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INVESTIGATION 0F MUEIING

Tlli GROW”! UP TIIE HYBRID 3550 653M!!!”

(PEIAREUNIUM X IIURTORUM BAILEY ’RED ELITE’I

By

Douglas ‘Alan flapper

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Horticulture

l985

ABSTRACT

INVESTIGATION OF MODELING
THE GROHTH OF THE HYBRID SEEO GERANIUH
(PELARGONIUH x HORTORUH BAILEY 'RED ELITE')
3Y

Douglas Alan Hopper

A computer simulation model was developed to predict the growth
of Pelargonium X hortorum Bailey 'Red Elite' for days 14-126 from
sowing. A central composite design of 15 growth chamber treatments
studied the environmental effects of irradiance (photosynthetically
active radiation), day temperature, and night temperature. Multiple
linear regression was used to create state equations relating the envir-
onment to the measured plant parameters. The model was checked for
accuracy against treatments in the original data set, and the model was
validated with data sets collected from an unstressed and a stressed
greenhouse conditions. The actual and predicted values agreed quite
closely for total plant, stem, and leaf dry weight with the original
data set, while leaf area was underpredicted. Time to visible bud and
flower was predicted best under similar and moderate (200 C) day and

night temperatures under moderately high irradiance (250-350 umol

s'lm-2).

This is an arduous task, and one beyond my strength. yet
in addressing myself to it I am trusting not in my own
talents, but in the illumination of the Giver 'who gives to
all liberally and upbraids none'.

Dante Alighieri
Dem—heml-l
Nicholl's translation

Scripture: James i:5 KJV

ii

ACKNOWLEDGEMENTS

Great appreciation and thanks to my major professor, Dr.
William H. Carlson, for giving me many unique opportunities.
freedom to choose my own path, and help with seeing the
practical implications of my research while at Michigan State
University. I wish to thank the members of my guidance
committee, Drs. R. D. Heins, G. C. Stockman. and R. L.
Tummala for their time and suggestions.

Special thanks are directed to the Michigan State
Agricultural Experiment Station, the Western Michigan Bedding
Plant Association, and Ball Seed Company for their financial and
material support.

I also desire to thank the many supportive friends.
industrious coworkers, arduous assistants. instructive
professors. my loving family, and the Almighty God for their
kind words, intelligent conversation, sympathy, devotion,
encouragement, strength, shared happiness, and understanding.
This thesis is made possible only through their personal
sharings with me; it is really a tribute to their efforts and
character. I deeply appreciate all that they have done with and

for me.

TABLE OF CONTENTS

Page

LIST OF TABLES .......................................................... vi
LIST OF IIGURES ....................................................... v7"
INTRODUCTION ................. . ........................................... l
LITERATURE REVIEW ........................................................ 2
Evironmental Factors Affecting Plant Growth ............ . ............ 2
lrradiance ......... ...... ................ . .................... . 3
Temperature .............}. ............. . ....... ........... ..... 5
Miscellaneous Single Factors .... ..... ............... ........... 8

Multiple Independent Factors ...... ........... . ................ l0
Approaches to the Modeling of Plant Growth ................ . ........ l5
Plant Growth Ratios .............. . ................ . ........... l5
Functional Approach .............................. ............. l6

Dynamic Simulation of Plant Growth .................. ...... ......... 22

Physiological Considerations for Modeling Pelargonium
Development ................................................... 28
MATERIALS AND METHODS ................................................... 35
Experiment I - Growth Chamber ...................................... 37
Experiment 2 - Unstressed Greenhouse Plants ........................ 38
Experiment 3 - Stressed Greenhouse Plants ........ ......... ......... 39
RESULTS AND DISCUSSION .. ........ .. ..... .. .......... ... ......... ......... uh
Significance of Functional Relationships ........................... AA
Simplified Flowering Equations ..................................... 5i

Biological Significance of Equations ............................... 53

iv

lrradiance ....................................................

Day Temperature ............... . ................................

Night Temperature .............................................

Model Checking and Validation ......................................
Visible Bud and Anthesis ......................................

Total Dry Weight ..............................................

Stem and Leaf Dry Weight ......................................

Leaf Area .....................................................

Further Research ...................................................

TABLES .... .................. ................................... ..... ...
FIGURES . ...... . ... ............ ...... ..... ......... ........ .............
APPENDIX ....... ...................................... . ................
LITERATURE CITED .... ........... ..................... ........ ...........

Page
53

55
57
so

bl

LIST OF TABLES

Page

List of variables and their definitions ............................ 70

Actual and coded values for treatment combinations used in
the central composite design for growth chamber
experiments ........................................ . ............... 7l

Actual and coded values for treatment combinations used in
the central composite design for greennouse experiments .. .......... 72

Independent factors. regression coefficients. standard
errors of the coefficients.‘ and significance level for
regressions predicting days to visible bud and days to
flower for Pe£angan£um X hontonum Bailey 'Red Elite' grown
in growth chambers ....................................... ..... ..... 73

Independent factors. regression coefficients. standard
errors of the coefficients. and significance level for
regressions predicting node number before and after
visible bud stage for Pelargonium X hortorum Bailey 'Red
Elite‘ grown in growth chambers ........ ......... ........ . .......... 7A

Independent factors. regression coefficients. standard
errors of. the coefficients. and significance level for
regressions predicting stem dry weight before and after
visible bud stage for Pelargonium X hortorum Bailey 'Red
Elite' grown in growth chambers .................................... 75

Independent factors. regression coefficients. standard
errors of the coefficients. and significance level for
regressions predicting leaf dry weight before and after
visible bud stage for Pelargonium X hortorum Bailey 'Red
Elite' grown in growth chambers .................................... 76

Independent factors. regression coefficients. standard
errors of the coefficients. and significance level for
regressions predicting root dry weight before and after
visible bud stage for Pelargonium X hortorum Bailey 'Red
Elite‘ grown in growth chambers .................................... 77

vi

Table Page

Independent factors, regression coefficients. standard
errors of the coefficients. and significance level for
regressions predicting flower dry weight after visible bud
stage for Pelargonium X hortorum Bailey 'Red Elite' grown

in growth chambers ................................................. 78
Independent factors. regression coefficients. standard
errors of the coefficients. and significance level for

regressions predicting leaf area before and after visible
bud stage for Pelargonium X hortorum Bailey 'Red Elite'
grown in growth chambers ........... ........................ ........ 79

Independent factors. regression coefficients. standard
errors of the coefficients. and significance level for
regressions predicting stem height before and after
visible bud stage for Pelargonium X hortorum Bailey 'Red
Elite' grown in growth chambers .................................... 80

Independent factors, regression coefficients, standard
errors of the coefficients. and significance level- for
regressions predicting leaf canopy height before and after
visible bud stage for Pelargonium X hortorum Bailey 'Red
Elite' grown in growth chambers .................................... 8l

Independent factors, regression coefficients. standard
errors of the coefficients. and significance level for
simplified regressions predicting days to visible bud and
days to flower for Pelargonium X hortorum Bailey 'Red
Elite' grown in growth chambers .... ....... ......... ..... .. ......... 82

Comparison of measured time to visible bud and anthesis
for growth chamber experiments with predictions made using
simplified static regression equations. ............................ 83

Measured and predicted values for time to visible bud and
anthesis in the central composite design for growth
Chamber eXPeriments 0.0.00.0...O......OOOOOOOOOOOOOOOOOOOOO0..00.00. 8“

Influence of irradiance on flowering. height. and dry

weights of Peiangonium X hagtanum Bailey 'Red Elite' under
25 C day temperature and 20 C night temperature .................... 85

Influence of day temperature on flowering. height. and dry
weights of Pelangonium X honzonum Bailgy lged Elite' under
20 C night temperature and 250 u mol s m irradiance ............. 86

Influence of night temperature on flowering. height. and

dry weights of Pcianganéum X hontonum Bailey 'Red
Elite' undgfi _2 25 C day temperature and
250 u mol s m irradiance ..................................... 87

vii

Figure

LIST OF FIGURES

Page
Daily mean PAR measured in 2 greenhouse sections in East
Lansing, Michigan for summer l98h. ........ . ........................ 89
Generalized flowchart of the program flow for GERMOD. a
time-varying plant growth model simulating Peiaagonium X
hanzonum Bailey 'Red Elite' development. ...... . ..... . .............. 9l

Actual total dry weight means for growth chamber treatment l0
(250-20-20) and the values predicted by the plant growth model
GERMOD simulating Pelaagonium X hantonum Bailey 'Red Elite'
development for lh-IIZ days from sowing. ........................... 9h

Actual total dry weight means for growth chamber treatment 7
(ZSO-ZS-IS) and the values predicted by the plant growth model
GERMOD simulating Pe£angonium X hanzonum Bailey 'Red Elite'
development for lA-98 days from sowing. .................... ........ 96

Actual total dry weight means for growth chamber treatment I
(85-25-20) and the values predicted by the plant growth model
GERMOD simulating Peflangonium X hontonum Bailey 'Red Elite'
development for lh-l26 days from sowing. ........................... 98

Actual stem and leaf dry weight means for growth chamber
treatment IO (250-20-20) and the values predicted by the plant

growth model GERMOD simulating Pelangonium X hantonum Bailey
'Red Elite' development for lb-IIZ days from sowing. .............. IOO

Actual stem and leaf dry weight means for growth chamber
treatment 7 (ZSO-ZS-IS) and the values predicted by the plant
growth model GERMOD simulating Pelangonium X hontonum Bailey
'Red Elite' development for lA-98 days from sowing. ............... l02

Actual stem and leaf dry weight means for growth chamber
treatment I (85-25-20) and the values predicted by the plant

growth model GERMOD simulating Pe£aagonium X hontonum Bailey
'Red Elite' development for lA-l26 days from sowing. .............. th

Actual stem and leaf dry weight means for unstressed greenhouse
treatment l0 (l70-27-22) and the values predicted by the plant

growth model GERMOD simulating Pelangonium X hontonum Bailey
'Red Elite' development for lh-ll2 days from sowing. .............. l06

viii

IO.

ll.

Figure Page

Actual stem and leaf dry weight means for stressed greenhouse
treatment l0 (l70-27-22) and the values predicted by the plant
growth model GERMOD simulating Peiaaganzum X honzonum Bailey
'Red Elite' development for lA-98 days from sowing. .. ...... .. ..... 108

Actual leaf area means for growth chamber treatment IO
(250-20-20) and the values predicted by the plant growth model
GERMOD simulating Pefiangonium X hantonum Bailey 'Red Elite'

development for lA-lIZ days from sowing. .... ......... . ............ llO
l2. Actual leaf area means for growth chamber treatment 7

(250-25-l5) and the values predicted by the plant growth model

GERMOD simulating Peiangonium X hontonum Bailey ‘Red Elite'

development for lh-98 days from sowing. ........... ................ ll2
l3. Actual leaf area means for growth chamber treatment I

(85-25-20) and the values predicted by the plant growth model

GERMOD simulating Pelangontum X hontonum Bailey 'Red Elite'

development for lh-l26 days from sowing. .......................... llA
IA. Actual leaf area means for unstressed greenhouse treatment l0

(170-27-22) and the values predicted by the plant growth model
GERMOD simulating Pelangonium X hontonum Bailey 'Red Elite'
development for IA-llZ days from sowing. .... ..... .. ............... ll6

. Actual leaf area means for stressed greenhouse treatment l0

(170-27-22) and the values predicted by the plant growth model
GERMOD simulating Peflangonium X hantanum Bailey 'Red Elite'
development for lh-98 days from sowing. ........................... lIB

ix

INTRODUCTION

INTRODUCTION

One of the most popular bedding plants produced in the United
States is the geranium. Recently. production of geraniums has shifted
from prooagation by cuttings to growing hybrid cultivars from seed.
The length of time necessary to grow from seed to flower requires
proper scheduling to produce a crop for a specific market.
Environmental factors may be used to control the crop development. The
literature which has been reviewed suggests that temperature and
irradiance are the major environmental factors affecting geranium
growth. Since the study of all environmental factors would be
prohibited. in a single experiment. the major factors of day
temperature, night temperature. and irradiance level were chosen for
more close study while the other factors were held within desireable
levels which should have less significant effects upon plant growth.

This study will develop state equations relating plant ‘growth to
the environmental conditions during growth and to the state of plant
growth at a previous time. These functional relationships will be
incorporated into a computer plant growth model which can track the
growth of Pe£angonium X honzonum Bailey 'Red Elite' based on the
environmental conditions. This model will be checked against the
original data for accuracy and then validated using data from plants
grown under both a stressed and an unstressed greenhouse environment.
The fit of the model to the original and 2 different data sets will be

discussed.

LITERATURE REVI EN

LITERATURE REVIEW
Environmental factors affecting plant growth

Many plant species show marked resoonse to changes in major
environmental factors such as temperature and light. Light has been
quantified precisely by defining spectral quality as cummulative
photosynthetically active radiation (CPAR). which only includes
wavelengths in the LOO-700 nm band, and designating photoperiod of
irradiance so that the exact quantity of useable radiation received by
plants may be measured. The ADO-700 hm band was selected since it has
been shown to have the greatest effect on plant growth, morphology, and
flowering (81). Spectral quality appears to alter plant morphology and
growth (20) as well as physiology (5l,80). Photoperiod of irradiance
has been shown to influence plant growth and development (50.68) as has
the mean quantity of PAR received over time (5,l0,33.5l.80).
Temperature as it relates to plant growth has been measured in terms of
mean daily temperature (22.75). mean day and mean night temperature
(7.8,h6). or with some form of degree day unit measurement (l3.h7.73).
The use of many methods to measure temperature suggests that its effect
upon plant growth has not been precisely defined, or that the plant
response to temperature differs greatly depending upon the type of
response being studied. The study of effects of temperature.
irradiance, and other important environmental factors will be discussed

in the first section of this review.

lrradiance

To properly measure the effects of irradiance upon plant growth,
the method by which plants intercept light energy should be understood
and described. Monteith (Bl) developed simple relationships to model
light diatribution in field crops based on the leaf area index.
Radiation profiles were measured within crop canopies. and parameters
were defined to properly account for transmitted and absorbed
radiation. The system described what fraction of incident light, 5.
passed through L layers of leaf canopy. and also included the effect of
leaf angle as described by the mean transmission coefficient, t.
Integrating the absorbed light over the layers in the plant canopy
could define the energy absorbed by the plant which was available for
photosynthesis. A further assumption that solar radiation varied
sinusoidally allowed daily photosynthesis to be estimated by using
photoperiod and irradiance level. When respiration was considered
proportional to leaf area. accumulated dry matter could be reasonably
predicted for sugar-beet, sugar-cane. kale. and clover.

Spectral quality. or designated wavelengths of radiation, has been
studied to determine its effect upon plant growth. Studies by Cathey
et al. (20) found plant growth to vary in quantity as well as
morphology to the different spectral quality under 7 types of
fluorescent lamps used for supplemental irradiation. Lamps having
higher relative amounts of far red radiation promoted greater stem
elongation in Laczuca, Lycapeaaican, and Petunia, while 5 other plant
species showed no change in response. Plants were shown to have

variable response in fresh weight 'to the different light sources

depending upon the species. The use of incandescent lighting along
with cool white fluorescent bulbs increased fresh weight in 5 of the 8
species tested. However, the efficiency of the lamp in converting
electrical energy to visible radiation was more important to
influencing plant growth than was spectral quality. This was supported
in a study by Nilsen et al. (65) where plants were exposed to specific
wavelengths by using a copper sulfate solution in a double acryi
greenhouse covering to preferentially absorb infrared radiation and
promote cooling. Plant growth was not decreased from that measured in
a control greenhouse.

The use of supplemental irradiance by Carpenter and Anderson (l9)
increased branching of 'Forever Yours‘, 'Shocking Pink'. and 'Red
American Beauty' roses, and reduced the time from cut to cut. although
stem length. node number, and fresh weight were decreased for the
latter 2 cultivars. The method of lamp arrangement and photoperiod of
exposure was stipulated. but the exact quantity of PAR was not
precisely defined in terms of quantum or raidiometric units. A higher
amount of far red radiation and increased photoperiod from incandescent
lighting improved the quality of 'Forever Yours'. but not of the other
cultivars. Lighting the plants for more than 9 hours daily reduced the
number of nonflowering shoots per plant.

