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dissertation entitled

Prediction and Control of Stem Elongation and
Flowering in Poinsettia and Easter Lily

presented by

PAUL ROBERT FISHER

has been accepted towards fulfillment
of the requirements for

Ph . D . degree in Hortigul 124:9

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DATE DUE DATE DUE DATE DUE

       

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

PREDICTION AND CONTROL OF
STEM ELONGATION AND FLOWERING 1N
POINSE'I‘TIA AND EASTER LILY
By

Paul Robert Fisher

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

DOCTOR OF PHILOSOPHY

Department of Horticulture

1995

ABSTRACT

PREDICTION AND CONTROL OF STEM ELONGATION AND FLOWERING IN
POINSETTIA AND EASTER LILY

By

Paul Robert Fisher

Control of plant height and flowering date is essential for many ornamental flowering crops
including poinsettia (Euphorbia pulchern'ma Klotz.) and Easter lily (Lilium Iongrflorum
Thunb.). An existing tool for graphically tracking plant height over time on a control chart
was firrtha developed in a computer decision-support tool. A process control algorithm was
used to interpret whether poinsettia height was taller or shorter than desired, based on

deviation from target height and elongation rate projected by a simulation model.

The simulation model was developed to predict the shoot elongation of single stem poinsettia
in relation to timing of flower initiation and growth retardant applications. The simulation
model explicitly models three phases of elongation: an initial period of exponential growth,
a linear phase of regular intemode development and expansion, and a final plateau phase. The
three-phase function has broad application to a range of plant growth-modeling problems
where the length of lag, linear, or plateau phases are likely to vary. Model parameters have
clear biological meaning. A knowledge-based system was developed to recommend
appropriate greenhouse temperature set points and growth retardants based on the control

chart and simulation model.

The process control methodology was applied to Easter lily to control plant height. The
height control model was combined with a comprehensive model of plant development fi'om
leaf tip emergence through to flower that integrates existing models and recommended
practices. The resulting overall model was used to set greenhouse temperatures for crops at
three locations in order to achieve targets for flowering date and, secondarily, plant height.
The model successfully achieved the target flowering dates, but in the absence of growth
retardant applications plants finished 5 to 10 cm taller than desired. In the process of
implementing the Easter lily model, technologies were developed for linking biological models
into greenhouse environmental computer control systems, and for tracking leaf count on a

control chart.

 

ACKNOWLEDGEMENTS

This has been an enjoyable and rapid-transit degree, and I would especially like to thank my

wife Rosanna for her love and support throughout - she makes it all worthwhile.

I feel privileged to have worked with my advisor Royal Heins, who has always been extremely
supportive, an inspiration for new ideas, and willing to provide me with whatever is needed
to produce results. The floriculture section of the Department of Horticulture of Michigan
State University is, I believe, superb at identifying and solving industry problems and has been
the perfect place to develop my skills and interests. I am indebted to Tom and Cara Wallace
and the army of students who collected data, without whom my long-distance degree would
not have been possible. Several growers have become partners in developing and testing the
models, notably Bordines Better Blooms, Andy Mast Greenhouses, Henry Mast Greenhouses,
Neal Mast Greenhouses, Meirings Greenhouses, Post Gardens, Ron Sportel Greenhouses, and

Wooden Shoe Greenhouses.

I would also like to thank my committee - Will Carlson, Ken Pofi; Joe Ritchie, and Jon
Sticklen - who have been very flexible and supportive of what has been an unorthodox but
rewarding degree. Niels Ehler in the Royal Veterinary and Agricultural University in
Copenhagen Denmark has been an important role model for me, and the opportunity to work
with him in Denmark showed me that science is best done over a fine glass of port. I would

like to thank Heiner Lieth at the University of California at Davis - between Heiner, Niels and

iv

Royal I have been lucky enough to work with the top people in the world in my field.

Finally, I would like to thank my family for their long-distance support, and our wonderful
Michigan State family, especially Lee and Jane Taylor for the millions of things they have
done for us, Art and Marlene Cameron for sailing and hacky-sack, John, Jean and Laura
Everard for car repairs, Bruce Fox for conferences at the Harrison Roadhouse, Samira
Daroub for being Samira, Brian Baer for his hospitality, and Bane and Dragana Djordjevic for

late-night coffee breaks.

We gratefiilly acknowledge fimding for this project by University Outreach at Michigan State

University, and by Paul Ecke Poinsettia Ranch.

TABLE OF CONTENTS

LIST OF TABLES .................................................. viii
LIST OF FIGURES .................................................... x
INTRODUCTION .................................................... l
l. A PROCESS CONTROL APPROACH TO POINSETTIA HEIGHT CONTROL . . . 4
ABSTRACT ................................................... 5
MODELING APPROACH ........................................ 7
APPLICATION TO POINSETTIA HEIGHT CONTROL ................ 11
CONCLUSION ................................................ 22
LITERATURE CITED .......................................... 24

2. MODELING THE EFFECT OF SHORT DAY DATE ON STEM ELONGATION OF
POINSETTIA WITH A THREE-PHASE MATHEMATICAL FUNCTION . . 31

ABSTRACT. .................................................. 32
INTRODUCTION .............................................. 32
MATERIALS AND METHODS ................................... 38
DISCUSSION ................................................. 46
CONCLUSIONS ............................................... 5]
LITERATURE CITED .......................................... 51
3. MODELING THE DOSE RESPONSE OF POINSETTIA TO A CHLORMEQUAT
GROWTH RETARDANT APPLICATION ........................... 63
ABSTRACT .................................................. 64
INTRODUCTION .............................................. 64
MATERIALS AND METHODS ................................... 66
RESULTS .................................................... 74
DISCUSSION ................................................. 79
LITERATURE CITED .......................................... 84

4. A DECISION-SUPPORT SYSTEM FOR REAL-TIME MANAGEMENT OF EASTER
LILY (Lilium longiflorum Thunb.) SCHEDULING AND HEIGHT. 1. SYSTEM

DESCRIPTION ................................................ 98
ABSTRACT .................................................. 99
INTRODUCTION .............................................. 99
METHODS AND MATERIALS .................................. 101
DISCUSSION ................................................ l 19
LITERATURE CITED ......................................... 120

5. A DECISION-SUPPORT SYSTEM FOR REAL-TIME MANAGEMENT OF EASTER
LILY (LILIW LONGIFLORUIM THUNB.) SCHEDULING AND HEIGHT.

2. VALIDATION ............................................. 134
ABSTRACT. ................................................ 135
INTRODUCTION ............................................. 135
MATERIALS AND METHODS .................................. 137
RESULTS .................................................. 144
DISCUSSION ................................................ 147
LITERATURE CITED ......................................... 151

6. GRAPHICAL TRACKING OF LEAF NUMBER TO SUPPORT CROP TIMING
DECISIONS ................................................. 160

ABSTRACT ................................................. 161

LITERATURE CITED ......................................... 166
APPENDICES
A. SAS program for fitting the three phase firnction to untreated control. ......... 169
B. SAS program for estimating the g(t) fimction by chlormequat concentration. . . . . 171

LIST OF TABLES

Section 1

1

Simplified action table for growth retardant applications to poinsettia crops. . . 26

