ELAI = LAI/GC.





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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