Photoperiod has been shown to have important influences on plant
growth. Both photoperiod and light quality effects have been
demonstrated for petunias ( PetunIa X hybnida ) by Merritt and Kohl
(59). Long photoperiods promoted greater leaf area index. greater dry
weight. greater efficiency of dry weight gain. and larger leaves. The

effect of photoperiod has also been demonstrated for Chngxanzhemum

moniéoflium. Post (68) found flower bud formation to occur under short
photoperiods. and other researchers have reported photoperiods of IO
hours or less to be necessary for Chagaanthemum flowering (26,50).
Flower initiation in some species is insensitive to photoperiod
and spectral quality. Flower initiation for both Tagczcs pazufia and
Paiangonium X hattonum Bailey have been shown to be most influenced by
CPAR to initiate flowering (5,7.8,l0). However. Armitage (7) found
that the positive initiation response to PAR was dependent on higher
night temperatures (30°C) for Tagctca pazuia. Minimum time to flower
occurred when high irradiance and high day temperatures were combined
regardless of the night temperature. This suggests that plant response
to irradiation must be studied with respect to the prevailing day and

night temperatures.

Temperature

The effects of temperature alone.have been studied for many crops
and different strategies have been explored to account for the effect
of temperature on crop yield. The most obvious influence of
temperature is its effect upon the reaction rate of physiological plant
processes. Sharpe (75) adopted a functional relationship proposed by
Arrhenius to model the effects of absolute temperature on
photosynthetic rate. This model was inherently correct because it
reflects the actual biochemical reactions occurring at the molecular
level. Sharpe's approach sought to aggregate the effects on a
microscopic level to successfully model plant growth macroscopically.
It was also necessary to introduce rate constants into the equational

relationships to account for variations in growth rates at different

temperatures.

A tulip forcing model proposed by Charles-Edwards and Rees (22)
which was used to predict the necessary cold requirement was based
simply on the temperature. The interconversion of carbohydrates from
storage to labile pools was described in terms of linear polynomials.
and this in turn predicted the growth rate of the shoot.
Unfortunately. this system did not appear to be strictly valid. meaning
that additional factors needed to be considered.

Armitage et al. (7) used both the day and night temperatures
along with irradiance level to describe environmental effects on both
Tagctca paxwfla and Pcficutgam'um X houamm Bailey. This strategy was
also followed by Karlsson (A6) to predict time to flower, dry weight.
and stem height of Chnyaanzhemum monifioflium. The method was used to
develop second degree polynomial equations which could model both
temperature and irradiance effects simultaneously. Both were
considered to remain constant over the life of the plant. and thus
values could be assigned to each variable to calculate the dependent
growth effects.

Realizing that temperatures vary substantially under actual field
or greenhouse conditions, several attempts have been made to utilize
degree days or accumulated heat units to account for variable
temperature effects upon plant development. Johnson and Lakso (Ah)
found shoot length and leaf area of apple to be significantly related
to accumulated degree days. Shreiber et al. (73) incorporated the
degree day concept into a model for predicting the growth of alfalfa
IMcdicago aaxiva L. ) using maximums and minimums from actual weather

data. The model also used solar radiation to simulate 6 weeks of early

spring growth . Basically, plants grown at lower temperatures
maintained vegetative growth for longer periods, and irradiance had
less influence on growth rates as the temperature increased.
Morphologically, alfalfa was observed to develop larger leaves under
cooler temperatures (l3). The degree day method was modified slightly
by Kobayash and Fuchigami (A7) to use a degree hour unit for predicting
the breaking of dormancy for buds of Red-osier Dogwood (Cannux senxcea
L. ). The hourly units were accumulated using linear relationships to
determine the effective of chilling on dormant dogwood plants. No
significant bud development was seen to occur at 20°C. but the
developmental rate was observed to increase with decreasing temperature
down to 5°C. The chilling requirement necessary for dogwood bud
development would seem reciprocal to that experienced by most
herbaeceous plants native to the tropics. Yet. such herbaeceous plants
may undergo similar physiological changes in response to the
accumulation of thermal units within some normal ambient temperature
range.

The accumulated heat unit or degree day concept has been
criticized for its inability to account for several important factors
(79.8h). First. plants may change their response to temperature at
different stages of their life cycle. Secondly. the threshhold
temperatures for degree day calculation may change with other
environmental conditions. Lastly, the interaction of temperature with
other environmental factors is basically omitted. Allen (I) contended
that the normal degree day calculation assumes a symetrical sine wave
function of daily temperature fluctuation. and a slight modification is

actually necessary to properly calculate the degree days. Merely

accumulating degree days may have merit under some combinations of
environmental conditions for some crops. but the limitations must be
kept in mind. and the models may need to be modified to overcome some
inherent problems.

Chen (73) proposed that the method of degree days be modified to
include a normally distributed random factor when describing the
accumulation of heat units. He used a monthly distribution function to
generate daily mean temperatures. and through a Monte Carlo analysis
developed a probability table to describe the heat units accumulated
over the span of a year. He found a definite relation between sowing
date and the length of the growing period. The system predicted the
blossoming of Japanese cherry trees in Washington. D. C. His method
improved the prediction of variations in blossoming between years. The
heat unit concept appeared to be an adequate environmental measurement
for use in plant modeling for this specific instance.

Cooper and Thornley (27) measured changes in dry matter
accumulation and partitioning as well as carbon to nitrogen ratios
present in young vegetative tomato plants due to changes in root
temperature. The model which they developed predicted the relationship
between net assimilation rate and relative growth rate. Plots of
actual and predicted values found some discrepancies in the model.
suggesting that root temperature alone may not be sufficient to model

crop development.

Miscellaneous single factors
Other single factors have also been chosen upon which to base

plant development. Several researchers have chosen time as a factor

for modeling growth. Patten (67) devised a model for biomass
accumulation in aquatic ecosystems based solely on time. The growth of
flower buds of Liiium £0n945£ogum was found by Erickson (3!) to be an
exponential function of time alone which could be linearized. Anther
length and bud length could then be related by the use of a simple
loglihear function. Janssen (A3) proposed a simple method for tracking
seed germination by fitting parameters to the data using nonlinear
equations based upon time. The use of time alone may be adequate for
such simple plant processes as germination and flower bud elongation
under relatively constant environmental conditions. but other factors
may be necessary in models which attempt to describe more complicated
growth patterns over a wide range of environments. For example. Bould
and Abrol (lb) conducted work on seed germination. finding it to be
describeable as a function of time. but they improved the prediction by
building a second equation into the basic model. When comparing the
predicted germinations with those actually observed for certain seed
populations. discrepancies were thought to be a result of differences
in seed vigor between subgroups within any sample studied. Thus,
different seed subgroups needed to be properly identified in order to
reliably use the model.

The effects of plant competition must also be considered when
attempting to model growing plant systems. Hara (kl) studied the
self-thinning of white pine (Pinua Aznobual to ascertain that a
logarithmic based model was sufficient to describe the response of the
population. He concluded that a 3/2 power law which had been proposed
by others worked successfully. A McMurtrie and. Wolf (58) sought to

mathematically describe the competition between trees and grass for

available irradition. water. and nutrients. The model accounted for
preferential radiation interception by the tree population and direct
competition between the 2 species for available water and nutrients.
Growth parameters in the equations could be altered so as to alter the
tree to grass biomass ratio, even to the extent of producing pure
monocultures. Since most present agricultural production is based upon
monoculture, such competition between species might seem trivial, but
the competition between individual plants within a species should not
be ignored in the formulation of useful generalized plant growth

models.

Multiple independent factors

Models involving one factor or environmental condition are
desireable because they act to simplify the complexities of plant
growth. Unfortunately. oversimplification by using just one factor
often constrains the model to very specific situations. More
generalized models have been designed which include both temperature
and light as major parameters. and seek to make use of the interactions
between these factors in predicting plant growth. Voldeng and Blackman
(83) modeled Zea Maya growth over 2 whole growing seasons. basing
predictions upon the solar radiation and air temperature. Multiple
regression equations were developed to predict the net assimilation
rate, relative growth rate, and leaf area ratio from mean weekly
radiation and the mean. minimum, and maximum air temperatures. The
model accounted for over 80 percent of the variation for data collected
in 1966. but lesser amounts were accounted for in l965. The

discrepancies between the 2 years were attributed to differences in

correlation between radiation and ambient temperature.

An approach by Johnson and Lakso (Ah) used actual weather data
from Geneva. New York to test a carbon accumulation and partitioning
model for apple. Light and maximum and minimum temperatures were
considered due to their influence on photosynthesis and respiration
rates. Increased radiation induced greater export of carbohydrates
from shoots. but higher temperatures most strongly influenced transport
by causing substantiatlly greater export from the shoots later in
development. This suggests that the interaction between light and
temperature is crucial to the development of an effective plant growth
model.

Glenn (37) sought to develop curves to predict the length of a
crop cycle for 3 varieties of lettuce grown in a greenhouse using day
and night temperatures and seasonal changes in total daily incident
radiation. The best growth predictor was the product of the day
temperature and the natural logarithm of the radiation. a predictor
which explained the diferences between seasonal crops quite well.
Radiation alone could satisfactorily predict the growth of lettuce if
seasonal levels were high enough. Similar to the findings of Johnson
and Lakso. higher temperatures were found to be detrimental. especially
since higher temperatures promote bolting in lettuce. Exceptionally

high radiation levels of over #50 cal cm-2 day-‘ ( 1000 u mol s-

lm-Z)
were also indicated by Mattel et al. (55) to inhibit lettuce growth,
and saturation of the light response occurred around 250 cal

I ( 550 u mol s-‘m-2). Thus, at higher irradiance levels

cm"2 day.-
temperature was more important for maintaining an accurate model.

Under more controlled growth chamber environments, Armitage et al.

12

(7) studied the interactions of temperature and irradiance upon the
development of Tagczea patuia. The effects of both temperature and
irradiance were found to be quite dependent on the stage of plant
growth. Until visible bud. irradiance most significantly affected
development. although low day temperatures might become limiting. With
low night temperatures (ISOC) from time of visible bud to flower,
development was mostly influenced by temperature. but increased night
temperature (above 2l°C) allowed irradiance to have more effect upon
final time to flower. Overall. high day temperatures (26°C) and high
irradiance ( 600 u mol s-]m-2) treatments had the shortest time to
flower. High irradiance levels resulted in the largest dry weight
accumulation regardless of the night temperatures. with high day
temperatures also inceasing the response. The maximum absolute rate of
dry weight gain occurred earlier in development under higher levels of
irradiance. Maximum leaf area occurred under high night temperature.
high irradiance. and moderate day temperature. Plant height was seen
to increase with increased day temperature regardless of night temp.
with higher irradiance producing shorter plants.

Armitage and Carlson (8) found in a separate study that lower day
and night temperatures enhanced the anthocyanin content in Tagetea
pazuza foliage. Combinations of either high day and low night
temperatures or low day and high night temperatures produced similar
chlorophyll content in leaf tissue. Anthocyanin content was not
significantly correlated with potassium or phosphorus content. The
above interacting relationships were fit to the data using multiple
linear regression to find polynomial equations. and response surface

plots were made to demonstrate the interacting effects.

l3

Karlsson (A6) studied the effects of day and night temperature

along with irradiance on Chnyaanthemum manxfioflium growth. Increasing
night temperature from IA to 26°C delayed flowering, while increasing
irradiance from 50 to 600 u mol 5.1m“2 accelerated flowering. Day
temperature had no significant effect on flowering time. but stem
length increased with increased day temperature, a result similar to
that seen by Armitage (7) in french marigolds. Partitioning of dry
weight to roots and leaves decreased with increased irradiance. where
higher proportions went to stem and leaf tissue. Multiple regression
equations were used to describe these interactions as they affected
plant growth at the time of flowering.

Similar response surface techniques were used by Hammer and
Langhans (AG) to study the effects of irradiance, root temperature.
daylength. and air day and night temps in controlled environment growth
chambers on Heliunthua annuua and Zinnia elegana. Fresh and dry
weights of shoots and roots. and total dry weights for H. annuua were
successfully modeled with response surfaces. No significant models
could be fit to the Z. ezegana data for any of the parameters studied.
By using the canonical forms of the fitted multiple regression
equations, Hammer concluded that the maximum growth of H. annuua would
occur at some point outside of the design space which was studied. He
also emphasized the importance of studying the interactions between the
measured environmental factors to correctly model plant growth, and
this was further substantiated by Armitage (7) and Karlsson (A6) as was
discussed.

Thornley and Hurd (78) studied the influence of interactions

between irradiance and carbon dioxide on plant growth. Both the nature

IA

of the source and sink were important to the prediction of growth as
shown by the relative growth rate (RGR). A maximum RGR occurred when
when the total growth tissue was saturated with carbohydrates under
high CO2 and irradiance. The data were divided into clases designated
for younger or older vegetative plants to obtain better fit to the
overall data set. Temperature effects were also accounted for in the
model.

Other studies have attempted to include an even larger number of
independent parameters in multiple regression models to effectively
model plant growth. Rao (69) studied the possible effects of IO unique
environmental factors on A varieties of jute (Conchanua otitoniua L. ).
finding 6 factors to have significant effects. About 9h percent of the
variation could be accounted for. and comparisons of the predicted and
actual growth found good agreement. Some sizeable discrepancies in
growth rate prediction were seen within the first 60 days. although
predicted cumulative growth agreed well with the actual data. In a
study by Lewis and Haun (52), IO environmental factors were considered.
as terms for multiple regresssion used to predict leaf growth rate for
carnation (DIanthux canyophyliua L. ). An arbitrary morphological
scale of development was designated to measure leaf growth. Data were
collected daily, and lags in growth were correlated with conditions
occurring up to 5 days previously. Fitting the linear. quadratic. and
cubic terms for all the factors found a significant 7-term equation for
predicting the leaf growth. Although the R2 value was only .25. the
prediction of cummulative leaf and bud growth appeared to fit the

actual data quite well. This may suggest that consideration of a

relatively large number of environmental factors will tend to predict

l5

plant growth accurately in the long run. although the model may be
inaccurate on a day to day basis. The use of multiple regression
equations makes it possible to include all the significant interactions

in the model.

Approaches 3_ he Modeling g: Plant Growth

Plant growth ratios

One of the most simple methods for representing plant growth is
through plant growth ratios. Williams has defined both relative growth
rate and net assimilation rate (89). Relative growth rate. termed R or

RGR. is calculated:

RGR d w / a:

 

W (l)
where d W / dz is the change in dry weight of the whole plant per unit

time, and W is the total plant dry weight.

The net assimilation rate. given as E (89) or MAR (82) is defined:

E _ d w / dz

L (2)
where d W / dt is the change in dry weight of the total plant per unit

 

time. and L represents some changing leaf attribute such as leaf area,
leaf weight , leaf protein-nitrogen, or leaf total nitrogen. The leaf
canopy itself might be described by the leaf area ratio (LAR) or leaf

area index (LAI) (83.3A). The leaf area ratio is defined:

LA

w (3)

LAR '

l6

where LA is the total plant leaf area, and W is the total plant dry
weight. A similar statistic. leaf area index. relates leaf area to

available growing space instead of plant mass as follows:

LAI . LA
P (A)
where LA is total plant leaf area and P is the soil surface or land

area which an individual plant occupies. When these ratios are used to
describe plant growth the method is termed the classical approach.
These ratios have been used in many studies to predict plant growth

(25.27.35.53.72.78.83).

Functional apgroach

Another popular method for plant growth modeling. termed the
functional approach, is to develop more sophisticated equations that
predict growth. These may be linear. intrinsically linear, or
intrinsically nonlinear depending upon the process modeled. and might
actually be used to implement the classical approach if the functions
predict the plant growth ratios (83).

Typical linear regression analysis attempts to determine a
relationship between 2 or more variables which are linearly related in
the estimated parameters. The general equational model is represented:

Y - be + b 2 + b 2 + ... + ann + c (5)

l l 2 2

where values of Z are functions of some measured variables, Y is some
variable to be predicted, b values are the linear parameters .and e is
an error term (30). From the study of biological mechanisms. it has

been questioned whether such a model possessing linear qualities is

indeed a ,proper representation of changes in biological systems.

l7

particularly when considering the modeling of plant growth (82).
Still, a real advantage of using multiple linear regression equations
is to consider the effects of many factors and their interactions
simultaneously as was previously described (7.8,3l,h6.52.69.82).

An alternative is to explore the use of models which are nonlinear
in the estimated parameters. Such models fall into 2 readily
distinguishable categories. The first. termed intrinsically linear,

has the form:

2
Y=e(e]+92t+2) (6)

which may undergo a logarithmic transformation to produce a model of

linear form:

lnY - el + thz + c (7)
The transformation reveals that equation 6 is actually linear in the
estimated 6 parameters, while t represents some predictor variable, Y
or InY is the variable to be predicted. and the error term. a . has the
expected value of zero and some assumed variance 02.
The second category, intrinsically nonlinear. cannot be

transformed to a linear relationship in the 9 parameters. and must be

analyzed in the form:

GI ( e -62*t _ e -Bl*t ) + 2 (8)

BI-OZ

where again values of 6 are estimated parameters, t is the predictor
variable, Y is to be predicted, and e is a randomn error term.