2. Estimates of K, and K" PID parameters using regression analysis ............ 26
Section 2
l. Phenological and growth data (mean i 95%) for each photoperiod treatment. . 53
2. Parameter estimates for the jg“, model fit individually to each photoperiod
treatment. .................................................... 54
3. Analysis of variance and parameter estimates from fitting the fw, model to all data
(‘the all treatments model'). ....................................... 55
4 List of abbreviations and parameters ................................. 56
Section 3
1. Analysis of variance and parameter estimates from fitting the fhmmodel to the
untreated control data from the calibration experiment. .................. 86
2. Increase in height before and alter the growth retardant application at time t", and
estimates of the initial rate parameter ([3) by growth retardant treatment. ..... 87
3. Estimates of a and b used to calculate persistence P and duration D parameters in the
gL(t) and g(t) models respectively. .................................. 87
4. Analysis of variance and parameter estimates fi'om fitting the fw model to the
untreated control data from the validation experiment. ................... 88
5 List of abbreviations and parameters ................................. 89

Section 4

1 Parameter estimates for Equation (6) ................................ 122
2 Action table for DIF recommendations .............................. 123
3 Parameter estimates for K, and K, based on linear regression of interview data 123
4 Constraints for temperature recommendations (°C) during Easter lily production
stages. From SF to EML, values represent soil temperatures, and after EML, values
represent air temperature settings. ................................. 124
5 Variables, abbreviations, and parameters used in this study ............... 125
Section 5
1. Comparison of consultant and CARE temperature recommendations ........ 153
2 Variables, abbreviations, and parameters used in this study ............... 154

LIST OF FIGURES

Section 1

1. Basic components of a control chart. ................................ 27
2. Components of a graphical control chart for poinsettia height control. ....... 28
3. Graphical height control charts fi'om a production trial at Michigan State University

with three cultivars: (A) Annette Hegg Dark Red, (B) Celebrate 2, (C) Supjibi.
Legend: + plant height, I actual growth retardants applied by the expert (1500 ppm

chlormequat foliar sprays), [3 control index values ....................... 29
4. Modified graphical control curve for taller-growing cultivars ............... 30
Section 2
1. Components of the f3,p,m function elongation curve ..................... 57
2. (a) Mean stem length and (b) leaf count over time for the three short day treatments
(meand:95% confidence intervals, ‘= SD 13, EJ= SD 26, .= SD 54). (c) A= average
temperature and <>= DIF (average day minus average night) temperatures during the
experimental period .............................................. 58
3. Final intemode lengths (average of five plants) for the short day treatments
( ‘= SD 13, Cl= SD 26, .= SD 54). .......................... 59
4. Fitting the fw function (solid line) separately to each observed mean data (0) fi'om
short day treatment (a) SD 54, (b) SD 26, and (c) SD 13. ................ 60
5. Pit of the overall fW, model (solid line) to observed mean data (0). (a) SD 54, (b)
SD 26, and (c) SD 13. ........................................... 61
6. Model predictions for three short day date (SD) assumptions (short days 15, 30, and

45 days afier transplant), a starting height of 50 mm, and I3 equal to 0.116. Arrows
represent SD, and 12 occurs 42 days afier SD ........................... 62

Section 3

1.

Alternative g(t) dose response models proposed by Larsen and Lieth (1993). (a) a
linear g,_(t) model where the initial efl‘ect of a growth retardant application at time t,
is represented byML, and the declining growth retardant efl‘ect persists for P days. (b)
an exponential dose response model with declining growth retardant efl‘ect after an
initial amplitude ofME. ........................................... 90

Plot of observed and predicted average stern length over time for the untreated plants
during the calibration experiment: 0 = mean observed height :I: 95% confidence
intervals, solid line = fit of the fawn, firnction. ......................... 91

Observed average elongation during the first day after application (i.e. between t“ and
10+ 1) during the calibration experiment for difl‘erent growth retardant treatments
(mean 3: 95% for five plants per treatment). ........................... 92

Parameter estimates (0) for (a) the persistence P in the linear g(t) model and (b) the
duration parameter D in the exponential g(t) models respectively. The solid lines
represent the linear regression (Eq. 13) fit to the parameter estimates where the y-
intercept constant represents the parameter a and the gradient constant represents
b. ........................................................... 93

(a) Comparison of gL(t) (dashed line) and g(t) (solid line) dose response models
assuming a 1500 ppm chlormequat application, O=difi‘erence between models (gLfl)
minus g£(t)). (b) The percentage height of chlormequat-treated plants with respect
to the final height of untreated plants for a growth retardant applied tn=34 days after
transplant (0), and growth retardant persistence for various concentrations (Cone)
using the gL(t) model (C!) .......................................... 94

(a)—(t) Plot of observed average stem length (0) for growth retardant treatments over
time during the calibration experiment and predicted height from the exponential gg(t)
model (solid line). The dashed line represents heights predicted by the fwm model
in the absence of a growth retardant application. ....................... 95

(a)—(t) Plot of observed average stern length for growth retardant treatments over time
during the calibration experiment (0) and predicted height from the linear gL(t) model
(solid line). .................................................... 96

(a)-(d). Plot of the validation data set showing observed average stem length for
control and growth retardant treatments over time (0) and predicted height from the
exponential g(t) model combined with the fig”, function fit to the untreated
validation control plants (solid line) ................................. 97

Section 4

1.
2.
3.

6.

7.

Easter lily models and phenological stages used in the DSS. .............. 126
An example graphical tracking control chart for Easter lily height. ......... 127
An example graphical tracking control chart for Easter lily leaf count. ...... 128
Example control indices for graphical tracking situations. ................ 129
Steps required to make a decision on greenhouse temperature settings. ..... 130
Modular structure of The Greenhouse CARE System .................... 131
An example screen from the View module in The Greenhouse CARE System. 132

Section 5

1.

Distribution of (a) flower date (FL) and (b) visible bud date (VB) in the real-time
control experiment at three locations (KVL, MSU, and UCD). Visible bud date for
each plant was not recorded at KVL. ............................... 155

Leaf count and average daily temperature in the real-time experiment at three
locations ((a) KVL, (b) MSU, and (c) UCD). ' = observed ADT, :l = ADT setting,
A = observed leaf count, :1: 95% confidence intervals. ................... 156

 

Leaf count over thermal time using a base temperature of 3.5C. (a) Data from the
real—time control experiment (0 = KVL, Cl = MSU, V = UCD, :1: 95% confidence
intervals). (b) Data from the Grower Database of commercial crops (0 = grower 1,
CI = grower 2, v= grower 3). The solid lines in (a) and (b) are the leaf counts
predicted by the LUR model. ..................................... 157

Observed and predicted average daily temperature after VB in the real-time control
experiment at three locations ((3) KVL, (b) MSU, and (c) UCD). O = the observed
ADT averaged for all days between the data point and the flower date (FL) (for
example, 34 days before FL in KVL, Fig. 4(a), the average of temperature over the
next 34 days was 16.1C). V = the ADT predicted at VB by the Erwin and Heins
(1990) thermal time model. CI = the ADT predicted by the bud length model. 158

Average daily temperatures recommended by the DSS and the three consultants for
the crop at KVL. O = the ADT recommended by the DSS, and the solid lines
represent the maximum and minimum of the three consultants' recommendations on
each date ..................................................... 159

Section 6

l.
2.

An example leaf count graphical control chart. ........................ 167

A generalized representation of the process control chart for horticultural problem
areas. ....................................................... 168

INTRODUCTION

Control of plant height and flowering date is essential for many ornamental flowering crops,
especially crops that are marketed to strict specifications such as poinsettia (Euphorbia
pulchem'ma Klotz.) and Easter lily (Liliwn Iongrflawn Thunb.). The overall objective of this
study was to develop models and technologies that could be used to help growers achieve

these specifications.

The original goal of the research was to develop an expert system that would interpret
graphical track control charts to help make height control recommendations. Graphical
tracking is a technique where actual plant height is compared against a target curve over time
on a graphical control chart. We recognized that graphical tracking shares many
characteristics of other process control problems in engineering, for example quality control
charts used in industry. Techniques used in process control, for example proportional-
integrative-derivative control algorithms, could therefore be applied to the height-control and
timing problems. A process control algorithm was used to interpret whether poinsettia
height was taller or shorter than desired, based on deviation from the target height. An expert
system was developed to make recommendations based on the process control algorithm,
historical temperatures and growth retardant applications, and stage of crop development.
The process control algorithm and knowledge-based system are described in Section 1.

1

2

It was apparent that expert height control recommendations were determined not only by
historical growth, but also by expected elongation rate. A simulation model was developed
to predict the shoot elongation of single stem poinsettia in relation to timing of flower
initiation. The simulation model explicitly models three phases of elongation: an initial period
of exponential growth, a linear phase of regular intemode development and expansion, and
a final plateau phase. The resulting model (Section 2) closely fit the observed poinsettia data,
and parameters have clear biological meaning. The three-phase function has broad application
to a range of plant growth-modeling problems where the length of lag, linear, or plateau
phases are likely to vary. The model was formulated to allow dynamic simulation using rate
equations to incorporate the effect of environmental perturbations. The dose response of
single-stem poinsettia to a single foliar application of the growth retardant chlormequat was

incorporated in the model (Section 3).

The process control methodology was applied to Easter lily to control plant height. The
height control model was combined with a comprehensive model of plant development fi'om
leaf tip emergence through to flower that integrates existing models and recommended
practices (Section 4). This model was incorporated into a computer decision-support tool
called The Greenhouse CARE System, as a module in a similar format to the poinsettia model.
The resulting overall model was validated using crops grown at three locations in order to
achieve targets for flowering date and, secondarily, plant height (Section 5). The model
successfirlly achieved the target flowering dates, but in the absence of growth retardant
applications plants finished 5 to 10 cm taller than desired. In the process of implementing the

Easter lily model, technologies were developed for linking biological models into greenhouse

3

environmental computer control systems, and for tracking leaf count over time on a control

chart (Section 6).

SECTION 1

1. A PROCESS CONTROL APPROACH TO POINSETTIA HEIGHT CONTROL

Paul R. Fisher and Royal D. Heins
Department of Horticulture, Michigan State University, E. Lansing, MI 48824-1325

HortTechnoIogy (in press)

ADDITIONAL INDEX WORDS technology transfer, knowledge-based system, control

chart, graphical tracking, process control, Euphorbia pulchen'ima Klotz., greenhouse

ACKNOWLEDGMENTS: We gratefirlly acknowledge funding by University Outreach at
Michigan State University. We also thank Dr. Niels Ehler of the Royal Veterinary and

Agricultural University at Copenhagen, Denmark for his thoughtfirl discussions and input.

5

ABSTRACT. A methodology based on process-control approaches used in industrial
production is introduced to control the height of poinsettia (Euphorbia pulchern'ma Klotz.).
Graphical control charts of actual versus target process data are intuitive and easy to use,
rapidly identify trends, and provide a guideline to growers. Target reference values in the
poinsettia height control chart accommodate the biological and industrial constraints of a
stem-elongation model and market specifications, respectively. A control algorithm
(proportional-derivative control) provides a link between the control chart and a knowledge-
based or 'expert' computer system. A knowledge-based system can be used to encapsulate
research information and production expertise and provide management recommendations to

growers.

INTRODUCTION

The widespread use of computers for environmental control and monitoring in greenhouses
provides an opportunity to implement model-based process control to manipulate
temperature, humidity, CO2 concentration, nutrients, and pesticide inputs. In this type of
control system, environmental variables are modified in real time based on plant requirements
rather than rigid calendar timetables (e.g., Fynn et al., 1989; Jones et al., 1988). Several tasks
are common to model-based control problems, including defining production targets,
monitoring production variables, identifying deviations from the desired performance,

optimizing corrective actions, and implementing system changes.

6

In process control, actual and target performance levels can be compared over time in a
graphical control chart (Ewan, 1963). For example, the measured diameter of an industrial
component can be charted against the allowed minimum and maximum size to provide the
decision-maker with immediate performance feedback in an intuitive visual format. A control
algorithm, generally referred to as proportional-integrative-derivative (PID) feedback control
(Murrill, 1981), can be used to quantify trends in observed deviations in terms of a control
index (CI). The control index represents the change in the system needed to retum the
observed performance to the desired level; for example, to raise or lower temperature in a
thermostat system. Knowledge-based or ‘ expert' systems (Stock, 1987) that capture
qualitative expert knowledge in a computer program can interpret the control chart (Cook et

al., 1992) and control index to suggest remedial action.

A decision area that lends itself to a process-control approach is height control of flowering
potted plants such as poinsettia (Euphorbia pulchem’ma Klotz.). Incorrect height-control
decisions can reduce the market value of a flowering potted plant for aesthetic and economic
reasons: consumers pay less for both ‘leggy' and undersized plants, overly tall plants are more
expensive to ship, and contract orders for poinsettia crops usually specify an acceptable height
range for the finished plant. The inherent challenge is to produce a crop to specified market

height limits without adversely affecting scheduling, quality, and profitability.

In this article, a novel use of process control is described to control the height of a poinsettia
crop. Process-control approaches (control chart and PID control) are discussed in the first

part of the article and then are applied to poinsettia height control. The implementation of

7

these process-control approaches in a poinsettia growers decision-support tool called fire
Greenhouse CARE System is discussed in terms of its three main components: developing a
graphical control chart, characterizing and interpreting the graph, and providing management

recommendations on the basis of the analysis.

MODELING APPROACH

Control charts provide useful and easily understood diagnostic tools (Ewan, 1963; Miller,
1985). In a control chart (Fig. l), a reference value is established as the desired average level
of a controlled variable (Ewan, 1963). When the measured value of the controlled variable
remains close to the reference, i.e., inside action limits, the system is in control.
Determination of action limits can be based on statistical or industrial criteria. Based on the
magnitude and frequency of deviations from the desired mean, actions are taken to modify
actual performance. However, a control chart plot alone does not demonstrate why a certain

trend exists or what corrective actions should be taken (Miller, 1985).

Knowledge-based technology has been used to identify and interpret out-of-control situations
on a control chart (Cook et al., 1992) in a quality-control application for plywood
manufacturing. A statistical control chart was developed, and eight antecedent-consequent
(if..then) rules based on statistical probability (Nelson, 1985) were used to identify when
sufficient data points were above or below the reference value to identify a trend. For

example, if six consecutive data points were increasing or decreasing, then the mill operator

8

was alerted to a significant production trend. Another module in the plywood application

used additional rules to provide management recommendations after a deviation occurred.

An alternative to heuristic interpretion of control charts is to employ a PID control algorithm,
which is used widely in the design Ofself-regulating control processes (Murrill, 1981) and can
be linked to a control chart to quantify deviations fi'om the target value. In the case of
thermostat-regulated temperature control, deviations of the controlled variable (temperature)
from a desired setpoint are monitored, and a representation of a PID control algorithm in the
thermostat is used to correct the error by changing a manipulated variable (fuel supply to the
boiler). Three components of error that relate to the deviation of the controlled variable fi'om
the setpoint are defined in P11) control. The proportional component is the absolute deviation

e(t) of the measured value x(t) from the setpoint s(t) at time t, where

e(t) - 3(1) - x0) (1)

The integral component e(t)dt is the sum of errors over a defined period of time, which
represents the longer-term trend in error. The derivative component de/dt represents the rate

of change in deviation (the deviation rate) toward or away fi'om the setpoint.