Equations in the form of 8 cannot be analyzed using common linear

18

regression techniques, but must be analyzed by other methods using
iteration (30).

Both intrinsically linear and intrinsically nonlinear equation
models have been developed for use in biology. It has been found that
although intrinsically nonlinear models exist in several different
forms, a single characteristic equation may be used to represent them
all as long as one realizes that certain parameters progress toward
limiting values to produce each type of equation (30.32.70). The most
basic nonlinear model likens plant growth to compounding of interest
(12,32). This model proves to be intrinsically linear when it
undergoes a logarithmic transformation. The general model has the
form:

W . Aekt (9)

and may be transformed to:

an - lnA + kt (l0)

where W is some predicted value after time t. A is an initially
determined value at t-O. e is the actual logarithm base. k is a
constant parameter to be estimated, and t is the time measured on some
selected scale. These definitions for variables will remain the same
for subsequent models unless otherwise noted. From this equation the
relative growth rate has been defined to be (dx/dz ) / W (32). The
model is limited in that it only predicts a continuing increase in
growth and growth rate.

A slightly more complicated model has been termed the

monomolecular equation and takes the form:

l9

-kt

w - A ( I - be ) (II)

In contrast to the first model. A here represents the ultimate size
which may be achieved by the plant. and this definition will remain
true for the models discussed later. The other parameters were
previously defined except for b which must be estimated by an iterative
solution. Unfortunately, b has no biological significance since it
relates only to the measurement made at time zero., and this is easily
altered depending upon the type of study conducted (82). The growth
rate for this model is defined as k(A-W). and the model is limited in
that the rate of growth continually decreases until reaching zero.
Graphically the function has no inflection point. Although useful on a
chemical basis. the equation lacks practical application on a
macromolecular scale for predicting plant growth.

A related model called the logistic or autocatalytic function is
more useful in that it possesses an inflection point, and thus allows
for a symetrical increase and then decrease in the growth rate around

some central point (70.82). The model is:

w . A / ( I + be ’kt )

(12)

The parameters are the same as discussed for the monomolecular model,
but the growth rate takes on the form of kW(A-W)/A. An alteration can
be made in the basic logistic function by substituting a cubic function
of time for kt, producing what is called the generalized logistic
function (82). This function possesses considerably more flexibility.
but requires that 5 instead of 3 parameters be estimated. and the

resulting meaning of the various terms is less clear.

The Gompertz function has increased flexibility in that it is

20

asymetrical about its inflection point. It is represented by:

-kt
w . Ae 'be (l3)

This function is more readily understandable from its logarithmic

transformation:

kt

an . lnA - be- (1A)

The growth rate may be defined as kW*ln(A/W) (70). or the relative

growth rate may be expressed as:

In( d an / dt ~) - A - k't (l5)

This model has proven useful for animal as well as plant growth
(2.32).

Another model was developed by von Bertalanffy for use with animal
studies. Richards (70) found that by altering some of the restrictions
which von Bertalanffy had made upon the model, the previous
intrinsically nonlinear functions could all be obtained. The function

is described by the 2 equations:

-kt)l/(l-m)

W 8 A ( l + be m >l (16)

w - A ( I - be 'ktll/(l'm) m <l (17)

By substituting m-O into equation 17. the monomolecular function of
equation 11 is obtained, and by substituting m-Z into equation 16 the
logistic function of equation 12 is obtained. Although no solution
exists for m-l, Richards showed that both equations 15 and 16

approached the form of the Gompertz function as m approaches 1. As the

21

value of m changes from 0 to 2. the shape of the curves change from
monomolecular, to Gompertz, to logistic. The absolute growth rate in
any of these cases can be expressed as:

kW [ (A/II)"m - l] / (l-m) (18)
while the relative growth rate is shown by:
l-m
k L (A/W) - l] / (l-m) (19)

The constant k represents the rate at which some function f(W) changes.
Curves of the same form may be compared in terms of their k values.
with larger k values representing larger relative growth rates.
Different equation forms cannot be compared since the functions of W
are different. In all instances. though. it can be shown that
Ak/(2m+2) defines the average plant height predicted by the model (70).
Thus, for any family of curves having A as a final size for a plant
species. the k values may be compared as proportional rates of growth.
Revisions may be made in these equations to adjust to specific
situations. To account for both initial and final locations of defined
points of an elongating root tip. Salamon et al. established a ratio
similar to the relative growth rate termed the relative elemental

growth rate or RELEL. This ratio is given by:

Z
RELEL . d_§_1_dl_di

d x / dz (2°)

where X is the distance traveled by some point on the root surface.
d X / dx is called the stretch ratio, and dzx / dx dz is termed the
change in the stretch ratio. This alteration in the model

distinguished between elongation toward the root tip apart from the

22

cells. and growth propagated along with the cells. Such modifications
or similar parameter estimations act to improve prediction ability.

A very unique modeling technique was used by Grafius (38) to model
the results which could be obtained from crossing certain wheat
breeding lines. Each variety was represented by a vector which
included components for desireable characteristics which the plant
breeder wished to select for in future crosses. The vectors were then
mathematically crossed to determine a resultant which would represent
the genetic content of the progeny received from making the actual
cross. Resultant vectors which most closely resembled some favorable
combinations were then chosen to be made as the crosses in the breeding
program. Grafius found this to be an adequate method for selecting the

most desireable crosses out of the almost limitless possibilities.
Dynamic Simulation 9: Plant Growth

Effective plant growth models must be able to track the growth of
plants through all the stages which are of interest. Ideally. changes
could be made in the crop growing system to maximize some plant
characteristic. Under field conditions. the changes cannot
realistically be far from the ambient environmental conditions. but‘
crops grown in a greenhouse could be significantly altered by gross
changes in the major environmental factors.

Takakura et al. (77) integrated both a greenhouse environmental
balance model and a leaf temperature based crop model into one
simulated system. Energy flux into the greenhouse was received

primarily from solar radiation, and such processes as condensation,

23

evaporation, exiting thermal radiation. and conduction through the soil
accounted for the thermal heat losses. Moisture balance was quite
crucial to the model's effectiveness. The temperature measured on a
plant surface was used to model reactions of the plant canopy to the
thermal balance in the greenhouse. Bot (15) used a similar procedure
to model greenhouse climate. He measured the effects of ventilation in
great detail. and was mainly concerned with the energy balance in the
greenhouse while ignoring the crop growing inside.

Udink ten Carte (81) identified 3 types of plant growth models.
The first. a transpiration model. is based on plant water relations.
Factors such as crop canopy climate and root water uptake are
variables, while leaf temperature and stomatal opening are considered
as output variables. A second model type. crop groth and development.
studies growth of plants over time. Certain output variables. such as
dry weight production. are correlated with environmental factors which
are present over the time of the study. A third model type is the
production model which represents a weighted sum of all integral
variables. The single scalar result of a production model is easy to
understand and react to for governing control of the greenhouse
environment. Growth and development models are empirical, while
transpiration models study causal mechanisms.

Any of the 3 model types may be static. i.e. not changing with
time as the plants develop, or they may be dynamic so that the results
of the equations change over time of the study. A thorough systems
science approach develops a network of interacting equations to predict
desired results based upon the inputs. The nature of these system

equations can be studied to determine the controlling systems equations

2A

and parameters that will optimize the system outputs (53). The dynamic
modeling approach will thus predict which cources of action are
preferred when the previous environmental conditions and the the plant
stage of development is known.

Karlsson and Johnson (A5) developed a feedback control method for
modeling the dynamic 2h hour petal rythm of Kafianchoc bfioaaéediana
which was oscillatory in nature and returned to stability after
exposure to brief perturbations in irradiance. The irradiance bursts
tended to cause phase shifts in the system oscillations. The authors
also discussed how such a model might relate to rythms in other plants
such as sunflower or oat.

Whole ecosystems might be modeled with a dynamic procedure if the
total system were defined very simply. Gutpa and Houndeshell (39) used
both differential and difference equations to model an aquatic
ecosystem which included several phyla of phytoplankton. zooplankton.
and nekton. The model included a predator-prey relationship and
considered competition for nurients. Environmental factors and
nutrient levels had time-lagged effects upon the system balance. Over
100 constants were fit to the model using gradient techniques. The
equations were highly coupled, meaning that slight changes in one
portion of the system may cause major changes in other parts of the
system. The interdependence of the equations in the system indicated
that the system dynamics account for a sizeable part of the outcome
from any single simulation.

A dynamic computer program devised by Cock et al. (25) sought to
describe the ideal growth of cassava (Manzhat eaculenta Crantz ) to

obtain a maximum yield The crop growth was related to the leaf area

25

index, with increases occurring up to values of 3.5 to A. Yields of up
to 25 metric tons per hectare per year could be realized if the
radiation measured AOO-A50 cal cm-2 day”l ( 890-1000 u mol 5-]m‘2).
The model predictions agreed closely with those measured by actual
data.

Since dynamic models by nature change over time, time series
analysis may be used to determine autocorrelations which exist among
variables. Kuehl et a1. (A8) used time series analysis to study the
boll retention of cotton (Goxxgpium hinxuzum L. ), defining the
autocorrelations which were present between separate time series. The
percent boll retention was highly correlated with the 5 day minimum
temperature average beginning with the day before anthesis. This
indicated that the accumulation of high night temperatures near
anthesis might have the most important effect on the boil retention.

Hari et al. (A2) explored the effect of temperature on plant
height for Rubua Aaxazizix by using dynamic modeling. They found
temperature to markedly affect the daily increment in plant height and
determined the overall rate of maturation. Data were collected at the
end of 2 hour periods. and this method suggested that inherent growth
rythms in plant development must be accounted for with a dynamic model.
Time alone was not found to be a suitable individual factor upon which
to base the model. However. a time lag of 6 hours occurred for the
growth response when temperature was used as the main factor in the
model. The model fit the data well except near the very beginning and
end of the time period under study.

Several studies have used dynamic modeling to study the dry matter

accumulation in response to environmental factors for several plant

26

species. Fukai and Silsbury (35) simulated potential dry matter for
clover species Tnifioflium aubzcnnaneum L. Both irradiance and
temperature were used to predict dry matter yield, achieving estimates
within 20% of actual yields after 100 days. Leaf area index seemed
quite important in determining the total dry matter. The authors
concluded that the effect of temperature on plant growth was dependent
both on the dry weight present and upon the irradiance level.

Work by Barnes et al. (11) showed that both growth and nutrient
composition of plants were dependent upon soil nitrogen and potassium
levels. The irradiance. plant composition. and soil moisture were
considered in the ‘model. It correctly predicted the pattern of
response of cabbage using soil, crop. and actual weather data as inputs
to the model. The interactions between the effects of nitrogen and
potassium were also found to be significant. A dynamic model proposed
by Waun et al. (85) found that ambient temperature and irradiance
together were necessary for modeling the early vegetative growth of
tobacco (Nicoziana tobaccum L.). Both photosynthesis and respiration
were considered in partitioning of the plant carbohydrate pool using a
set of nonlinear differential equations. The model. based on data from
growth chambers, was found to reasonably simulate the dry weight of
tobacco plants grown in greenhouses.

Rickman et al. (71) applied a simpler nonlinear model. a modified
Blackman compound interest formula. to describe the dry weight
accumulation of winter wheat (szztcum dabtivum 64p. vulganc
Vill,Host ) up through the time of crop maturity. Two components which
were necessary to the model were related to temperature, irradiance.

nutrition, and available moisture. Daily values for dry weight and

27

water budget were accurately predicted up until the time of anthesis,
but after anthesis the model tended to overpredict the dry matter
content. An improvement in prediction might have been possible with
more accurate measurement of available water and an alteration in the
model equations to be used post anthesis. Curry and Chen (29) used
daily weather conditions in a dynamic model to describe the
partitioning of net photosynthate which was available after integrating
together equations for photosynthesis. respiration, and
evapotranspiration. lrradiance. temperature in the form of degree
days. and evapotranspiration effects accumulated hourly to predict
growth and development of corn (Zea mayx L. ). Certain growth
parameters were estimated and allowances were made for competition
between plants. They questioned how much detail was necessary and
describeable to calibrate and then validate an effective model.

Similar procedures were used by Patefield and Austin (66) to find
the effects of for temperature and irradiance on the photosynthate.
partitioning for Beta vulganix L. They proposed that error in the
model may result from 3 basic sources:

1. Inadequate model formulation

2. Inaccurate or biased estimation of constants

3. Inaccurate or biased environmental measurement.

Also. varietal differences were purported to be partially responsible
for the discrepancies between simulated and actual growth curves. An
extensive comparison of values assigned to various growth parameters
found that small changes of around 12 could have marked effects on the
final plant dry weight. This suggests that great care must be taken in

fitting such parameters to data sets so as to create accurate

28
predictive models.

Physiological considerations fig; Modeling Pelargonium Development

The previous discussion has explained the necessity for
understanding considerable physiology about a plant species when
formulating a growth model. Many interacting environmental factors
control the ultimate growth. and small changes in key parameters may
have significant consequences. This section will review some of the
studies which have looked at the influence of environmental factors on
the physiology of geraniums (Peiangoniumi.

Electron microscope studies by Cline and Neely (2A) have described
the distribution of carbohydrtates in Pciangonium X hantonum 'Yours
Truly’ cuttings which contributed to the wound healing and formation of
adventitious root primordia. Under 21-23°C day and l6-18°C night
temperatures in the greenhouse root primordia developed in 7 days. and
periderm tissue was present in lA-21 days.

Nilsen (6A) found that rooting was quite dependent upon the
environment of the mother plants from which cuttings were taken.
Pzzangonium X hantonum mother plants were irradiated with 3000-6000 lux
( 50-110 u mol s-lm-Z) supplemental fluorescent bulbs to produce a
significant increase in overall cutting production during the winter
months. Extension of the photoperiod using incandescent bulbs did not
increase cutting production. At 15°C the production of cuttings was
lessened by slower growth rate, and at 21°C the branching response was
suppressed. so that a night temperature of 18°C appeared optimum for
maximum cutting production. The rooting of cuttings from

non-irradiated plants was faster and had more initials than those from

29

irradiated plants up until February. but this situation reversed with

cuttings that were taken later. This indicated either that the effects

of supplemental irradiance might not initially be realised in plant
tissue or that increased natural irradiance might have altered the
overall rooting response. Also, cuttings from young mother plants

rooted faster in the early season, but later on there was no difference
in the speed of rooting of cuttings from either young or old mother
plants.

Work by Sweatt and Davies (76) found that a mycorrhizal
association with Pe£angonium X hanzanum Bailey roots could increase the
fresh and dry weight of plants under constant nitrogen and variable
phosphorus levels. It appears consideration of such factors may be
necessary to create an effective growth model. Even storage conditions
for seed may have significant effects. Cairns and Lenz (l6) discovered
that although storage of 'Ringo Scarlet' and 'Rosita' seed for over 2
years did not significantly alter germination percent. germination rate
was decreased. Scarified seeds germinated twice as rapidly as
unscarified seeds after 27 months of storage. a fact which could
substantially influence the long-term effects of plant growth modeling.

Amer and Williams (2) studied the leaf area growth of Peiangonium
zonaze in response to different watering regimes and fit nonlinear
Gompertz curves to the observed weekly growth. Normal daily waterings
were compared with drying periods of up to 5 weeks in length. A growth
parameter, b. which represents the degree of dependence of growth rate
upon instantaneous plant size and the deviation from some potential
maximum. was found to be rather constant under the watering regimes

studied. Armitage et al. (9) determined the effect of water stress on.

30

net photosynthesis. Pelangonium X hanionum Bailey 'Sprinter Scarlet'
was grown under greenhouse conditions and exposed to a period of water
stress. Photosynthesis went from a steady-state maximum to a state of
total inhibition. Measurment of leaf water potential was found to be
an indicator of photosynthesis decline. Although photosynthesis was
again elevated to a steady-state within 3 days after watering stressed
plants. the maximum attained was only 90% of the initially observed
rate.

Marousky and Harbaugh (5A) studied other detrimental effects which
might occur to geranium metabolism. particularly through stress which
may occur during plant shipment. Seedling plants held for 3 days at
relatively high temperatures (23.5°C) were observed to lose chlorophyll
and exhibit chlorosis. with decreases in fresh weight occurring during
later growth. Plants treated with ethylene at rates up to 10 u l/liter
air developed greater chlorosis. abscised leaves. and showed poorer
subsequent growth. Darkness during the 3 day period also contributed
to chlorosis. They concluded that although temperature was the
variable of primary importance during shipment. increased ethylene
levels and darkness promoted by the shipping container itself
contributed significantly to the plant damage. Plant models might be
required to consider such effects for proper prediction of plant
growth.