The basic equation used to calculate the control index, a value that causes a change in the

controller, can be represented by

C1 - Kat“) o K100” 0 K1? (2)

where K, K, and K, are constants assigned to each error component to stimulate the desired
response item the controller (Quinn-Curtis Inc., 1990). Murrill (1981) and Quinn-Curtis Inc.
(1990) compared characteristics of control systems with various combinations och, K, and
K, components. A high K, term leads to a rapid response proportional to the current
deviation Proportional control alone is simple and easy to tune, but is not sensitive to trends
in process disturbances over time. Integral control is capable of tracking disturbances, and
the integral term is proportional to the sum of previous process errors in the system. A high
K ,. term is therefore affected more by long-term trends than the current deviation, and
continues to add to the controller output until the sum of previous errors equals zero. The
derivative component "anticipates" the error, providing a larger control response when the
error term is going in the wrong direction (away from the reference) and a dampening

response when the error term is going in the right direction.

If control actions are continuous, Eq.(2) can be used without modification to change the
manipulated variable. However, in agricultural processes, the decision is often a mix of
discrete and continuous options; for example, whether to apply a pesticide and at what rate.
Where discrete management options are employed, CI in Eq.(2) can be rounded to an integer
value and each control-index value can be described qualitatively based on potential
management actions. For example, a control index of 0 can indicate that the system is under
control; -1, that a slight decrease in the controlled process variable is required; and +3, that

it is imperative to increase the controlled process variable. The control index therefore

10

includes both a direction (the Sign) and magnitude (the absolute value) of required control

actions.

A control situation can be defined further by dividing the production season into a series of
decision stages within which recommendations do not vary as a function of time. Beck et al.
(1989) described an approach used in the development of a knowledge-based system for
soybean insect control where decision stages were identified as a result of interviews with a
domain expert (Stock, 1987), but more importantly on the basis of expat responses to
problem scenarios. The boundaries for each stage were defined by Beck et al. (1989) in
production rules based on easily observable plant phenological events, for example senescence

or harvest.

An infinite number of possible control situations can therefore be characterized into a discrete
number of scenarios. If viewed as a matrix (or action table) with the decision stage in the x-
axis and control index in the y-axis, expert recommendations for each cell can be elucidated
by interview techniques. By computing the control index and locating the relevant cell, the

resulting recommendation can mimic that of the expert.

11

APPLICATION TO POINSETTIA HEIGHT CONTROL

Developmem of the graphical contrQl chart

The graphical control curve for poinsettia height control was based on a sigmoid stem
elongation model for pinched poinsettia (Berghage and Heins, 1991). Pinching refers to the
manual removal of the stem apex to promote lateral branching. The dynamic intemode-based
model from Berghage and Heins (1991) was run with assumptions of constant 21C day and
night temperature, and flower-inducing photoperiods beginning 25 days after pinch. The
resulting model shoot length data then were converted to relative time and relative height by

scaling both axes from zero to one. The Richards firnction (Richards, 1959)

H - H, [1 . new. - 1711"" (3)

was then fit to the resulting normalized data. Parameter estimates for H0, 11,, n, and It were
0.0131, 1.018, 0.3923, and 5.8138, respectively, and the R2 was 0.99. In order to develop
a control chart for a particular crop, the time axes were scaled from pinch to flower dates.
Market contracts for poinsettia usually specify an acceptable range in final plant height, and
the height axes were scaled to the minimum, maximum, and average final height specifications

(Fig. 2).

The shape of the process control curve corresponds with physiological development of the
crop. Immediately after the plant is pinched, there is a lag in stem elongation rate as lateral

shoots begin development fiom dormant axillary buds. Stem elongation rate is approximately

12

linear as new leaves unfold and internodes elongate until the terminal flower buds are visible.
Several weeks after flower initiation, the bracts of the poinsettia begin to develop the final
color (red, pink, or white) at a developmental stage generally called ‘first color.‘ Bracts
expand over the next month, and large bracts are a desirable market feature. During the
period of bract expansion, stem elongation rate slows to a plateau as the plant approaches
flowering. Final plant height, detemrined by the length of side shoots, is a function of the

number of leaves on a shoot and the length of internodes between leaves.

Use of the graphical control chart for height control, termed graphical tracking, has been
adopted widely by poinsettia, chrysanthemum, and Easter lily growers (Carlson and Heins,
1990). Growers either generate their own graphical control chart from published instructions
(Carlson and Heins, 1990) or are sent a facsimile of customized graphs fiom Michigan State
University. Growers measure plant height with a mler twice each week and plot the
measurement on the graphical control chart (Fig. 2). Actual and reference heights are
compared. If actual plant height is above the upper action limit, the crop is too tall, and
action should be taken to decrease stem elongation rate (e. g., applying a growth retardant);

conversely, stem elongation rate should be increased if the height is below the target window

height.

13
The ' 11 1e
One of the authors of this article, Paul Fisher, was the knowledge engineer (Stock, 1987) in
this project, and Dr. Royal Heins was the primary source of expertise (and is hereafter
referred to as ‘the expert'). Heins developed the graphical height control technique, has
regularly advised growers about poinsettia production, and has conducted considerable
research related to height control techniques (Berghage and Heins, 1991; Carlson and Heins,

1990; Erwin and Heins, 1990; Erwin et al., 1989; Heins and Erwin, 1990).

Following interviews, we defined five decision stages for poinsettia height control: (Stage 1)
early growth until one week before first bract color, (Stage 2) the week before first bract
color, (Stage 3) the first week of bract color, (Stage 4) the period of bract expansion, and
(Stage 5) the ten days before flowering. Optimum temperatures (Berghage and Heins, 1991)
and the desirability of applying a growth retardant (Barrett and Nell, 1993) varied with stage
of development and, within each decision stage, expert recommendations with respect to
temperature and growth retardants were made based on consistent criteria. The phenological
events that delimited the decision stages could be observed readily by a grower or, for the

start of Stage 2, could be predicted based on flower initiation date.

The range of possible recommendations within each decision stage then was structured in an
action table (Table 1), a two-dimensional matrix that encapsulated growth retardant and
temperature recommendations in an eight-point control index. For reasons of brevity, only
growth retardant recommendations are presented; however, each cell in the action table also

contains a specific day and night temperature setpoint recommendation. In the control index

14

approach, a value of -3 represented a strong need to reduce current stem elongation rate, a
value of 0 meant current elongation rate could be maintained, and a value of 4 represented
a strong need to promote stem elongation. Forty possible control scenarios were therefore

defined: five decision stages times eight control-index values.

Growth retardant chemicals reduce stem elongation rate primarily by interfering with
gibberellin biosynthesis (Grossman, 1992) and are most usefirl during vegetative and early
development of poinsettia because later applications reduce bract size (Barrett and Nell,
1993). The recommended rate or number of growth retardant applications (Table 1)
increased with more negative control indices during the early growth stages. When the
control index was 2 zero, a growth retardant was not recommended. During growth stages
two to four, the action table warned that growth retardant applications may reduce bract size
and/or delay flowering. Near the market date, no retardants were recommended because
there was little potential for firrther stem elongation, and growth retardants were unlikely to

be efl‘ective.