Welander (87) looked specifically at the effects of irradiance and
temperature upon both vegetative and reproductive growth of Pelangonium
X hantahum Bailey 'Radio'. He found increased irradiance tended to
increase leaf number. leaf area, branching. and the number of

inflorescences produces. The number inflorescences (flowers) was

31

increased at irradiance levels of A W m-2 ( 20 u mol s-lm-z). while
leaf and shoot number were seen to increase at irradiance levels of 22
W In“2 ( 100 u mol s-]m-2). Increased temperatures at high irradiance
promoted vegetative growth, but tended to decrease inflorescence
number. This suggests that the carbohydrate balance and rate of plant
metabolism has significant effect upon Pefiangonium X hontonum floral
initiation. Nilsen (63) also found high temperature to inhibit floral
initiation for Peflangonium domeaticum Bailey under normal irradiance,
and the critical temperature for flower bud formation differed between
cultivars. Low temperatures during cutting propagation were seen to
hasten flowering. a response which may not be the same as that of
Patagonian X hamtonum Bai leY-

Both temperature and irradiance have been shown to have
considerable effect upon growth and flowering of Pciangonium X hontanum
Bailey. Tsujita (80) found supplemental high pressure sodium (HPS) and

2 ( A0 a mol s-lm-2) cumulative

natural irradiance levels above A00 E m-
photosynthetically active radiation (CPAR) to decrease flowering time.
Four weeks of supplemental irradiance at 17°C night temperature
promoted earlier flowering. Exposure to supplemental HPS irradiation
for Over 8 weeks could shorten flowering time by up to 2 weeks.
Temperatures below 17°C were observed to delay flowering. while 6-8
weeks irradiation removed the delay and produced higher quality plant
growth. Responses were seen to vary between cultivars.

Armitage et al. (10) found similar effects for irradiance levels
on Pezanganium X hantonum Bailey. They also found low irradiance to

increase total leaf area while resulting in lower dry weights.

Specific leaf area and leaf thickness were positively correlated with

32

net photosynthetic rate. Some significant differences in response were
seen for ‘Sprinter Scarlet'. 'Sooner Red‘, and ‘Ringo‘ cultivars. but
irradiance was definitely seen to affect initiation and floral
maturation.

Other work by Armitage et al. (8) found irradiance and
temperature to have varying importance to development based upon the
plant growth stage. For temperatures ranging from 10 to 30°C. time to
visible bud for; Pe£angonium X honzonum Bailey ‘Sooner Red' was
negatively correlated with irradiance. From visible bud to flowering,
increased temperature was seen to hasten development. while irradiance
had no significant effect. Leaf thickness and leaf dry weight were
negatively correlated with temperature, while specific leaf weight was
positively correlated to irradiance at a constant temperature. Net
photosynthesis rate was observed to be optimum between 20 and 30°C.
Armitage and his coworkers proposed that Pezanganium X hoatonum Bailey
development be studied in 2 separate stages. the first being from
sowing to visible bud stage, and the second from visible bud to
flowering.

Wetzstein and Armitage (88) used scanning electron microscopy to
conduct a study of floral initiation and development of the leaf
primordia. Stages of floral development were defined using a pictoral
sequence.

To determine the relationship between vegetative growth and floral
initiation. Armitage (3) conducted a series of defoliation experiments.
He discovered that total plant leaf area had a significant effect on
the time to visible bud and flower. and a minimum amount of

photosynthetic area appeared necessary to promote flowering. He termed

33

the first 6-8 basal leaves as the critical leaves in which greater
surface area would promote earlier flowering. Time from visible bud to
flower was not influenced by leaf area for any of the treatments given.
A minimum number of nodes was necessary for flower initiation. but this
was thought to be cultivar dependent. He theorized that although high
temperature and irradiance have been shown to accelerate floral
development. these environmental factors were actually working to
promote more rapid leaf emergence. The increased rate at which leaves
assimilated carbon tended to reduce the time to floral initiation and
anthesis.

This explanation might be generalized to account for the effects
of chlomequat (cycocel or CCC) upon flower initiation. Miranda (60)
found that application of CCC between 35 and A2 days from sowing both
decreased final plant height and caused earlier bud initiation.
Armitage et al. (6) also described a significant interaction between
cycocel and supplemental HPS irradiance on the flowering time of
Pezangonium X hontanum Bailey. When used together, CCC and HPS
irradiance reduced flowering time by 31 days. but inferior quality
resulted. Schwartz and Payne (7A) found that the effects of CCC could
carry over for extended periods to significantly reduce plant height.
Early CCC applications used with some acceptable irradiance level might
promote flowering and yet maintain the desired level of quality.

The information which has been reviewed suggests that temperature
and irradiance are the major environmental factors affecting
Pelangonium X hoazanum Bailey growth. However, proper moisture levels
and nutrition are essential to maintain reasonable growth which may be

effectively modeled dynamically over time. The effect of growth

3A

regulators and competition between plants must also be considered
significant enough to affect the plant growth model. Since the study
of all these, and possibly other factors. would be prohibited in a
single experiment, the major factors of day temperature, night
temperature, and irradiance level were chosen for more close study
while the other factors were held within desireable levels which should
have less significant effects upon plant growth.

This study will develop state equations relating plant growth to
the environmental conditions during growth and to the state of plant
growth at a previous time. These equations will interrelate the
various plant parameters in the model so that a reasonable agreement
between the plant parameters may be maintained. These functional
relationships will be incorporated into a computer plant growth model
which can track the growth of Peflangonium X hontonum Bailey 'Red Elite‘
based on the environmental conditions. This model will be checked
against the original data for accuracy and then validated using data
from plants grown under both a stressed and an unstressed greenhouse
environment. The fit of the model to the original and 2 different data

sets will be discussed.

MATERIALS AND METHODS

35

Materials and Methods

Three experiments consisting of l5 treatments each were arranged
according to a Central Composite design {36). Similar procedures among
the 3 experiments are described below. The first experiment was
carried out in controlled environment growth chambers; the second and
third were both performed under strictly controlled greenhouse
conditions using a computerized environmental control system. The
second and third experiments were similar except for a high light and
high temperature stress treatment given to third experiment plants when
they were 21-31 days old. Seeds of geranium (PeLangonium X hontanum
Bailey) cv. Red Elite were sown in plastic cell paks of size 32 cells
(each cell 8X8 cm) per 28x56 cm plastic flat and covered approximately
1/2 cm with medium to manintain an even moisture. A medium of 2 parts
finely ground Sphagnum peat, 1 part perlite, and 1 part fine
vermiculite was used throughout all the experiments. The pH of the
medium was adjusted to 5.0 at the beginning of the experiment using
ground dolomitic limestone, and the pH raised to 6.2 during the
experiment due to akalinity of the water.

Seeds for all treatments were germinated in the greenhouse over a
1A day period under night conditions of 21 i 2°C and day conditions of
25 1 3°C , afterwhich the seedlings were moved to their respective
treatments. Data were recorded every 1A days. beginning immediately
after the germination period. to measure development of the plants
under the treatments. Six plants were randomly sampled from each

treatment for data collection at each sampling. The last sampling for

36

a treatment was taken at the time when over 50% of the plants in the
treatment had reached anthesis. The following plant parameters were
measured every lA days, except for the flowering parameters which were

measured when anthesis had occurred:

1. Day of emergence

2. Time to visible bud

3. Time to flower

A. Node number (number of leaves)

5. Height of apical meristem

6. Height of leaf canopy‘

7. Fresh weight of roots. stems. leaves. and flowers

8. Dry weight of roots. stems. leaves. and flowers

9. Total leaf area

10. Area of dead leaves

11. Peduncle length

12. Flower radius

13. Number of florets

1A. Number of branches

15. Number of leaves on branches

16. Leaf area of branches
A list of abbreviations and the definition for each variable is given
in Table l.

The data on root development were only collected for the plants
grown in the growth chamber experiment. Initially the seedlings were
considered to have no stem. but measurements were taken on the roots

and leaves. with the point of cotyledon attachment used to

37

differentiate between the root and the above ground portion of the
plant parts. Three times during plant development: at 3 weeks. 6
weeks, and final sampling. The individual leaf areas and petiole
lengths were recorded to obtain information on individual leaf

development for each treatment.

Followin is an explanation of the procedures thCh differed
9 .

between the 3 experiments .
Exgeriment l - Growth Chamber

Treatments were conducted in environmentally controlled growth
chambers (Sherer-Gillete. Marshall. Michigan) beginning April 1983 and
continuing through May 198A. Due to limited growth chamber space. all
treatments could not be grown simultaneously. A minimum of 5A
seedlings were placed in each treatment. The treatments were
determined using the Central Composite design to dictate the conditions
of day temperature, night temperature. and PAR as shown in Table 2
(36). For some treatments it was not possible to adhere rigorously to
the assigned conditions, and alterations were made in one of the
factors in order to achieve actual conditions. These modifications
changed the realm of the measured responses to the environmental
conditions, but did not alter the application of the statistical design
in determining a model from the data. An area of 3-dimensional space
was studied centering around the point of primary interest which .was
suspected to produce optimal plant growth. The central point was coded
0. 0. 0 and contained the treatments 25°C day temperature. 20°C night

'2

temperature. and 250 u mol s-Im irradiance.

38

Characteristic parameters of plant growth as listed above were
measured for 6 randomly selected plants from each treatment every 1A
days until 50% of the plants had reached anthesis within a treatment.
The point of anthesis and the final recording of data for a treatment
varied from 8A to 126 days. After the final sampling. pictures were
taken of each treatment. and flowering data were collected from all the
plants remaining within a treatment. The final flower data were used
to determine a time of visible bud and flowering for each treatment.
Analysis was conducted to fit both linear and nonlinear models to the
data so that plant growth could be effectively simulated from sowing to

anthesis.
Experiment 2 - Unstressed Greenhouse Plants

Seeds of geranium were sown as described on May 16,1983 and moved
after germination to 8 computer controlled greenhouse sections on May
31. Treatment 9 was eliminated from the Central Composite design due
to lack of available greenhouse sections. Actual measured greenhouse
conditions for each treatment are given in Table 3. An Apple II
microcomputer with controlling software from Oglevee Computer Systems
(Connelsville. Pennsylvania) both monitored the greenhouse environment
and controlled the heating and venting. Supplemental high pressure
sodium (HPS) irradiance was given to the high PAR treatments for 16
hours daily at 60 and 90 u mol s-Im-2. Low levels of PAR were obtained
by reducing natural irradiance using 85 8 and 65 3 shading made of
plastic netting placed on supports over the plants. The moderate PAR

level.was taken to be the naturally occurring incident PAR. Data were

collected at intervals as in Experiment 1 for only the first 9 items

39

listed above. The dry weight of roots and individual leaf areas were

not measured for the greenhouse grown plants.
Experiment 3 - Stressed Greenhouse Plants

Seed of geranium were sown Mav 25. 1983 and after germination were
moved into the greenhouse treatments described for Experiment 2 on June
6. Plants received the same 1A treatments as Experiment 2 (Table 3)
except for the period 21-31 days from sowing. During that time plants
were moved to a stress condition in a separate greenhouse section where
all plants recived the same treatment of 30°C constant day and night
temperature along with 2A hours of supplemental HPS irradiance at 200 1

50 u mol 5-1m-2. Natural irradiance levels averaged 190 u mol

s-lm.2 over the period of stress. After 10 days in the stress
treatment the plants were returned to their original treatment

conditions for subsequent growth and development. Data were recorded

in the same manner as explained for Experiment 2.

The daily incident PAR was measured for both Experiments 2 and 3
using Li-l9OSB Quantum sensors in 2 adjacent greenhouse sections
attached to a Kaye Instruments Digitstrip datalogger (Kaye Instruments
Inc.. Bedford. Mass. ). The daily accumulated PAR was recorded for
each sensor location. and the mean of the 2 readings was taken as the
daily PAR (Figure 1). The mean was taken over the 2 week periods
between plant data recordings. and these means were used as the PAR
received for use in the subsequent model validation. The plant growth

model was also developed based upon the assumption that 2 week means

A0

for PAR and temperatures as measured in the growth chambers were used
as inputs to the model.

Regression ecuations were derived for 10 different plant growth
parameters based on the measurements taken from the growth chamber

«-

exoeriments. Ihe abbreviations for the independent and dependent
variables are listed in Table 1. Treatment means of 6 plants were used
at each sampling to allow for logical prediction of future plant
parameters from present plant parameters. Except for flowering data. 2
equations were fit for each plant parameter. the first to the time
prior to visible bud (samplings 1-5), and the second fit to the data
from visible bud until the conclusion of data collection (samplings
5-9). Data from sampling 5 was included in both regressions so that
the prediction periods for the 2 equations would overlap. and thus at
no point in time would the final model containing both equations be
discontinuous. The regressions for flowering data could only be fit
after the visible bud stage, thus only permiting one equation to be
derived for each flowering parameter.

Stepwise regression was not always adequate to determine the
‘best‘ equation. The addition of one term early might cause the
exclusion of others later. and equations containing different terms
could be found to have similar R2 values and significance levels for
individual terms. Successive runs were made for the most critical
plant parameters to select the independent factors which were most
significant and maintained the smallest residuals. This procedure was
applied to the equations for node number. days to visible bud. days to
flower. and the dry weight of stems. leaves. and roots prior to the

time of visible bud. Computer costs and time limitations did not allow

A1

such a thorough analysis for the other plant parameters or for the time
period subsequent to visible bud.

The regression equations were developed in an assigned order to
approximate the flow of energy and carbohydrates within the plant. The
equation for node number (NN) was developed first because it was highly
temperature dependent, was found to be simply modeled with few terms,
and could be thought to represent a general developmental stage of the
plant. The regression was conducted using environmental parameters and
values for the plant parameters determined 2 weeks earlier. The stem
and leaf dry weight (DWS.DWL) equations were developed independently
while including node number as a possible term in the regression along
with the environmental and previous plant parameter terms. These 3
plant parameters were taken to represent a ‘growth stage‘ from which
the state of all other plant parameters was calculated. The other
plant parameters were then fit in the following order. using previously
fitted parameters to be used in the equations which were fit later:
_root dry weight (DWR). leaf area (LA). stem height (height of apical
meristem - HAM). leaf canopy height (HLC). days to visible bud (DVB).
flower dry weight (DWF). and days to flower (DTF). This strategy
allowed the equations for the model to be quite interdependent. The
equations developed were actually state equations as defined in the
strictest systems sense: the equations would need to represent changes
in rates of development for each plant parameter to be considered
difference or rate equations.

All of the regression equations fit for growth parameters were
included in the overall program model. A simplified flowchart

representation of the plant growth model is included in Figure 2. A

A2

listing of the model is given in the appendix. The model began
simulation at day 1A since the regression equations were fitted to data
collected from 1A to l26 days after sowing. Since the stem height
(HAM). defined as the length of the stem from the cotyledon petiole
attachment to the point of first flower bud peduncle attachment. and
leaf area (LA). defined as the area of the leaves below the first
flower bud, were such that they would not increase after the time of
flowering, the equations for these parameters after visible bud were
not included in the model. The use of equations predicting visible bud
and flowering at times in early development resulted in unreasonable
values for each since they were actually being used outside of their
design space. After 50 days of elapsed time from sowing. the equation
for visible bud was found to predict reasonable values. When the
predicted value became less than the actual elapsed time, a bud was
assumed to be visible and the second set of equations were then used to
predict plant growth. Since no treatment was found to advance from
visible bud to flower in less than 20 days. this condition was required
for predicting flowering. To feasibly include this in the model, the
time to flower was checked for occurrence only after each successive 1A
day step in time.

Environmental data from the growth chamber experiments were used
as inputs to the plant growth model to check how well the model could
predict the values for the plant parameters as measured in the original
data. A comparison was made between predicted and actual mean values
for days to visible bud and days to flower. Plots of the original data
and predicted values were made to portray the usefullness of the model

to predict the results of 3 specific treatments. To very simply

A3

validate the use of the model in other practical greenhouse situations.
the environmental data as measured for the unstressed and stressed
greenhouse treatments were used as inputs to the model. Comparisons

were made between predicted and actual mean "alues for treatments

h)

from the greenhouse grown experiments.

RESULTS AND DISCUSSION

AA

RESULTS AND DISCUSSION

 

To develop a successful model to predict the growth of
Pefiaagonium X hontonum Bailey, it was first necessary to develop
equational relationships between the environment and plant parameters
based on data collected from plants grown under controlled growth
chamber conditions. These relationships were assembled into a
working time-varying computer simulation model which could be checked
for accuracy of prediction against the original growth chamber data
set. The model was validated using 2 sets of data collected from
plants grown under greenhbuse conditions. First the general

relationships found in the functions will be discussed. and secondly

the predicted results of the model will be compared to the 3 data
sets.

Significance pi Functional Relationships

Regression equations were developed for 10' different plant
growth parameters. The abbreviations for the independent and
dependent variables are listed in Table l. The independent factors.
fitted regression coefficients, standard errors of coefficients. and
significance levels are presented in Tables A-13. Before considering
the influence of independent factors and interdependence between
plant growth factors. it should be noted that greater variability
existed in the data after visible bud than prior to visible bud.
This was evident by studying the simple correlations between factors

when various groupings of samplings were run for analysis. The

“5

increased plant variation in later development was reflected in the
lower R2 and lower F values footnoted in each table. This
variability was due in part to the difference in time of initiation
between plants. Different plants in the population were thus at
different physiological stages. such as slightly before and slightly
after flower initiation, and this would contribute to different
values being measured for individual plant parameters. Other
uncontrolled factors. such as genetic -dlversity even within a
cultivar or exact location of a plant within a growth chamber. would
contribute to the variability, suggesting that a mean of a sample of
plants is best used for prediction in a model.

The time from sowing to visible bud (DVB) was found to be
largely dependent on both the mean daily and accumulated PAR (LT.ALT)
and day temperature (DT.ADT). while night temperature terms (NT.ANT)
did not have a significant influence on time to visible bud and were
not included in the model (Table A). DVB was dependent on certain
plant characteristics such as node number (NN). stem height (height
of the apical meristem: HAM). and root dry weight (DWR). along with
the previous dry weight of stem and leaf tissue (PDWS.PDWL). The
days from sowIng to flower (DTF) were found to be dependent on
temperature (DT,NT,ANT). while PAR did not significantly influence
flowering time if DVB was known and included (Table A). Thus.
initiation of the flower bud was affected by irradiance and day
temperature, while development of the flower bud was affected by both
day and night temperature and less affected by irradiance. This
agrees with the work of Armitage et al. (8) which found PAR to

significantly effect flowering early in plant development. but

A6

temperature appeared to be more influential in later stages of
development after initiation had occurred. Increasing stem height
(HAM) was also found to Significantly delay time to flowering.
Increased stem height may indicate a greater potential for stem
tissue to store carbohydrates and thereby act as a sink competing
more strongly for carbohydrates. so less are available for the bud
and development may be slowed, with the result being later flowering.

The node or leaf number (NN) was found to be primarily
influenced by the mean daily and accumulated PAR (LT.ALT) along with
the mean daily and accumulated night temperature (NT.ANT), while the
day temperature had no significant effect on the growth in terms of
node number previous to the time of visible bud (Table 5). After the
visible bud stage, interactions between day and night temperature as
well as PAR with day and night temperature were found to be the
environmental factors with the most influence on MN. The existing
dry weight of the stem and leaves (DWS,DWL) as well as the previous
conditions of node number (PNN), and dry weight of the roots and
leaves (PDWR,PDWL) were included in the equation for development
after visible bud. The manner in which the data were collected
defined NN as the number of nodes up to the location of the first
inflorescence (or flower). For this reason, only the equation for
the time before the visible bud was included in the overall
time-varying model. and NN was considered to be constant after
visible bud.

Stem dry weight (DWS) was found to be most influenced by the
accumulated day and night temperatures (ADT.ANT) and the previous dry

weights of stems and leaves (PDWS,PDWL) during early development.

A7

while the accumulated light (ALT), the accumulated interaction
between PAR and day temperature (PSLD), mean daily night temperature
(NT), and node number (NN) were found to be influential after
initiation if the previous stem dry weight (PDWS) was included
(Table 6). Temperature may function to alter the balance between
carbohydrate metabolism. transport. and storage in the stem during
vegetative development. After initiation, the effects of PAR
collected by the photosynthetic machinery of the leaves appeared to
control how much carbohydrate could be stored in the stem. The added
competition with the flower bud for the carbohydrates might have
caused the change in the dry weight accumulation in the stem.

The accumulated effect of PAR (ALT). day temperature (ADT), and
night temperature (ANT), as well as the accumulated interaction
between day and night temperature (PSDN) seemed to be the
environmental factors having the most significance on leaf dry weight
(DWL) prior to visible bud. (Table 7). The previous plant
parameters of leaf area (PLA). leaf dry weight (PDWL). and root dry
weight (PDWR). along with the present stage of development as
reflected in node number (NN) also seemed to influence leaf dry
weighs early in plant development. This suggests that a complicated
balance between the environmental factors and plant parameters
affected the accumulation of dry weight in the leaves and transport
of carbohydrates to other tissues. After visible bud stage the
accumulation of day and night temperature appeared to have no
significant effect upon the partitioning of carbohydrates to the
leaves. although the accumulated interaction between day and night

temperature (PSDN) as well as the accumulation of PAR (ALT) were

A8

still influential (Table 7). The only plant parameters to
significantly effect the leaf dry weight after visible bud were the
previous stem and leaf dry weight (PDWS,PDWL) and the present leaf
number (PNN). Notice also the loss in explained variance using the
equation for later development (R2 I .768 ) as compared to that
explained prior to visible bud (R2 I .951).

Root dry weight was found to be significantly affected by the
mean daily and accumulated night temperature (NT.ANT). the mean day
temperature (OT). and the existing leaf dry weight (OWL) during early
development (Table 8). After visible bud. previous leaf dry weight
(PDWL) and the existing stem dry weight (DWS) were important along
with the day temperature. These relationships suggest that the
partitioning to roots was affected by both day and night temperature
during early development, while only the day temperature affected the
partitioning in later development. The state of the leaves appeared
more important during vegetative growth. while the state of the stem
was more influential after initiation. The increased importance of
the stem later in development might be due to the increased
competition between stem. bud. and roots for the excess carbohydrates
produced by the leaves. Large stores of carbohydrates in the stem
might allow extra carbohydrate reserves to be more readily

transported to the roots and bud.

Flower dry weight was found to be influenced by the existing
stem and leaf dry weights (DWS.DWL). a ratio between those dry rates
(DWS/DWL). the time elapsed since sowing (TIME). and previous stem

and leaf dry weights (PDWS,PDWL) if the days to visible bud (DVB)

“9

were assumed known (Table 9). The inclusion of the ratio between
stem and leaf dry weights indicates that a balance between other
parts of the plant could significantly influence the amount of
partitioning to the flower bud. The inclusion of time in the
equation was not totally desireable since it tends to overlook the
direct effects which environment could have upon the bud growth. but
the regression indicated that time was an adequate term to include
with days to visible bud. A further regression analysis may produce
a more effective generalized equation by removing the time factor.
The leaf area was found to be best estimated by the existing
leaf dry weight (OWL), the‘ previous values for leaf dry weight
(PDWL), and leaf area (PLA) during early development (Table 10).
After the visible bud stage. the mean incident PAR (LT). accumulated
night temperature (ANT). and previous root dry weight (PDWR) were
also included in the equation. The amount of variance explained

(R2 . .85A) was less than that for the early stage equation

(R2 . .935). This indicates that leaf area prior to visible bud was
found to be exclusively a function of leaf dry weight and the
previous leaf area. while environmental factors became more
influential in later development. Yet. the increased variation in
later development could not be well explained even with the
additional terms. The high dependence between leaf mass and area
might cause the overall time-varying model to underpredict leaf area
under low PAR where leaf' area was observed to increase, but
accumulated dry weight was observed to decrease.

Stem height (HAM) was found to be significantly affected by day

temperature (DT, DTZ) and the accumulated day temperature (ADT) for

50

the time previous to the visible bud stage (Table 11). A high

portion of the varianace could be explained prior to visible bud
7

(R‘ a .830), while a considerably less amount of of the variance was

explained after visible bud (R2

= .510) so that the regression
equation was not significant at the .05 level. Since the meristem
height was defined from the point of cotyledon attachment to the base
of the peduncle of the first inflorescence. the stem height value
would only increase slightly due to stem elongation once initiation
occurred due to the morphology of Peiangonim X honzanum Bailey
development. To simplify the model and preserve the nature of the
original measurement. the first equation for stem height was used in
the model up until visible bud. and the second equation was not
included in overall time varying plant model.

Height of the leaf canopy (HLC) was found to be a function of
day temperature (DT.DT2), accumulated day temperature (ADT. ADTZ) and
the accumulated interaction between irradiance and day temperature
(PSLD) prior to visible bud (Table 12). After visible bud. day
temperature and accumulated day temperature remained important to the
equation, while accumulated night temperature (ANT), irradiance by
day temperature (LD) and irradiance by night temperature (LN)
interactions. as well as the accumulated day by night temperature
interaction (PSDN) were also included. Considerably more variance
was explained prior to (R2 - .826) than after (R2 I .596) visible
bud, and the regression after visible bud was not found to be
significant at the .05 level. As with the stem height. only the
equation prior to visible bud was included in the model due to the

nature of the plant development.

51

As was explained in the materials and methods, node number was
first calculated from the environmental parameters and previous
values of plant parameters. Then stem and leaf dry weights were
calculated considering the effects of the environmental and previous
plant parameters along with the node number. The root and flower dry
weights were calculated by considering node number, stem dry weight.
and leaf dry weight as possible independent plant parameter terms in
the equations. Leaf area was then calculated while considering all
the dry weight parameters and node number as possible terms in the
equations. Plant stem and leaf height were calculated lastly. using
the values of other plant' parameters as possible independent
variables. This order approximated the flow of irradiance energy
into the leaves and partitioning of the fixed carbohydrate to other
plant parts (first to the stem. and then to the roots and flowers).
Leaf area and plant height parameters were calculated lastly since
they described the appearance of the leaf and stem overall structure
which would be dependent on the available dry weight partitioned to
each plant part. This order was necessary to properly arrange the
equations when making calculations in the overall time-varying plant

growth model.

Simplified flowering equations

Simplified regression equations were developed for both days to
visible bud and days to flower (Table 13). These equations can be
used to predict flowering by assuming environmental conditions are
constant over the development of the geranium plant.

Day temperature and night temperature linear terms, the

52

quadratic lrradiance term, the irradiance by night temperature
interaCtion, and the day by night temperature interaction term were
significant at the .05 level in the days to visible bud equation
(Table 13). Comparison of the measured and the predicted values for
visible bud is shown in Table IA. Visible bud is predicted within

: 5 days for all but 3 of the 15 treatments.

For the days to flower equation. linear day and night
temperature terms, the irradiance by night temperature interaction.
and the day by night temperature interaction term were significant at
the .05 level (Table 13). The actual and predicted values for days
to flower for the 15 treatments are listed in Table 1A. All but 2 of
the treatments were predicted within 1 6 days.

The simplified static equations more closely predicted both time
to visible bud and time to flower (Table 1A) than did the equations
in the dynamic model (Table 15). This increased error in the dynamic
model prediction is most likely due to error in the plant parameter
estimates made by the model itself which were in turn used to
calculate the flowering parameters. If a static environmental
condition were known to exist. the simplified equations may result in
better predictions. Unfortunately, greenhouse and field conditions
are dynamic. and a full simulation model is necessary to track the
development under such conditions. A further alteration in the model
might predict flowering based upon a long-term environmental
averaging for the environmental parameters. and the simplified
equations might be incorporated into the dynamic model. Optimization
routines such as Complex or Powell (A9) might be used to determine

the optimum number of days to be used in long-term averaging which

53

would most accurately predict flowering even with the dynamic
environmental data as input to the model. For accurate computer
simulation, the dynamic model is a necessity. but the simplified
equations may be used to make reasonable estimates under field or

greenhouse conditions.

Biological Significance p: Eguations

lrradiance

Table 16 shows the response of geranium flowering, height . and
and dry weight accumulation to_irradiance level as predicted by the
model after 126 days of simulated development. Both days to visible
bud and days to flower decreased with increases in irradiance level
at constant day (250 C) and night (200 C) temperature. This agrees
with the findings of Armitage et al. (8.10) who found time to flower
to decrease to some asymptotic minimum for 3 hybrid geranium
cultivars as irradiance increased from 100 to 1200 u mol s-‘m-2. The
minimum possible days to flower was found to be near 100. 88. and 98
days for 'Sprinter Scarlet‘, 'Sooner Red'. and ‘Ringo‘. respectively.
The model results in Table 16 indicate an asymptotic minimum of about
75 days to flower for 'Red Elite‘ at 25° C day temperature and 20°C
night temperature. Higher day and night temperatures throughout the
experiments of Armitage et al. (10) of 25 i 30 C or 28 1 2° C may
have effectively raised the asymptotic minumum as will be discussed
later under day and night temperature effects on geranium growth.

Both stem and leaf canopy height were shown to decrease with

increased levels of irradiance (Table 16). Lower irradiance levels

. 5A

may permit auxin production to cause stem elongation while increases
in irradiance may work to inhibit auxin action. resulting in less
elongation of stem and leaf tissue. This response to lower
irradiance would promote elongation under crowded growing conditions,
a response which would appear advantageous to allow individual plants
in cultured or natural states to collect maximum available incident
irradiance.

Root, stem. and leaf dry weights were shown to increase with
increased levels of irradiance (Table 16). These findings parallel
those found for Chnyxanzhemum (A6). The additional energy available
under higher irradiance levels enables more carbon to be fixed and
stored in plant tissues. Geranium flower dry weight attained a
maximum value at 250 u mol s-'m-2. while total dry weight reached a

maximum at 300 u mol 5-1m-2 (Table 16). The decrease in total dry

weight with irradiance increases above 300 u mol s.‘m-2 can be
attributed to both the change in plant growth morphology once
initiation has occurred and a related partitioning of the available
carbohydrate. Following initiation, new leaf emergence is slowed due
to the increased competition with the bud for carbohydrates. Earlier
initiation, as accompanied by decreased time to visible bud. would
generally be associated with a lower total amount of carbohydrate at
the point of initiation. The tendency of the bud to be a strong sink
for carbohydrate would enable it to outcompete newly emerging leaves
for the carbohydrates available.

If the initiation occurred early enough in development so the

carbohydrate pool was too small to supply both the bud and new

leaves. the new leaves might be inhibited in their development.

55

Since new leaves would be slower to develop and would attain a
reduced size. less irradiance could be intercepted and converted to
carbohydrates. Thus. competition of the bud with newly emerging
leaves could cause reduced ability to produce carbohydrate in the
future. with an end result that potential total dry weight would
appear decreased. Since the carbohydrate pool at initiation was low,
the amount available to the rapidly growing bud would be reduced, and
the final dry weight attained by the bud itself would also be less.
Thus, the model indicates that the greatest overall flower and plant
size could be potentially realized between 250 and

300 u mol 5-1m 2 irradiance level.

Q21 temperature

Table 17 shows the response of geranium flowering, height. and
dry weight accumulation to day temperature as predicted by the model
after 126 days of simulated development. Minimum time to visible bud
occurred at 2A0 C day temperature. while minimum days to flower and
minimum time from visible bud to flower occurred at 27° C. This
suggests that 2A° C is optimum for initiation. and 27° C is Optimum
for flower bud development. Armitage (8) fit a simple quadratic
regression model which showed most rapid flower bud development to
occur near 270 C constant temperature. At this temperature flower
size was found to be reduced from that seen to occur at lower
constant temperatures. Thus, although most rapid flower development
occurs under higher temperatures. lower temperatures are necessary to
allow flowers to attain a maximum size and quality.

In general, one would expect low temperatures (below 10°C) to

56

slow both initiation and flower bud development due to the slowing of
chemical reactions within the plant. Excessively high temperatures
(above 30°C) might also slow initiation or bud development due to
excessive metabolism of carbohydrate reserves which are necessary for
flowering. Some optimum temperature should exist between these
extremes. In the stressed greenhouse experiment, initiation was seen
to be promoted at constant 30°C temperature and high
(200 i 50 u mol 5.1m"2 ) supplemental irradiance early in
development. The higher day temperature may have enabled the plant
to make use of the higher incident irradiance energy. Under lower
irradiance, less energy would be available to the plant. and higher
day temperature would raise plant metabolism to use more of the
carbohydrate reserves. Under normal greenhouse conditions.
i.e. lower irradiance levels. the optimums predicted by this and
Armitage‘s (8) work would be expected. The differences in minimums
for initiation and bud development suggest that 2Ao C day temperature
from sowing to visible bud and 27° c from visible bud to flower would
achieve the minimum time to flower for geranium. although maximum
flower size would not be seen to occur from using this strategy.

Both stem and leaf canopy height showed a trend to increase with
increasing day temperature (Table 17). This trend is the same as
that observed for Chnyxanthamum (A6). However. above 280 C day
temperature the plant canopy height tended to decrease. As with
flowering, the metabolism of the carbohydrate reserves at high
temperatures might lnterfer with the petiole elongation. The general
trend for taller plant growth with increased day temperature could

result from either an increase in cell number or increased cell

57

elongation. Further work is necessary to determine which one, or if
both, of these plant responses actually occurs.