15

Em ' g the Entrol index
We used the PID algorithm to mimic the expert's interpretation of the control chart. An initial

heuristic approach, in which rules were used to define how concerned the expert was with
particular scenarios, was discarded because the number of rules rapidly increased and were
dificult to verify for completeness. Eq.(2) was modified so that the control index (CI) was
rounded to the nearest integer and limited to -3 and +4. Because of infi'equent measurements
(once every three days), we wanted the system to respond rapidly to deviations fi'om the
reference height; therefore, the integral constant K, which afi‘ects the lag in control response,

was set to zero. These changes modified Eq.[2]

CI - round(ch(t) 0 Kg), -3 5 CI 3 4 (4)

where time t was measured in days, the error e(t) was measured in cm, de/dt was in cm/day,

Kc had units of cm", and K, was cm/day.

The expert was presented with a random selection of height and stem elongation rate
combinations at the five decision stages and identified which control index in the action table
best matched his recommendation. Linear regression then was used to estimate K, and K, by
using the control-index values estimated by the expert as the dependent variable, and plant
height and elongation rate as the independent variables. Results of the linear regression to
estimate K, and K, (Table 2) indicated that Eq. (4) adequately represented the expert's choice
of control index. An example control chart (Fig. 3a) shows how Eq. (4) was used. Actual

heights for September 14 and 17 were 19.3 and 21.4 cm, respectively, and reference heights

16

were 17.7 and 18.2 cm. The control index for September 17 was calculated as
CI = round(-0.51(21.4-18.2) - 2.84((21.4-18.2)-(19.3-l7.7))/3)
= round(-1.63 - 1.51 )
= 3round(—3. 14)

=-3

Control recommendations

The knowledge-based system is composed of 125 ‘if. .then..' antecedent/consequent rules that
are used to develop text recommendations in a brief report. The first task in the knowledge-

based system is to identify the growth stage and calculate the control index. For example

IF Current date > First color date + 7
AND Current date < Flower date - 10
THEN Growth stage = ‘4. Bract expansion'

Rules then copy text into a section of the report that describes the current situation (growth

stage and control index) to the user. For example, one rule states

IF Control index = -1
AND Actual height > the target height
THEN Copy to the report ‘Yhe crop is taller than desired, and steps should

be taken to reduces stem elongation rate. '

17

The next part of the report deals with whether a growth retardant should be applied, and if
so What chemical type, application method, and concentration. Each cell in the action table
is represented as a rule, and rules are similar to but more detailed than the cells in Table 1.
By looking up the appropriate rule (action table cell), the growth retardant recommendation

is obtained, for example

IF Growth stage = ‘1. Early'

AND Control index = -2

THEN Apply a growth retardant = Yes

AND Concentration = Medium rate

AND Appropriate chemicals = chlormequat, daminozide/chlormequat mix,
and ancymidol

In exceptional situations in which the elongation potential of the cultivar or the history of
growth retardant applications apply, the basic action-table recommendations are modified by
additional rules. For example, one rule avoids recommending growth retardants to short-
growing cultivars in the first two weeks after pinch, even if crop height is above the target

window:

18

IF The control index <= 0

AND Thegrowthstage=‘l.Early'

AND Current date < pinch date + 14

AND The cultivar = ‘ short-growing'

THEN Apply a growth retardant = no

AND Copy to the report ‘Although plant height is above the target window,

do not apply a growth retardant at this stage. This cultivar tends to

be slaw—growing and the situation is not yet a problem. '

The consequent parts of many rules, including the one above, contain text recommendations
that are copied to the report. An example growth retardant recommendation based on the

crop's being in growth Stage 1 with a control index of -3 (September 17 in Figure 3a) reads:

"Apply a medium-rate growth retardant. A second application may be required in

3-4 days. Consider one of the following rates:

ancymidol cb'ench : 0.25-0.50 mg/I5cm pot
daminozide/chlormequat spray : 1000 ppm each
chlormequat spray : 1 5 00 ppm

chlormequat drench : I 5 00 ppm "

19

Implementation

Working closely with a beta-test group of eight Michigan poinsettia producers, we
incorporated the graphical control chart, PD algorithm, and knowledge-based system into an
overall program All were innovative growers, but their operations differed in scale, technical
sophistication, and computer usage. All but one grower were experienced with poinsettia
production. Between 1990 and 1993, growers were visited regularly and sent progam
updates. Over two million plants were grown with the support of the program during this
period. The progam was refined based on other industry sources, greenhouse experiments,
comments hour the eight poinsettia producers, and comparison between the knowledge-based
system and grower actions. Initial versions of the program combined an expert system shell,
which is a progarnming language written specifically for developing knowledge-based
systems (Stock, 1987), and a spreadsheet. The knowledge-based system primarily relied on
a forward-chaining inference procedure (Stock, 1987) where all data needed to make a
recommendation were stored in a database or calculated fi'om the control chart. The program
version described in this paper was written entirely in Turbo Pascal Version 6.0 (Borland
International, 1990) to permit a consistent user interface and rapid data exchange among

difi‘erent modules of the program.

A production trial was undertaken to verify that the knowledge-based system produced
recommendations similar to the original expert whose knowledge was used to develop the
program. Poinsettias were gown in 15-cm-diameter (2,570 cm’) pots by the expert to height
specifications of 35-40 cm. Rooted cuttings were transplanted August 20, 1991, were

pinched September 1, and were gown under natural day lengths with a target flower date of

20
November 25. One tall cultivar, ‘Annette Hegg Dark Red,‘ and two shorter cultivars,

‘ Supjibi' and ‘Celebrate 2,‘ were gown as three separate crops of thirty plants each in the
same geenhouse at Michigan State University. Twice each week during the production trial,
the heights of three plants per crop were manned and entered onto a control chart. Growth
retardant and temperature decisions of the expert were recorded and were implemented to
control plant height. The expert gaphically tracked crop height, but did not use the
knowledge-based system to help make decisions. After the experiment was completed, data
were entered into the knowledge-based system. Expert recommendations were compared
with recommendations of the knowledge-based system (for reasons of brevity, only gowth

retardant recommendations are discussed).

The control charts for the three crops are shown in Fig. 3. All of the crops finished within the
target window, although they were shorter than the reference value. The ‘ Annette Hegg Dark
Red' crop (Fig. 3A) was above the window until October 2, and five gowth retardant
applications (chlormequat applied as a foliar spray at 1500 ppm, 5 ml/plant) were made by
the expert to reduce the rate of elongation The expert was prepared to drop below the target
window during mid-October with the expectation that the crop would gow back into the
window by flowering date. This strategy was chosen because during the previous season
rapid stem elongation was observed in mid-October in response to canopy closure as the crop
matured. No gowth retardants were applied to the remaining two crops. The ‘Celebrate 2'
crop (Figure 3B) was below the target window for most of the production season, whereas
‘ Supjflri' (Figure 3C) tended to remain within the window. All crops finished within the lower

range of the final height specifications.

21

The knowledge-based system generally provided similar recommendations to that of the
expert. Control indices for each crop are presented in the lower part of Figs. 3a, b, and c.
Looking up the control index in the action table (Table 1) for a given gowth stage shows the
gowth retardants recommended by the knowledge-based system. Similar to the expert, five
gowth retardants were recommended by the knowledge-based system for the ‘Annette Hegg
Dark Red’ crop, and no gowth retardants were recommended for the remaining two crops.
The knowledge-based system recommended an application on September 21 to the ‘Annette
Hegg Dark Red’ crop that was not applied by the expert and did not recommend a gowth
retardant on October 6 because the crop was within the target window. In addition, the
knowledge-based system recommended four low-rate applications (800 ppm chlormequat)
and one medium-rate application (1500 ppm), whereas the expert applied only medium-rate

applications.