Root, stem, leaf. and total dry weight were all observed to
decrease as day temperature increased under constant night
temperature and irradiance (Table 17). At day temperatures lower
than 200 C, dry weight at some point would be expected to decrease
with decreasing day temperature due to the slowing of chemical
reactions in the plant. Above 30°C the dry weights would be expected
to decrease with increasing day temperature since higher day
temperatures require more carbohydrate reserves for plant growth and
maintenance functions. Flower dry weight was predicted to be
greatest at 23°C. This conflicts with the results found for the
Chhyaanthemum, where increased flower dry weight occurred with
decreasing temperature (A6). Because of the differences in optimum
temperatures for the rate of flower bud development and flower dry
weight, it does not appear likely that earliest flowering and maximum
flower size can be obtained simultaneously by merely controlling day
temperature. Some trade off must be made between achieving earliest

possible flowering and obtaining maximum flower size.

Night temperature

Table 18 shows the response of geranium flowering, height, and
dry weight accumulation to night temperature as predicted by the
model after 126 days of simulated development. Both days to visible
bud and days to flower increased with increases in night temperature
as day temperature (250 C) and irradiance (250 u mol sn‘m“2 ) were

kept constant. Karlsson (A6) found the same trend for flowering for

58

Chnyaanthemum, although night temperature was less highly correlated
to flowering than were irradiance or day temperature. Data in Table
1A show that at 15°C night temperature the time to visible bud (67
days) was increased over that at 20 and 25°C (62 and 61 days,
respectively). Also, flowering was hastened at 25°C night
temperature (82 days) over that seen at 15 and 20°C (88 and 92 days.
respectively). The model did not reflect these results. suggesting
that although these trends appear in the data means. the values for
the individual plants varied substantially enough that the regression
equations based on the data would predict values which were not
significantly different statistically. Sampling of a greater number
of plants would have enabled the model to be more sensitive to the
night temperature and reflect trends which naturally vary less
greatly in magnitude. In general. the results could not indicate a
significant change in visible bud or flowering times over the 15-25°C
range for night temperature. although the data indicate low night
temperatures delay both visible bud and flowering.

The geranium model shows night temperature to have less effect
on the absolute change in time to visible bud and flower than either
irradiance or day temperature (Tables 16 and 17). Also. since night
temperature was not included in the days to visible bud equation. the
night temperature effect on initiation must occur indirectly such as
through transport of carbohydrates to the storage pool in the stem.
Delay in both visible bud and flowering may be due to the increased
metabolic rate necessary for plant growth and maintenance competing
for the available carbohydrate pool. No significant change in days

to flower occurred between 17 and 25°C night temperature.

59

Stem height was shown to increase with increased night
temperature. while leaf canopy height was maximum at 17°C (Table 18).
The effect of night temperature was less in absolute terms than the
effect of day temperature (Table 17). Karlsson (A6) found similar
results for Chngsanthcmum, indicating day temperature to
significantly affect stem height. while night temperature had no
significant effect. Since the natural error in measuring leaf canopy
height was near .5 cm. the effect of night temperature on leaf canopy
height can be considered not significant for 15-21°C. while decreased
leaf canopy height at higher temperatures might be influenced by the
added competition of all plant tissues for available carbohydrates.

Root. stem, and leaf dry weights increased with increases in
night temperature (Table 18), while the magnitude of the changes were
not as great as those as those seen for day temperature (Table 17).
Day temperature may be thought to have a greater effect on dry weight
of these tissues than the night temperature. Increased night
temperature over the 15-25° C range studied might act to promote
transport and storage of carbohydrates which were assimilated by the
plant during the daytime. Flower dry weight was shown to decrease
with increased night temperature (Table 18). possibly indicating that
although more carbohydrates are stored in root, leaf. and stem tissue
over dark periods. fewer carbohydrates are transported to the flower
bud, and a higher metabolism rate at higher night temperatures uses
up a portion of the bud‘s internal reserves. Although maximum total
plant dry weight was shown to occur at 22°C night temperature. the
total dry weight change over 20-25°C was most probably not

significant. The gain in total dry weight between 15-20° C may

60

result from increased transport and storage in root, stem. and leaf
tissue with increased temperature. while above 200 C the additional
stored carbohydrates are used up with increased rates of metabolism.
Considering these effects. changes in day temperature and irradiance
both have more marked influence on dry weight than changes in night

temperature .

Model checking and validation

A model should be accurate in reproducing the data from which it
was derived and also be able to predict the results found from other
data if the other studies were conducted inside the model‘s original
design space. With a static single-equation model the original
measured values should be very easily reproduced. In time-varying
models where several parameters are interdependent. the agreement
between measured and predicted values may be prone to error which is
accumulated over time. causing short-term errors to be enlarged in
the long run. The time-varying model must be checked against the
original data to assured that the approaches taken are correct to
reproduce the original conditions accurately. To be truly effective
models. both static and time-varying models must be tested under new
conditions which should be within the confines of the original
design. A model which accurately predicts the results obeserved
under new situaions can be successfully used in new practical
situations. This section discusses both the model‘s accuracy in

reproducing the trends found in the original data and also in

61

predicting the results found under 2 different greenhouse situations.

For figures describing the same plant parameter, the y-axis
scale is kept constant to permit easy comparison of the figures.
After the first reference to a treatment by the number corresponding
to those listed in Table 2. a sequence of 3 numbers is used to refer
to the levels of PAR, day temperature. and night temperature which

were used over the course of the treatment.

Visible Egg ppg Anthesis

A comparison was made between the data measured in the growth
chamber experiment and the predictions made by the model for times to
visible bud and flower (Table 15). Predictions within A days of the
actual values were made for visible bud for 9 of the treatments:
predictions within A days were made for days to flower for 7 of the
treatments. Best estimates occurred under moderately high PAR levels

-1-2)

(350 u mol s m , while treatments having very low (80 u mol

s-lm- ) or very high PAR (A20 u mol s-lm-z ) were underpredicted
(Table 15). Treatment 5 (150-28-23) which had moderately high day
and night temperatures and lower PAR had the greatest differences for
visible bud (19 days) and flower (1A days). Sizeable discrepancy
also occurred in treatments 7 (250-25-15) and 9 (250-30-20) where the
differences between the day and night temperatures were greatest
(10°C). Although large differences between actual and predicted
values for flowering seemed to occur with large differences in time
to visible bud (treatments 1.5.7), prediction was in some instances

closer for flowering time regardless of large differences occurring

for visible bud (treatments 9,1A.15). and for some treatments the

62

differences in prediction for flowering were greater than for visible
bud (treatments 2,A,8,10). In general, the model best predicted both
visible bud and flowering under conditions of similar and relatively
low day (20-22°C) and night (17-20°C) temperatures with mooerately

high PAR (250-350 a mol s"m'2 I.

Flowering of a greenhouse crop
would be best predicted under conditions of moderately low day and

night temperatures with application of supplemental PAR.

Total Dry Weight

The actual and predicted values for plant total dry weight (DWT)
are plotted for 3 treatments from the original growth chamber
experiment in Figures 3-5. The actual and predicted curves agreed
best in absolute terms prior to A2 and after 98 days for treatment 10
(250-20-20). with the greatest difference occurring around 8A days
(Flgure 3). For treatment 7 (250-25-15). close agreement occurred up
until 70 days. with greatest error also occurring at 8A days
(Figure A). Treatment 1 (85-25-20) agreed quite well prior to 56
days and after 98 days from sSwing. with the greatest absolute error
occurring again at around 8A days (Figure 5). The lower light
85-25-20 treatment tended to underpredict. while the 250-25-15
treatment containing high day temperature and low night temperature
tended to overpredict the total dry weight. Interestingly. the
greatest absolute errors tended to occur at around 8A days for all 3
treatments. The nature of the model to linearize the apparently
nonlinear plant response using 2 separate equations may have
contributed to this error.

The model accurately predicts the plant growth trends for total

63

dry weight. Greatest total dry weight accumulation over time was
seen to occur under the 250-20-20 treatment. conditions of moderate
PAR. moderate day temperature. and moderate night temperature.
Minimum total dry weight accumulation occurred under low PAR
conditions for treatment 85-25-20. With moderate PAR levels.
moderately high day temperatures. and low night temperatures
(250-25-15) the plants had an increase in total dry weight observed
to be between those of the other 2 treatments (Figures 3.A.and 5).
The model functions as an accurate representation of the total dry
weight trends seen in the original data. Total dry weights measured
in both the stressed and unstressed greenhouse experiments cannot be
compared with the predicted model estimates because root dry weights
were not measured in the greenhouse experiments. Only values for the
separate plant parts may be compared with the model for those

experiments.

Stem and Leaf 9&1 Weight

Comparisons of the actual and predicted dry weights of stems and
leaves are plotted in figures 6-8. Very good agreement exists for
both the 250-20-20 and 250-25-15 treatments (Figures 6 G 7), but both
parameters tended to be underpredicted for the 85-25-20 treatment
(Figure 8). The model underpredicts the absolute stem and leaf dry
weights under conditions of low PAR. The overall trends in dry
weight accumulation were quite accurately predicted. The model
predicted maximum dry weight accumulation for both stems and leaves
under conditions of moderate PAR (250 u mol s-lm'z). and also

moderate day (20°C) and night (20°C) temperatures (Figure 6). Low

6A

night temperatures (250-25-15) under moderate PAR were associated
with moderate dry weight accumulation (Figure 7), while low PAR
conditions and moderate night temperature conditions (85-25-20) were
associated with lower dry weight accumulation (Figure 8).

The model results have been compared with the stem and leaf dry
weight data from both the unstressed greenhouse (Figure 9) and
stressed greenhouse experiments (Figure 10).' The overall predictions
of leaf and stem dry weight fit quite closely the results measured in
the unstressed greenhouse experiment (Figure 9). although the
measured data makes considerable deviation from a smoothly curved or
straight line. The mean environmental inputs may be described as
170-27-22 for the treatment. but the actual measured environment
changed over time. Two-week means of the actual measured greenhouse
conditions were used as inputs to the model.

Two-week means were also used as the environmental inputs to the
model when predicting the stressed greenhouse growth. The constant
high temperature (30°C) and high supplemental high pressure sodium
(HPS) irradiance (150-250 a mol s-‘m-2) for days 21-33 from sowing
caused overprediction of the leaf dry weight and underprediction of
the stem dry weight at A2 days of growth. The model appeared to
recover more quickly from the stress treatment than did the plants
themselves and thus overpredicted leaf dry weight in later
development. The model also made slight overpredictions in stem dry
weight after 8A days in response to the leaf dry weight
overprediction beginning at around and after 70 days from sowing.
These results indicate that the model functions quite well to predict

PelangonIum X hantonum Bailey growth under normal greenhose

65

conditions. but the model could be too insensitive to stresses to
allow it to accuratelly follow plant growth under relatively abnormal

growing conditions.

 

 

Actual leaf area measurements from the growth chamber
experiments and the model predictions are plotted in figures 11-13
for 3 treatments. Predictions agreed quite well with the data from
treatments 250-20-20 (Figure 11) and 250-25-15 (Figure 12). although
a sizeable discrepancy for the treatment 250-20-20 occurred after 98
days. The randomized sampling of plants at 98 days for this
treatment may have selected 6 plants with larger than average leaf
area: this is suggested by the abnormally high leaf area at 98 days
which does not fit well into the general trend of increasing leaf
area over time exhibited in Figure 11.

The model underpredicts leaf area for treatment 85-25-20
(Figure 13). These deviations were due to the functional
relationship between leaf dry weight and leaf area. since leaf dry
weight was also underpredicted for this treatment (Figure 8). This
also shows the effect of accumulating error over the long run, since
leaf area is functionally dependent on the previous leaf area as
well. The model effectively portrays the trend of increased leaf
area under moderate day and night temperatures and moderate PAR
levels (Figure 11), but underpredicts the values measured for lower
light conditions (Figure 13). Alterations in the functional
relationships for leaf area could improve this prediction. A

function for leaf area including environmental terms along with the

66

plant parameter terms might allow better prediction of leaf area even
when values for leaf dry weight tend to be low.

When the model was used to predict leaf area for unstressed
greenhbuse grown plants (170-27-22). the underpredition became quite
apparent after 56 days (Figure 1A). The model was not able to
completely recover from the earliest underpredicted values. This
might have been due in part to the PAR received which was below the
mean PAR level used in the growth chamber experiments. and partly due
to leaf dry weight which was underpredicted for days 56-70 from
sowing. A comparison of the model estimates with measured leaf area
for stressed greenhouse grown plants found quite close agreement up
until 56 days. and close agreement around 112 days (Figure 15). The
slower change in the model predicted values for leaf area after the
applied stress treatment seemed to parallel the actual response of
the plant to a stress treatment. This suggests that the model might
be improved for predicting growth after stress treatments by adding
factors to the equations or subroutines which would decrease their
response to the environmental conditions occurring subsequent to a

stress .

Further Research

Further work could be conducted to improve both the single
equations and the overall predictability of the model. A truly
dynamic systems approach based on derived rate equations would be
preferred over the state equations used in this model. Equations
which are nonlinear instead of linear in nature would seem more

appropriate for predicting plant growth responses which other

67

researchers have described as nonlinear (2.12.32.70.71.81,82). The
model could be further broken down into plant growth stages. such as
the time up to the fifth leaf stage. the subsequent time to visible
bud, the subsequent time to anthesis for the first inflorescence, and
the subsequnt time to anthesis for each successive inflorescence.
The model equations might be refit to the data. grouping the
treatments on the basis of the mean PAR level received. or grouping
may be made based on specific temperature ranges. The equations
might also be based on the individual plant data instead of the
treatment means at each sampling. but this would incur considerable
increases in computer costs' and programing complexity. The 2
approaches, individual plant and mean plant growth data, might be
compared directly to determine if the sample means alone are indeed
adequate. In particular. the prediction of flowering alone could be
improved through regressions with individual plant data rather than
from the means. Any of these changes in the model equations could
potentially improve the prediction by the simulation model.

The total model structure might be reorganized in attempt to
improve prediction over a wide range of environments. Addition of
subroutines for sismulation of stress treatments would appear quite
helpful, or separate subroutines might calculate growth parameters
under different mean levels of PAR to simulate the actual seasonal
fluctuations. The method for determining the time to visible bud and
flower may have been oversimplified in the present model, and more
elaborate and creative approaches might be implemented. Total dry
weight might be calculated via a single regression equation. This

method would effectively predict the partitioning by fusing the

68

various plant parts into a single regression. and then separating the
overall carbohydrate gain into the different parts by using
relationships estabished for the percentages partitioned under
different environments. These major alterations in the model
structure might all be used to increase the model's accuracy of
prediction over a wider range of environments.

Studies could also be conducted using the existing model. A
Monte Carlo analysis run with the existing model could explore the
effects of random daily or seasonal fluctuations in PAR or
temperature upon plant growth. Data collected by the weather service
over successive years might' be used as input to the model and
comparisons could be made between the years to determine the maximum
and expected variability which would be observed for crops in
successive years. The input data might need some sort of
transformation before application could be made to the growth of
plants under a greenhouse situation. A thorough sensitivity analysis
should be conducted to determine which plant parameters are most
sensitive to changes in the measured environment. Since not all
plant characteristics could be feasibly measured in this study,
optimization routines such as Complex or Powell (A9) could be used to
estimate unknown plant parameters. The existing model structure
could eaSily be adapted to preform any of these useful studies.

Further analysis could be conducted to check if the most basic
assumptions of the existing model are indeed valid and desireable. A
most basic step would be to change the order in which the plant
parameters were calculated. and appropriate regressions for that

order be fit to the data, with the realization that the implied

69

causal relationships are in no way absolute. Interestingly, the
chicken-egg argument might be the most releveht issue in deciding
which model approach to use. However. satisfactory models might be
possible for simulation of practical situations without complete
understanding of the actual causal relationships: unnecessary theory
and abstractions should be avoided in favor of simplicity and

functionality.

70

Table 1. List of variables and their definitions.

 

 

TIME
PSID

PSI”
P30”

TIME
STEP
DVB
UTE
NW
0H5
DH!

UHF
0N7
[A
HAM
”LC
PA”
FONS
FOAM
POND
PIA

PCTDHM :
PCTDWG :
PCTDHI :
PCTDHF :

-l -2
Photosynthetically agtive radiation (umol s m l
Day temperature / Cl
Night temperature ("Cl
Accumulated 2 week means of IT since sowing
Accumulated 2 week means of DT since sowing
Accumulated 2 week means of NT since sowing
Time elapsed since day if sowing (days!

Product sum of PAH and DT since sowing

IPAR1*DTi + PAR2*DT2 + ... + PARW*DTfll

Product sum of PAH and NT since sowing

(PAR1*NT1 + PARZ*NT2 + ... + PARfl*dTDi

Product sum of 07 and NT since sowing

lDTl*flTl + DT2*NT2 + ... + DTN*ATA/

Time since sowing (days)

A 14 day period (no units}

Days from sowing to visible bud (days)

Days from sowing to flower ldaysl

Node or loaf number (cotyledons are ll

Dry weight of stem lg/

Dry weight of leaves lg/

Dry weight of roots (91

Dry weight of flowers (9}

Total dry weight of plant lgl 2
Leaf area of leaves below first inflorescence (cm I
Height of apical meristem or stem height lcml
”eight of leaf canopy to tallest leaf (on)

Node number from previous sampling lg/

Dry weight of stem from previous sampling lg/
Dry weight of leaves from previous sampling lg}
Dry weight of roots from previous sampling lgl
Leaf area of leaves from previous sampling lg/
Root dry weight as percent of total /%/

Stem dry weight as percent of total /%/

leaf dry weight as percent of total /%I

Flower dry weight as percent of total 1%)

 

71

Table 2. Actual and coded values for treatment combinations used
in the central composite design for growth chamber

 

 

 

 

 

experiments.
0
PAR Temperature 1 Cl Coded Values
Treatment -- —
-1-2
number lumol s m / Day Night PAR DT NT
1 8D 25 20 -1.88 D D
2 150 22 17 - 1 - 1 - 1
3 150 22 23 - 1 - 1 1
4 150 28 17 - 1 1 - 1
5 150 28 23 - 1 1 1
5 250 25 20 D D D
7 250 25 15 D D -1.88
8 250 25 25 D D 1.68
9 250 3D 20 D 1.58 0
1D 25D 20 20 D -1.88 D
11 350 22 23 1 - 1 1
12 350 28 23 1 1 1
13 350 22 17 1 - 1 - 1
14 350 28 17 1 1 - 1
15 420 25 20 1.88 D D

 

72

Table 3. Actual and coded values for treatment combinations used
in the central composite design for greenhouse

 

 

 

 

 

experiments.
2 o
PAR Temperature 1 Cl Coded Values
Treatment
-1 -2
number lumol s m / Day Night PAR DT NT
1 25 29 23 -1.88 D D
2 8D 28 21 - 1 - 1 - 1
3 8D 27 23 - 1 - 1 ' 1
4 8D '28 21 - 1 1 — 1
5 80 - 3D 25 - 1 1 1
8 170 29 23 D D D
7 170 28 21 D D -1.88
8 170 28 25 D D 1.88
9 --- -- -- D 1.88 D
10 170 27 22 D -1.88 D
11 210 27 23 1 - 1 1
12 - 21D 30 25 1 1 1
13 210 27 22 1 - 1 - 1
14 210 29 21 1 1 - 1
15 230 29 24 1.88 D D

 

z PAR levels were adjusted by using 85 % and 85 % shade, natural
PAH, and 8D and 90 umol s.1 m-2 supplemental high pressure
sodium irradiance. Stressed treatments received 24 hours of
150-250 umol s-lm.2 supplemental DPS irradiance and 30°C

constant temperature during 21-31 days from sowing.

73

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Table 9. Independent factors, regression coefficients,
standard errors of the coefficients,
and significance level for regression
equation predicting flower dry weight
after visible bud stage for Pelargonium
X hortorum Bailey ’Red £lite’ grown in
growth chambers.

2
After Visible 8ud
Y .
Independent Regression Standard Significance
Factors coefficient error level

Constant -4.0401£-1 2.89185-1 NS

OHS/DH! 3.3209 5.98235-7 .01

0H8 ~2.9037 5.1188f-1 .01

0V8 -2.1230£-2 3.08405-3 .10

TIMI 1.40845-2 2.74805-3 .01

00M 5.68885-1 1.87845-1 .07

rows 7.2084 4.48825-1 .05

 

2 Time from visible bud stage through anthesis of
2

first inflorescence. R - .853 F - 5.83 **

Y HHS/8N1 - ratio of stem to leaf dry weight,
8H5 - stem dry weight, 0V8 - days to visible bud,
time since sowing, DH! - leaf dry weight,
eons - previous stem dry weight.

79

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icon r

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m<n_ 4<Dho< GIG

 

00¢

90

Figure 2. Generalized flowchart of the program flow for
GERMOD. a time-varying plant growth model
simulating Pafiangonzum X hontonum Bailey 'Red

Elite' development.

 

91

Figure 2.

 

C START )

 

 

r

PRINT HEADING

 

 

 

 

 

r

 

INITIALIZE
BOXC DELAY

l

INITIALIZE
EQUATION CONSTANTS
I

INITIALIZE
PLANT VARIABLES

 

 

 

 

 

 

 

 

 

 

 

 

7

STEP = 2 to 9 b——-@

 

 

 

 

 

 

    

READ
DATA FILE

GENERATE
RANDOM DATA

 

 

 

 

 

 

 

 

 

 

 

T

l in: 14 ‘L‘

l

CALL BOXC
DELAY

o

 

 

 

 

 

 

 

92

Figure 2. (cont'd.) Q

 

l

 

 

 

 

 

n A CALCULATE
$§§=3§fi§33 REPRODUCTIVE
” * PLANT VARIABLES

 

 

 

 

PLANT VARIABLES

 

 

      
 
  

DTP-DVB
3 20
9

 

 

 

INIT 2 TIME l FLR = TIME

 

 

 

 

 

 

 

 

 

 

    

DAILY 11+ DAY
PRINTING PRINTING

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3.

93

Actual total dry weight means for growth chamber
treatment 10 (250-20-20) and the values predicted
by the plant growth model GERMOD simulating
Paflangom’um X houowm Bailey 'Red Elite'

development for lh'llz days from sowing.

 

94

 

 

.0 MEDGE

o9 . mt. mm em on om we mm .1 I 0.0
m

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w
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m

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ON M
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. K E E... 85.8% ATS 1
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can

Figure A.

95

Actual total dry weight means for growth chamber
treatment 7 (250-25-l5) and the values predicted
by the plant growth model GERMOD simulating
Pdmgonéum X hon/town: Bailey 'Red Elite'

development for lh-98 days from sowing.

96

mNP .

 

 

 

.v meGE

 

ts >19 awhoammn. olo
._.>> *mo ._<2.0< ole

 

 

(5) .LHOIEM ABC ‘lViOJ.

Figure 5.

97

Actual total dry weight means for growth chamber
treatment l (85-25-20) and the values predicted by
the plant growth model GERMOD simulating
Peflangonium X honzonum Bailey 'Red Elite'

development for lh-l26 days from sowing.

 

98

 

 

 

 

.m mmDCE

 

its >mo omkoammd olo
._.>> 55 4<D._.o< I

lo.m

 

 

06

(6) iHSIElM ABC ‘IVICI

Figure 6.

99

Actual stem and leaf dry weight means for growth
chamber treatment l0 (250-20-20) and the values
predicted by the plant growth model GERHOD
simulating Peiangonium X honIOAum Bailey 'Red

Elite' development for lh-llZ days from sowing.

 

100

Mfdd .o MEDOE
Effie. mm em . on on me mm .1 o.

 

 

 

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5 En. es: .232 ......
. \ 5 $5 55 BEBE ole .
a\ E Ea 55 .222 o...

 

 

ON

Figure 7.

10]

Actual stem and leaf dry weight means for growth
chamber treatment 7 (250-25-l5) and the values
predicted by the plant growth model GERMOD
simulating Pefiangontum X honzonum Bailey 'Red

Elite' development for lA—98 days from sowing.

 

102

 

mm;

 

.N MEDGE

 

ts >mo “2m: om._.0_omm.n_ aim.
._.>> >mo .../DD ._<D_.o< Ill
._.>> 55 EEm QEQEMWE olo
...; >mo 23m ._<E.o< ele

 

 

ON

(6) iHOlE/Vl ABC

Figure 8.

103

Actual stem and leaf dry weight means for growth
chamber treatment l (85-25-20) and the values
predicted by the plant growth model GERMOD
simulating Peflangonium X hoatonum Bailey 'Red

Elite' development for lb-l26 days from sowing.

 

104

 

 

.m HEDGE

 

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._.>> >mO 25m OEbEmEn. ole
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ON

Figure 9.

105

Actual stem and leaf dry weight means for
unstressed greenhouse treatment l0 (170-27-22) and
the values predicted by the plant growth model
GERMOD simulating Pefiangonium X hantonum Bailey
'Red Elite' development for lh-llz days from

sowing.

 

106

 

ONF

m><O

.O mmDGE

 

._.>> >mO .../em... Omfioammm
.Es >mO .HZMD 4<DHO<
E 55 2m._.m Omfioammn.
._.>> >mO Eupm 4<DHO<

Elm

Ii!

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T

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6
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ON

Figure 10.

107

Actual stem and leaf dry weight means for stressed
greenhouse treatment l0 (170-27-22) and the values
predicted by the plant growth model GERHOD
simulating Pe£angonium X honzonum Bailey 'Red

Elite' development for lA-98 days from sowing.

 

108

 

 

is 55 .._<m._ Omfiofimmh. Elm
ts >mO need; ._<3._.O< III
E >mO s.....:.m Omzbammn. olo
._.>> 55 Emem 4<DHO< Ole

 

 

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in;

Figure ll.

109

Actual leaf area means for growth chamber treatment
l0 (250-20-20) and the values predicted by the
plant growth model GERMOD simulating Paflangonium.x
hontonum Bailey 'Red Elite' development for lh-llZ

days from sowing.

 

110

ON— N: mm

 

 

 

<mm< .._<m_.. OMHOEmmm olo
<mm< .._<m_.. ._<3HO< I

 

 

.wp mmDOE

(aw) vauv :l‘v’B'l

Figure l2.

111

Actual leaf area means for growth chamber treatment
7 (250-25-l5) and the values predicted by the
plant growth model GERMOD simulating PBKQAQOflXlun X
honzonum Bailey ‘Red Elite' development for llr-98

days from sowing.

 

112

ONF

NPP

 

 

 

<mm< i._<m.. empoammn. ole
<mm< ...<m_._ ._<D_.O< I

O

..OOP

1

low?

I

iOON

lomN

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loom

'

10mm

 

 

NF mmDOE

(3w) vaav :lVEl‘l

Figure 13.

113

Actual leaf area means for growth chamber treatment

l (85-25-20) and the values predicted by the plant
growth model GERMOD simulating Peflangonium .X
huhtonum Bailey 'Red Elite' development for lh-l26

days from sowing.

 

114

ONF

 

 

 

<mm< “Em: Om._.O_Om1n_ olo
<mm< .../DD ._<2.o< ole

 

 

.mp meGE

(aw) vaav sic-n

Figure lh.

 

115

Actual leaf area means for unstressed greenhouse
treatment l0 (l70-27-22) and the values predicted
by the plant growth model GERMOD simulating
Pe£angontum X honzonum Bailey 'Red Elite'

development for lh-llz days from sowing.

 

116

ON?

 

 

 

<mm< i._<m._ Omfioammm olo
<mm< ...«mj 4<DHO< ele

 

 

.vp mmDGE

(3w) wav AVE—l

Figure 15.

117

Actual leaf area means for stressed greenhouse
treatment 10 (l70-27-22) and the values predicted
by the plant growth model GERMOD simulating
Peflangonium X honzonum Bailey 'Red Elite'

develOpment for lh-98 days from sowing.

 

118

ON?

.mwmmDOE

 

 

 

<mm< .../em... Omfioammn. olo
<mm< i._<m.d 4<DHO< ele

O

IOOF

Ion?

lOON

IOON

loom

fiOmn

 

 

(awe) vaav :lVEl‘l

APPENDIX

119

Table A1. Listing of GERMOD program for simulating the growth of
Pelargonium X hortorum Bailey 'Red Elite'

 

 

*UOBCARD*.RGI.JC299.

ATTACH.ENV.TCENV9ACC.

EDITOR.E=ENV.
HAL.BANNER.HOPPERS.CHAMBER.GERANIUM.MODEL.
FTN5.ANSI.DB=PMD.

LGO.

SAVE.110-1810.TAPE5.

PROGRAM GERMODIINPUT.OUTPUT.TAPE5.TAPES)
C THIS PROGRAM IS IN FILE: TFMODELLIST
C THIS PROGRAM ATTACHES DATA FILE TCENVQACC WHICH CONTAINS THE
C 2 WEEK MEANS OF ENVIRONMENTAL DATA FOR THE GROWTH CHAMBER EXPERIMENTS
C THE FILES TGENVQACC AND TSENVQACC MIGHT ALSO BE USED FOR DATA
C FROM VALUES MEASURED FOR THE UNSTRESSED AND STRESSED GREENHOUSE
C EXPERIMENTS RESPECTIVELY
REAL DVB.DTF.NN.DWS.DWL.DWR.LA.HLC.HAM.LT.DT.NT
REAL BNN(7).BDWS(7).BDWL(10).BDWRI7).BLA(7).BHLCI7)
REAL BHAM(7).BDV8(12).BDTF(7).BDWF(7)
REAL BNN2I8).BDW52(7).BDWLZI7).BDWR2(7).BLA2(7).BHLC2I7).BHAM2(8)
REAL NNTR(14).DWSTR(14).DWRTR(14).DWLTR(14),LATR(14)
REAL LTA.DTA.NTA
INTEGER INIT.FLR
C IF IPRINT IS 0 THEN EACH DAY IS PRINTED. ANY OTHER VALUE USED FOR

C IPRINT WILL PRINT EVERY 14 DAYS
IPRINT ' 1
C IE IRAND IS 0 THEN RANDOM ENVIRONMENTAL DATA IS GENERATED ABOUT
C AVGLT.AVGDT. AND AVGNT. ANY OTHER VALUE USED FOR [RAND WILL
C ATTEMPT TO READ FROM AN ATTACHED DATA FILE (TAPES).
IRAND = 1
AVGLT 3 250.
AVGDT = 25.
AVGNT 3 25.
C
C THIS OUTERMOST LOOP ALLOWS SEVERAL TREATMENTS TO BE RUN THROUGH
C THE MODEL IN THE SAVE BATCH JOB RUN: DATA FOR LT.DT AND NT
C MUST EXIST LOCALLY AS TAPES WITH THE FORMAT LISTED IN
DO 5000 ITRTS= 1. 19
WRITEI‘.‘)' TREATMENT ” '.ITRTS
WRITE(‘.')’ '
C
C PRINT OF HEADING FOR VARIABLES
WRITE(*.")I TIME NN DWS DWL DWR LA HAM HLC INIT
+ FLR DVB DTF LT DT NT ALT ADT ANT DWF DWT PCTS
+PCTL PCTR PCTFI
WRITE(#I e)’3:3:::================:=======:=:=:==:::::=::=========:
+sII=========a==z====z======================:======================
+I=============’
C
C SET LENGTH OF DTT. THE LAST PERIOD FDR STEP. AND THE LENGTH OF STEP.
C STEP SHOULD ALWAYS EQUAL 1.0: THE WAY THIS PROGRAM HAS BEEN WRITTEN
C ONE STEP IS A TIME PERIOD OF 14 DAYS

DTT 8 1.0 / 14.0

120

 

Table A1. (cont'd)
TLPER = 9.0 + DTT/1000
STEP 3 1.0
C
C A.B. AND C ARE STANDARD DEVIATIONS FOR LT.DT.AND NT IF IRAND = O
C AND THE USE OF RANDOM DAILY ENVIRONMENTAL DATA IS DESIRED
A = 75.0
8 = 2.0
C 8 .5

000

4000

C

C CDNSTANTS FOR

NOCY

CONTINUE

SUMNN

SUMDWS
SUMOWR
SUMDWL

SUMLA
NCNN
NCDWS
NCDWR
NCDWL
NCLA
PNN
PDWS
PDWR
PDWL
PLA

BNN (
BNN (
BNN (
BNN (
BNN (
BNN (
80w5(
sowst
Bow5(
BDws(
80w5(
80HS(
BDWL(
aowL(
BowL(
BDWL(
BDwL(
80wL(
BDVL(

1)
2)
3)
4)
5)
6)
1)
2)
3)
4)
5)
6)

uuuuuuuuuuuuulu

uuuuuuuuuuu

Ilfllllllllllu

“RUIN-b

O<DC>O<D

THE

OCDQCDCJOCDC>O<D O<DC>O<>§

O<DC>O<DC>O

O

.0001

.0001
.0010
.0001
.0080
.0001

INITIZALIZING VALUES FOR BOXC DELAY ROUTINE
VALUES FOR 5 DIFFERENT PARAMETERS

MUST BE INITIALIZED

REGRESSION EQUATIONS: VEGETATIVE STAGE

UltD-AQ—N

.4345
.5965
.8741
.4098
.9154
.1032

mmmmm

.0185302
.0000544755
.0008458553
.4370583
.2486944
.0000063742

.02664460

.00124988
.00022773
.43616284
.03908161
.00034706
.00221693

-2
'2
'2
‘2
‘6

)2)