The knowledge-based system therefore did not react as strongly as the expert to deviations
above the curve for ‘ Annette Hegg Dark Red'. The expert's recommendation to apply a
gowth retardant while the crop was within the target window indicated the target curve did
not represent his control strategy accurately. Following this production trial and analysis of
gaphs from beta test users, we are testing alternative reference curves for tall-gowing
cultivars such as ‘Annette Hegg Dark Red' that attempt to reduce plant height early in the
season compared with the standard curve. An initial arbitrary modification to the Richards
firnction (Eq. (3)), setting the H" parameter to 0.004, resulted in a curve that may be more
appropriate for tall-gowing cultivars (Fig. 4). Using the modified function as the reference

curve, the knowledge-based-system recommendations more closely mimicked the expert for

22

'Annette Hegg Dark Red'. The modified curve is viewed as a prototype, and research into

appropriate reference curves is ongoing.

CONCLUSION

In summary, process control theory provides a powerfirl tool for production of geenhouse
crops. Real-time geenhouse control problems have several features that lend themselves to
computerization (Jones, 1989): a well-defined and narrow problem domain, inputs and
outputs that can be defined completely and precisely, system goals are explicit, and success
is tangible. A process control approach has been applied successfully to height control of
greenhouse potted plants, a problem for which measurements can be taken cheaply and
fiequently, elongation responses to temperature and gowth retardants are well-quantified,
and computers already are widely used in the industry. The Greenhouse CARE System has
been well received by users and generally provides feasible guidelines and management

recommendations.

23

Fufle work

Further validation of the poinsettia application is necessary. Experiments are underway in a
research environment where the progam is being used in the role of a decision-maker to
gow a crop solely by knowledge-based system recommendations. At present, the progam
takes a narrow view of height control and makes important assumptions, especially with
respect to plant health and the lack of other production problems. For example, if a nutrition
problem occurred, the progam would recommend temperatures which increase height but
would not deal with the root causes of why the crop was elongating slowly. A further current
limitation in the knowledge-based system is that historical data are used to make
recommendations without considering firture projected elongation. In contrast the expert
grower considered expected weather, changes in plant density, and the residual activity of
gowth retardant applications when making recommendations. A simulation model is being
developed to incorporate into the knowledge-based system, so that the control index can be

calculated based on both projected and historical stem elongation.

The process control approach also could be applied to other crops, other time fi'ames (e. g.,
by measuring frequency in months rather than days), and other decision areas (e. g., soil
fertility or pest and disease management). The packaging of research information as gaphical
tools and decision-support systems provides a convenient delivery tool for transferring

technology to gowers.

24
LITERATURE CITED

Barrett, J. and TA Nell. 1993. Growth retardant practices to avoid efl‘ects on poinsettia bract
size. Georgia Commercial Flower Growers Assn. Nwsl. July-August, 1993 :7-8.

Beck, HW., P. Jones, and J.W. Jones. 1989. SOYBUG: An expert system for soybean insect
pest management. Agicultural Systems 30:269-286.

Berghage, RD. and RD. Heins. 1991. Quantification of temperature efi‘ects on stem
elongation in poinsettia. J. Amer. Soc. Hort. Sci. 116(1):14-18.

Borland International Inc. 1990. Turbo Pascal Version 6.0 User‘s Guide, Borland
International, Scotts Valley, California.

Carlson, W.H. and RD. Heins. 1990. Get the plant height you want with gaphical tracking.
GrowerTalks 53(9):62-68.

Cook, D.F., J.G. Massey, and C. McKinney. 1992. A knowledge-based approach to statistical
process control. Computers and Electronics in Agriculture 7:13-22.

Erwin, J .E., RD. Heins, and MG. Karlsson. 1989. Therrnomorphogenesis in Lilium
longrflorum. J. Amer. Bot. 76(1):42-52.

Erwin, IE. and RD. Heins. 1990. Temperature efl‘ects on lily development rate and
morphology from the visible bud stage until anthesis. J. Amer. Soc. Hort. Sci. 115(4):644-
646.

Ewan, W.D. 1963. When and how to use cu-sum charts. Technometrics 5(1): 1-22.

Fynn, RP., W.L. Roller, and HM Keener. 1989. A decision model for nutrition management
in controlled environment agriculture. Ag. Systems 31:35-53.

Grossman, K. 1992. Plant gowth retardants: their mode of action and benefit for
physiological research, p.788-797. In:C.M. Karssen, L.C. van Loon, and D. Vreugdenhil
(eds). Progess in plant gowth regulation. Kluwer, Netherlands.

Heins, R D. and J. E. Erwin. 1990. Understanding and applying DIF. Greenhouse Grower
8(2):73-78.

Jones, R, B.K. Jacobson, and J .W. Jones. 1988. Applying expert systems concepts to real-
time

geenhouse controls. Acta Hort. 230:201-208.

Jones, P. 1989. Agricultural applications of expert systems concepts. Ag. Systems 31:3-18.

25

Miller, RE. 1985. Time series analysis. Chem. Eng. June 10, 1985:85-90.

Murrill, P.W. 1981. Fundamentals of Process Control Theory. Instrument Society of
America. Research Triangle Park, NC.

Nelson, LS. 1985. Interpreting Shewart x control charts. J. of Qual. Technol. 17:114-116.

Quinn-Curtis Inc. 1990. Ch. 3, PID Control. Real-time science and engineering tools for
Turbo Pascal. Quinn-Curtis, Needham, MA, USA

Richards, El 1959. A flexible gowth function for experimental use. J. Exp. Bot. 10:290-
300.

Stock, M., 1987. AI and expert systems: an overview. AI Applications 1(1): 9-17.

26

Table 1 Simplified action table for gowth retardant applications to poinsettia crops.

 

 

Growth retardant recommendations duringgrowth stage

 

Control index 1. Early 2. Near first 3. First color 4. Bract 5. Near
color ermansion market
-3 medium rate‘, medium rate, low rate, no, warning no, little effect
repeaty warning‘ warning
-2 medium rate medium rate, low rate, no, warning no, little efi‘ect
warning warning
-1 low rate low rate, no, warning no, warning no, little efi'ect
wamins
0-4 no, not no, not no, not no, not no, not needed
needed needed needed needed

 

2Low- and medium-rate gowth retardant applications were defined as 800 and 1500 ppm chlormequat foliar
sprays, respectively.
yA second (‘repeat') medium-rate application is recommended in this case, rather than a high rate application.

"A warning refers to the likelihood ofreduced bract size or delayed flowering ifgowth retardants are applied

 

 

Table 2. Estimates of Kc and K, PID parameters using regession analysis.
Parameter Estimate :1: 95% confidence limits
Kc -0.51:l:0.03l cm'l
K, -2.84d:0.18 cm"d
Number of observations 104

r’ 0.85

27

 

 

 

 

 

10 upper action Ilmlt
./‘~.
I/ .3“.
deviation " ‘2‘ desired reference
(e.g. mm) x.“
actual performance
\\ 2’33”
.10 “a“. ,f lower action limit
\,_,-"'
correctlve
action
1 2 3 4

time (e.g. days)

—_._——>

Basic components of a control chart.

2.

28

    
    

 

 

 

 

Maximum height”
”CHM”
,/"'3 Reference value
a Minimum height
.r: --"""'"“"3
2’
o
.1:
E
2
0.
Initial plant height
Pot height
Pmch Target
date Date flower date

Components of a gaphical control chart for poinsettia height control.

29

E

 

          

 

4O . ...... Tn—
Growth retardants applied . .........
35- I I I I I ,.-"3 ........
x -- ----
8
S 30‘
§ 25
E 1
8
.a 20‘
E .
3 15, color
33'.
2 10‘
E 5, Control index values
0
Q 0 ocoooooonnfi n

 

 

(3)

 

 

Plant halght (cm), control Index

 

10-
51 Control lndex values
0 nonoooooo_oooooo _

 

(C)

 

 

Control Index values

Plant halght (cm), control Index

_o_°o__oo c1 0_ o

 

.1- an
vi we

6

 

 

 

M'MrTNB'1m'1ob' 11706'11720
09704 09/18 10102 10115 10130 11/13 11/27
Date

Graphical height control charts from a production trial at Michigan State University
with three cultivars: (A) Annette Hegg Dark Red, (B) Celebrate 2, (C) Supjibi.
Legend: + plant height, I actual gowth retardants applied by the expert (1500 ppm
chlormequat foliar sprays), Cl control index values.

4.

1.0

30

 

0.8 .

0.6-

Reletlve etem length

 

 
    
 
  

Standard
reference
curve

 

 

0.4-1 Curve for
taller-growlng
3 cultlvars
0.2-
0.0- IUFII‘VTfIVVTTVVU‘I'IIITTUIIWIIIYIIIYVITI'VY‘I
0.00 0.60
Relative time to flower

Modified gaphical control curve for taller-gowing cultivars.

 

SECTION 2

2. MODELING THE EFFECT OF SHORT DAY DATE ON STEM ELONGATION OF

POINSETTIA WITH A THREE-PHASE MATHEMATICAL FUNCTION

Paul R Fisher‘, Royal D. Heins‘, and J. Heinrich Lieth2

1. Department of Horticulture, Michigan State University, East Lansing, Michigan
48824-1345, USA

2. Department of Environmental Horticulture, University of California, Davis, California

95616-8587, USA.

To be submitted to the Journal of the American Society of Horticultural Science

ADDITIONAL INDEX WORDS. Euphorbia pulchen'ima, plant growth, height control,

Richards function, simulation

31

32

ABSTRACT. The objective of this work was to develop a model for stem elongation of
poinsettia (Euphorbia pulcherrima, Klotz.) using an approach that explicitly models the
sigmoid growth curve as three linked phases of elongation. These phases include 1) an initial
lag phase characterized by an exponentially increasing stern length, 2) a period when
elongation is approximately linear, where internodes reach a uniform length and expand fi'om
the meristematic tissue at equal intervals of time, and 3) a plateau phase where elongation rate
declines to an asymptotic maximum length Separate functions were formulated for each
growth stage, which agreed in height and slope at the transition points, and allowed phases
to vary in length based on environmental conditions. The resulting model fit the data with an
R’ of 0.99. Further validation under a range of conditions would be required before the
model is applied to horticultural situations, however the model is formulated to allow dynamic
simulation. Model parameters have clear biological meaning, and the approach is particularly
suited to situations in which the identification of growth phases is an important objective, or

where phase lengths are likely to vary.

INTRODUCTION

Under constant environmental conditions, shoot elongation of determinant growing plants
usually follows a sigrnoidal pattern over time. In general such patterns consist of three phases
(Richards, 1969): 1) An initial lag phase characterized by an apparently-exponential cell
expansion in which cells remain meristematic and continue to divide at equal times, followed

by 2) a period when elongation is approximately linear, where internodes reach a uniform

33

length and expand from the meristematic tissue at equal intervals of time and 3) through
limiting resources or maturation, a plateau phase where elongation rate declines until the

organism reaches an asymptotic maximum length.

Existing modeling methods have shortcomings when applied to the stem elongation of
poinsettia (Euphorbia pulcherrima, Willd.). Sigrnoid growth curves, for example the
Richards (1959) firnction, are usefiil when modeling individual plant organs but are less
appropriate where the length of the three phases can vary depending on environmental stimuli.
Individually modeling the elongation of each intemode (for example Berghage and Heins,
1991) is complex, requires intensive data collection, and the resulting stem elongation model
is difiicult to validate. Existing ways of combining multiple equations to describe multi-phasic
growth (for example Robertson (1923) and Koops (1986)) are highly empirical and not

suitable for dynamic simulation.

The objective of this work was to develop a model for stem elongation of poinsettia using an
approach that explicitly models each of the three phases of elongation using separate but
linked functions. Although the resulting model is highly empirical, separating growth into
phases resulted in a flexible curve that can be readily interpreted biologically. Features of
existing modeling approaches, including the Richards Function (Richards, 1959), are
discussed in the first part of the article. The three-phase model is then described, and is

applied to the elongation of poinsettia.

34

Existing methodologies
Several mathematical functions, including exponential, monomolecular saturation, logistic,

and Gompertz functions, have been developed to describe patterns of growth and elongation

rate that have the general form

~11 - 1(3) (1)

where H is the plant height and time is t (Richards, 1969). Increasing the number of
parameters in the relative growth function f(H) results in a correspondingly more flexible
curve and the ability to adjust to a wide range of data patterns (Richards, 1969). The

formulation of f(H) proposed by Richards (1959)

17.

 

 

w - we " -H "you ') (2)
has the solution
H
H ‘- °4 (3)
[your ”-Ho'): 4'

which is termed the Richards function. It usually achieves a close empirical fit to many
species and growth variables because its parameters can be adjusted to provide a wide range
of shapes. Of these parameters, H0 and A represent the initial and asymptotic heights,
respectively, and k and n are parameters related to the shape of the growth curve and the

location of the inflection point. Monomoleailar, Gompertz, and logistic functions are special

35

cases of the Richards firnction (Richards, 1959), with values of n of -1, nearly equal to zero,
and one respectively. Previous studies have used the Richards filnction to model shoot
elongation, for example chrysanthemum (Dendranlhema grandrflonnn) (Larsen and Lieth,
1993; Karlsson and Heins, 1994), and Easter lily (Lilian: Iongiflonnn Thunb.) (Lieth and

Carpenter, 1990).

The Richards function generally works well to describe the observed patterns of individual
organs, for example individual internodes of poinsettia (Berghage and Heins, 1991).
Berghage and Heins (1991) modeled the elongation of an entire pinched poinsettia shoot by
quantifying and summing the elongation of each intemode with the Richards function.
Parameters were varied depending on location of the intemode on a stem, day and night
temperature, crop maturity, and photoperiod. The resulting model successfully predicted
elongation of pinched ‘Annette Hegg Dark Red' poinsettia in a validation trial. However,
intemode models are complex, are dificult to validate fully, especially when the number of
environmental variables is increased, and require considerable data collection. The Berghage
and Heins (1991) model was based on one cultivar and may be dificult to apply to other
cultivars which have been observed to differ in leaf unfolding rate, flowering response time
and final stern length. It would therefore be advantageous to develop a stem-based poinsettia

elongation model that is flexible enough to incorporate complex biological responses.

We have encountered a fitting problem when applying the Richards firnction to stem
elongation of poinsettia grown as a single stern. Single-stem poinsettia exhibits an extended

vegetative phase during which internodes elongate regularly and result in an extended near-

36
linear phase and short transitions between lag, linear, and plateau phases. When fitting the
Richards function to this elongation pattern, biases consistently occur near the transition
zones. The final potential stern length and total elongation period also tend to be

overestimated.