 

Table A1. (cont'd)
80wL( 8) = - 1.00779406
BDWL( 9) = .00499474
BDVR( 1) . .69830337
BDUR1 2) = .00322577
80wR( 3) = .17439752
BDWR( 4) = - .00043884
BDWR( 5) = - .07547729
BDWR( 6) = .00200199
BDWR( 7) = - .00011356
BLA ( 1) = 10.76562
BLA ( 2) = 185.04139
BLA ( 3) = .93611
BLA ( 4) = -197.333
8HLC( 1) = .361642
BHLC( 2) = - .066404
BHLC( 3) = .032112
8HLC( 4) = - 1.55666 E -3
8HLC( S) = - 5.5711 E -4
BHLC( 6) = 3.2965 , E -3
BHAM( 1) = .057893
BHAM( 2) . .0098013
8HAM( 3) = .0064755
BDV8( 1) = 1.6874 E 2
BDVB( 2) = 4.3353 E -3
80V8( 3) = - 3.1263 E -2
BDVB( 4) = - 8.9843
80V81 5) = 1.606 E -1
BOVB( 6) a 1.3932
Bova( 7) = 1.6392 E -1
80V8( 8) = 7.9348 E -6
BDVB( 9) = 3.1173
BDVB110) = - 2.5333 E 1
80V8(11) = 3.6958 E 1
BDVB(12) = - 1.0160 E 1
BDTF( 1) = 67.790115
BDTF1 2) = 0.412528
BDTF( 3) = - 2.385916
BDTF( 4) ’ 0.354760
BDTF( 5) = - 0.022657
BDTF( 6) = 1.809343

0

C CONSTANTS FOR EQUATIONS AFTER VISIBLE BUD
8NN2 ( 1) = 8.1665844
8NN2 ( 2) = .00958846
BNN2 ( 3) = - 1.0292 E -5
BNN2 ( 4) = .3274393
BNN2 ( 5) = - 5.441442
BNN2 ( 6) = 2.53172
8NN2 ( 7) = - 2 04017646
eunz 1 3) = 1.109579
BDWS2( 1) = - .149415
BDws2( 2) = .905602
80ws2( 3) = 2.75449 E -4
BDWS2( 4) = - 9.2542 E -6
Bows2( 5) = .0134563
80w52( 6) = - 4.3831 E -6
BDHL2( 1) = - .327149
80HL2( 2) = .7810647
BDVL21 3) = 1.3261 E -4
BDWL2( 4) = .769690
80wL2( 5) = - 1.2096 E -4

Table Al. (cont'd)

122

 

80wL2( 6) = .0515193
BDWR2( 1) = .168627
80wR2( 2) = .114728
BDWR2( 3) = .348356
BDVR2( 4) = - 1.6742 -4
BDHR2( 5) = .085981
BowF ( 1) = - .404005
BDwF ( 2) = 3.320186
BDUF ( 3) = - 2.903705
BowF ( 4) = - .021230
BDWF ( 5) = .014084
BDHF ( 6) = .568680
BowF ( 7) = 1.208402
BLA2 ( 1) = 27.187467
BLA2 ( 2) = 126 54664
BLA2 ( 3) = .367976
BLA2 ( 4) = - .10430
BLA2 ( S) = 291.7804
BLA2 ( 6) - -102.650
8LA2 ( 7) = .43693
BHLC2( 1) = 3.10511
BHLC2( 2) 8 .0104752
BHLC2( 3) = 1.241657
BHLC2( 4) = .007519
8HLC2( 5) = - 4.50577
BHLC2( 6) a - .157386
c
C INITIALIZING PLANT DATA
TIME - 14.0
0V8 = 0.0
DTF = 0.0
MM = 1.5
ows = 0.0001
OWL = 0.0064
own = 0.0030
our = 0.0
OUT = 0.0095
LA . 2.3
HAM = 0.0001
HLC a 0.51
pCTows . ow /DWT
pCTouL - owL /DWT
PCTDHR a own /0wT
PCTDHF a UHF /DWT
INIT . o
FLR a 0
LT = 170.0
OT = 21.0
NT = 21.0
ALT = 170.0
ADT = 21.0
ANT = 21.0
LTA = 170.0
DTA a 21.0
NTA . 21.0
PSLN . 3570.0
PSLD . 3570 0
PSDN s 441.0
c A1 - 1.65

C THIS IS A DUMMY READ TO KEEP READ OF ORIGINAL DATA IN STEP
IF I IRAND .NE. 0 ) READ(5.10)LT.DT.NT

123

Table Al. (cont'd)

 

WRITE(‘.')’ ’

WRITE('.500)TIME.NN.DWS.DWL.DWR.LA.HAM.HLC.DVB.DTF,

+ INIT.FLR.LT.DT.NT.ALT.ADT.ANT.DWF.DWT.PCTDWS.PCTDWL.

+ PCTDWR.PCTDWF
C ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
C CREATING DO LOOPS STEP DAILY THROUGH TIME FROM 14 TO 126 DAYS
C ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
C THE FIRST LOOP ADVANCES THROUGH STEPS 2 TO 9

DO 1000 PRINTR 3 STEP'2.0.TLPER .STEP
C
C READ 2 WEEK ENVIRONMENTAL MEANS FROM ATTACHED DATA FILE (TAPES)

IF ( [RAND .NE. 0 ) READ15.10)LT.DT.NT
10 FORMAT(3X.3F5.0)

C

C3==3=BB=ISSSSISSSS======3323328:3===SSSSSSBI=8383222332332232322333228

C DAILY STATE VARIABLE CALCULATION AND CALLS TD ENVGEN

CSUBSQIISSISQCSI3.3338332==3832=S38838.333I'I3333::3.’83'I.'...I.SIICBI

C

C INNER DO LOOP TRAVELS 14 DAYS WHICH IS ONE STEP: THIS FEATURE
C FACILITATES PRINTING AND IS DEPENDENT ON IPRINT

C

DO 2000 T ' (PRINTR - STEP) + DTT- (DTT/10000).PRINTR.DTT
TIME 8 14.0 t T

00

CHECK IF RANDOM ENVIRONMENTAL DATA IS DESIRED: GENERATE THE VALUES
IF (IRAND .E0. 0 ) THEN
CALL ENVGEN ( A . ELT)

CALL ENVGEN ( 8 . EDT)
CALL ENVGEN ( c . ENT)
LT . AVGLT + ELT
DT : AVGDT + EDT
NT 2 AVGNT + ENT

END IF

()0

CALCULATE ACCUMULATED ENVIRONMENTAL AND INTERACTION TERMS
ALT = ALT + DTT ' LT
ADT 3 ADT + DTT * DT
ANT 2 ANT + DTT 3 NT

PSLN = PSLN + OTT*(LT*NT)
PSLD = PSLD + DTT*(LT*DT)
PSDN 3 PSDN + DTT‘(DT*NT)
C
C CALLS TO BOXC GIVE VALUES OF PREVIOUS PLANT PARAMETERS
C WHICH OCCURRED 14 DAYS EARLIER
CALL BOXC (NN ,PNN .NNTR .NC .NOCY.LLT.SUMNN )
CALL BOXC (DWS .PDWS .DWSTR.NCDWS .NOCY.LLT.SUMDWS)
CALL BOXC (DWR .PDWR .DWRTR.NCDWR .NOCY.LLT.SUMDWR)
CALL BOXC (DWL .PDWL .DWLTR.NCDWL .NOCY.LLT.SUMDWL)
CALL BOXC (LA ,PLA . LATR.NCLA .NOCY.LLT.SUMLA )
C
C CALCULATE PLANT PARAMETERS FOR TIME PRIOR TO VISIBLE BUD (INIT=O)
C OR FOR TIME AFTER VISIBLE BUD (INIT NOT EQUAL 0)
IF ( INIT .E0. 0 ) THEN
MN 3 BNN(1) + 8NN(2)*ALT + BNN(3)*ANT +
+ BNN(4)*LT + BNN(5)*NT + BNN(6)'ALT'ALT
DWS = BDWS(1) + BDWS(2)‘ADT + BDWSI3)*ANT +
+ BDWS(4)‘PDWS + BDWS(5)*POWL +
T BDWS(6)*ADT*ADT
DWL = BOWL(1) + BDWL12)’ADT + BDWL13)*ALT +
+ BDWL(4)*PDWL + BDWL(5)*NN +

+ BDWL(6)*PSDN + BDWL17)*PLA +

124

Table A1. (cont'd)

 

+ BDWL(8)*PDVR + 80WL19)*ANT
own = BDWR11) + 80HR(2)«ANT + BDWRI3)'DWL +
+ BDWR14)*DT + BDWR15)*NT +
+ BDWR(6)* NTtNT + BDwR17)vaDN
DWT = Dws + DwL + DWR
pCTDws = Dws /DWT
pCTDwL = DwL /DWT
pCTDwR = own /Dwr
LA a ( 8LA (1) + 8LA (2)’DWL + 8LA (3)*PLA +
+ 8LA (4)tPDWL )
HAM = BHAM(1) + BHAM(2)*LA + BHAM(3)'PLA
HLC = BHLC(1) + BHLC(2)*NN + BHLC(3)*LA A
+ 8HLC(4)* DT' 0T + BHLC(5)*ANT~ANT +
+ 8HLC(6)'PSDN
C
ELSE
C
Dws = 8Dw52(1) + 80HS212)~PDws + 80w5213)*ALT +
+ BDUS214)*PSLD + 80w5215)'NN +
+ BDws2(6)tNTcNT-NT
DWL = 80wL211) + BOUL212)'PDHL + BDVL213)'ALT +
+ BDVL2(4)‘PDHS + BDVL2(S)*PSDN +
+ BOWL2(6)'NN
DWR = BDWR2(1) + BDWR2(2)'PDWR + BDVR213)*DVS +
+ 80WR2(4)*DT*DT + 8Dw2215)~PDWL
DwF = BDwF11) + BDHF(2)'DwS/DHL + BDHF13)vas +
+ BDwF(4)-Dva + BDVF15)‘TIME + BDWF16)'DUL +
+ BDHF17)*PDWS
DWT a Dws + DwL + DwR + DwF
pCTDws = Dws /DwT
PCTDWL = DwL /DwT
PCTDWR = DWR /DWT
PCTDWF = DwF /DwT
IF ( FLR .50. 0 ) THEN
LA = ( 8LA (1) + 8LA (2)*DWL + BLA (3)-PLA +
+ 8LA (4)'PDVL )
HAM = 8HAM(1) + BHAM12)'LA + BHAM13)'PLA
END IF
HLC = 1 BHLC2(1) + BHLC2(2)*PLA + BHLC213)*HAM +
+ BHLC2(4)FLA + BHLC215)vPDWS +
+ BHLC2(6)*NN
END IF
C
C CALCULATE DAYS TO VISIBLE BUD AND AND CHECK FDR INITIATIDN
0V8 = BDV8(1) + 80V812)~LT + BDV8(3)*ALT +
+ 80V8(4)v DT + BDV8(5)* ADT +
+ 80V816)*NN + BDV817)*OT*DT +
+ BDV818)*ALT*ALT + BDVB(9)*HAM +
+ BDVB(10)*DWR + 80V8111)'PDWS +
+ 80V8112)tPDWL
IF ( DVB .LE. TIME ) THEN
IF ( INIT .E0. 0 ) THEN
INIT = DVB + .5
END IF
END IF
6
c CALCULATE DAYS T0 FLOWER
DTF = BDTF(1) + BDTF(2)‘DV8 + BDTF(3)*NT .
+ BDTF(4)*ANT + BDTF15)vDTvDT +
+ BDTF(6)'HAM

125

Table Al. (cont'd)

 

C PRINT DAILY VALUES FOR ALL PARAMETERS IF IPRINT=O
IF (IPRINT .E0. 0 ) THEN
WRITE(*.500)TIME.NN.DWS.DWL.DWR.LA.HAM_HLC.INIT.FLR.
+ DVB.DTF.LT.DT.NT.ALT.ADT.ANT.DWF.DWT.PCTDWS.
+ PCTDWL.PCTDWR.PCTDWF
END IF
2000 CONTINUE
C

ct‘.‘...*“*."‘..‘..I.**.titt..t#..lt"fi.tt*fl'fiI’VCCIIGV‘I’.C‘i‘IICC‘ltifi

C END OF LOOP MAKING DAILY CALCULATIONS FOR PLANT PARAMETERS.
Ciititttitifiiiltfififittitt‘tttittitti‘litlfiiifitttivvtttttvtfifititttOttvtfitit
C
C IF INITIATION HAS OCCURRED CHECK IF AT LEAST 20 DAYS HAVE PASSED
C AND CHECK IF DAYS TO FLOWER HAS OCCURRED
IF ( INIT .NE. 0 ) THEN
IF ( (DTF - INIT) .GE. 20.0 .AND. FLR .E0. 0 ) THEN
FLR 3 DTF + .5
END IF
END IF
C
C PRINT ALL PARAMETERS EVERY 14 DAYS IF IPRINT NOT EOUAL 0
IF (IPRINT .NE. 0 ) THEN
WRITE1*.500)TIME.NN.DWS.DWL.DWR.LA.HAM.HLC.INIT.FLR.
+ DVB.DTF.LT.DT.NT.ALT.ADT.ANT.DWF.DWT.PCTDWS.
+ PCTDWL.PCTDWR.PCTDWF
END IF
1000 CONTINUE
C
Ctttttittttttttttfittttttttvtvttttttntttfittntttttctctaatc¢tttt-cctttttttt
C END OF OUTER LOOP CONTROLLING THE STEP
CttttlttItttttttltttttttttttIttttttvutt-tttttttttvvtttovttt-tttttvctcct-
“RITE(‘.t)’:=a==================3=a==================a==s=======aa
+8332=aasslnnaassss==========a==:3:====================a=¢a==a=s==s
+===2==33=a==:=’
C
C FORMAT FOR ALL PRINTING AND WRITE OF LAST ENVIRONMENTAL VALUES
500 FORMAT(’ ’.F5.0.1X.F4.1.1X.3(F7.4 ).1X.3(F6.2).
+ I3.I4.1X. 2(F5.1.1X).3F4.0.1X.3F5.0.2F7.4,4F5.2 )
WRITE(‘.‘)’LT.DT.NT = ’.LT.DT.NT
WRITE('.‘)' '
wRITE(-.*)’ '

THE OUTERMOST LOOP WILL ALLOW SEVERAL TREATMENTS TO BE RUN
THROUGH THE MODEL ON A SINGLE BATCH dOB RUN; THE ENVIRONMENTAL
DATA MUST BE ATTACHED LOCALLY AS TAPES
5000 CONTINUE
END
Ct-ttt-ttttuwttntttttttvat ENVGEN SUBROUTINE ttttvvtrttwttvthtV'Itt‘ttrt
C THIS ROUTINE GENERATES A RANDOM FLUCTUATION ABOUT THE GIVEN
C ENVIRONMENTAL MEANS FOR AVGLT.AVGDT.AVGNT. EIN IS ONE STANDARD
C DEVIATION FROM THE MEAN: EOUT IS THE RANDOM FACTOR.
C ......................................................................
SUBROUTINE ENVGEN (EIN.EOUT)
REAL EIN.EOUT
PI = 3.14159
R1 . RANF ()
R2 = RANF ()
EOUT I EIN * ( (-2*LOG(R1)) 'F .5 ' CDS(2*PI'R2) )
RETURN
END

0(3F30

126

Table Al. (cont'd)

 

Citttutttntttttttsmut-tit: BOXC SUBROUTINE tttvtwttvttvtitvttrowititvtt
C THIS ROUTINE HOLDS THE VALUES OF NN.DWS.DWL.DWR. AND LA FOR ONE STEP
C OF 14 DAYS AND OUTPUTS PNN.PDWS.PDWL.PDWR. AND PLA. A CALL WILL ONLY
C OBTAIN THE VALUE FOR ONE VARIABLE AT A TIME.
C SEE DR. THOMAS MANETSCH IN SYSTEMS SCIENCE FOR A COPY OF THE ROUTINE.
C .......................................................................
SUBROUTINE BOXC (BINR.BOUTR.TRAIN.NCOUNT.NOCY.LT.SUMIN)
DIMENSION TRAINI14)
NCOUNT = NCOUNT + 1
SUMIN = SUMIN + BINR
IF (NCOUNT .NE. NOCY ) GO TO 1
BOUTR 8 TRAIN(1) / FLOAT (NOCY)
DO 3 I ‘ 2.LT
3 TRAIN(I-1) . TRAIN(1)
TRAIN(LT) ' SUMIN
SUMIN = 0.0
NCOUNT ' 0.0
1 RETURN
END
'EOF

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\/J

\J

11.

'2.

127

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