A more fimdamental problem occurs when the Richards firnction is used for dynamic
simulation: at any point in time its parameter estimates define the entire elongation trajectory.
Analysis of the first, second, and third derivatives of the Richards function by Nath and
Moore (1992) have been used to identify transition points between exponential, linear, and
decay phases in elongation. The length of each phase is, however, fixed by the Richards
firnction and is therefore inappropriate for situations where phase duration may vary. An
example where phase length may vary is the stem elongation of plant species whose
reproductive development is triggered by an environmental stimuhrs that can also vary in time,
for example a critical photoperiod or temperature. In commercial production of poinsettia,
a short day plant, growers vary the length of the vegetative, near-linear, elongation period
before flower induction by manipulating photoperiod to produce plants of a desired final plant
height. Causton et al. (1978) considered that the Richards function parameters, particularly
the asymptotic factor, become less meaningfiil when applied to an entire organism especially
where overall growth is not determinate. Richards (1969, p.36) suggested that whenever
separate growth phases arise, modeling the entire life history of higher plants would require
either fragmentation of a growth model into separate firnctions, or the separate modeling of

individual organs such as leaves or internodes.

37
Multiple functions have been combined in various ways to improve empirical fitting to data,
particularly in situations where difi'erent growth phases are hypothesized to occur over an
organism lifecycle. Brody (1945) described two phases of growth, modeling the first phase
with an exponential function, and describing the second phase using a monomolecular
function. Size, but not the first derivative was constant at the transition between Brody's
phases, and the transition between phases was estimated by observation. Hunt and Evans
(1980) divided growth data of maize (Zea mays L.) into phases which were fitted by splined
cubic polynomials. The polynomials at each phase met at statistically-determined points
termed ‘knots' where adjacent curves agreed in position, slope, and rate of change of slope,
thus ensuring smooth transitions and minimizing loss of degrees of fieedom. A technique
where the growth curve is calculated from the summation of two or more curves has been
applied to describe the increase in weight gain of humans and other mammals (Robertson,
1923; Koops, 1986) and for the growth in cheek diameter of peach fi'uit by Genard and
Bruchou (1993). Although all of these techniques provided a close empirical fit to observed
data, the resulting models were dificult to interpret biologically or were not suitable for

dynamic simulation.

38

MATERIALS AND METHODS

MM
Figure 1 represents the curve and the role of various parameters in the proposed three-phase

(fab) model described mathematically below. Elongation was considered to occur in three
phases: an initial lag phase (LAG), a linear phase (LIN), and a plateau phase (PLA). The
transition periods at which plants moved fi'om LAG to LIN and fi'om LIN to PLA were
denoted t, and r, respectively. Each phase of elongation was described with a separate

firnction, with a continuous stem length and equal first derivative at r, and t2

fad!) ............ for tst1
f I (r) . fun“) ............ for r1<rsrrrla=r2 (4)
[do ............ far or,

where

fuoflr) ' fwfl‘r)
fLM‘z) - fmltz)
1.1.4:.) 41w.) (5)
1101(5) ' fill-(‘2)

Equations were chosen that provided the empirical qualities desired to develop a sigmoid
curve. Increasing growth rate during the lag phase was described with an exponential
fimction where a is the starting length and B is a rate constant. Constant growth rate during

the linear phase was described with a linear fimction with elongation rate 7. A

39
monomolecular function was used to describe decreasing growth rate during the plateau,
where the quantity of growth remaining when the plateau phase begins is represented by 6 ,

and k,“ represents the rate at which the crop reaches the asymptote.

cum-1 ............................ for rsr,
f,,_.(r) - faction! for W“: (6)
{Mayan-cad”) ...... for or,

 

Final height (H) can therefore be calculated as:

The first derivatives of Equation 6 are:

6000 ................................... for 1st,

1’ I (t) . y ........................................... for tl<tst2 (8)
kms(¢‘*’“‘“'”) ........ far 9:,

So that fun ande have equal first derivatives at t,,

v - a.” (9)

Thus ify is given, 1, can be calculated as

_ ln(v)-ln(l3)
B

‘r

(10)

40

Equal first derivatives of flu and j)“ at time 12 means that

Y . kmbgww (11)

km can therefore be calculated as

0v|-<

(12)

Assuming H}, 1,, fuc(t,), fm,(r,),and km are calculated using Equations 7, 10, 6, 9, and 12
respectively, the model therefore requires the estimation of five parameters: a, B, y, t, and

6.

Model application to poinsettia gem elongation
Berghage and Heins (1991) described a sigmoid pattern of shoot elongation of pinched

poinsettia (pinching refers to the removal of the apical meristem to promote lateral branching)
which we have also observed in poinsettia grown as a single unpinched stern After the initial
pinch (or transplant in the case of unpinched plants), there is a period of rapid cell division
and increasing elongation rate. A vegetative period of intemode development and elongation
follows, during which leaf appearance rate is a fimction of average temperature. When flower
initiation occurs, induced by a critical minimum nightlength of about 11.75 hours (Larson and

Langhans, 1963), flower bud primordia are formed on the apical meristem and no firrther

41

nodal leaf primordia are developed. Intemodes that elongate alter flower initiation are
progressively shorter in length (Berghage and Heins, 1991). Where flower initiation does not
occur either because of night temperatures above 23 °C or long photoperiods, the
approximately linear growth continues for an extended period. Under continued long days
orhighnighttemperatures, theplarrtevennrallyfonnsaseries ofsterileterminal buds, and the

main stem ceases to elongate (Kofi'anek and Hackett, 1966).

Experimental design for poinsettia

Unpinched (i.e. single-stem) poinsettia ‘Freedom' were grown during 1994 in a Michigan
State University greenhouse. Three groups of rooted cuttings were transplanted into 15-cm
diameter, (2,570 cm’) pots with Metro Mix 510 media (Scotts, Marysville, Ohio) on August
4, September 1, and September 14 respectively. Plants were placed at 35 x 35 cm to avoid
inter-plant shading. Four-hour night interruption lighting from 2200 to 0200 was provided
for all plants until September 27. On September 27 five plants from each of the three-
transplant date treatmentss were placed under shade cloth to provide a night length of 15
hours thoughout the remainder of the experiment. This means that for the plants of each
treatment, short days were begun on day 54, 26, and 13, respectively (and were termed the
‘ SD 54', ‘ SD 26', and ‘SD 13' treatments respectively). Stern length fi'om the pot rim upward
and leaf number were recorded twice a weelg and plants were checked three times a week for
visible bud (defined as the first day at least one complete flower bud was visible without
moving leaves) and anthesis (defined as the first day anthers were visible on at least one
cyatheurn). Fmal leaf number, intemode length, and stem length were measured. Two hour

average air temperature was logged fiom an aspirated type G thermocouple with the air

42

intake at the plant can0py height. Day and night temperature setpoints were maintained at
a constant 21C, and observed temperatures were an average 21.4:t0.2C with a DIF

temperature (average day minus average night) of 0.8C.

Based on Berghage and Heins’ (1991) research, we hypothesized that the plateau phase would
occur some number of days VBPLA after visible bud date (VB) began, because at VB the
apical flower bud is visible and all internodes on the stern have begun to elongate. The model
was therefore reparameterized to estimate VBPLA and calculate (2 based on the visible bud

date:

r2 - VB . VBPLA (13)

By assuming that VB occurred SDVB days after the start of short days (SD), final height H,

could be predicted based on the timing of short days:

Hf.s.fm(so.snm.varzn (14)

The fgm, firnction was fit separately to observed height data fi'om each individual
photoperiod treatment using the SAS PROC NLIN (non-linear regression) procedure
(Statistical Analysis Systems Institute, 1988), and trends in parameter values were examined.

TheSAS programisincludedinAppendixA Themodelwasfittotheentiredatasetinone

43

combined analysis, assuming a, B, y, :2, and 6 were independent of short day treatment.
Difl‘erences between short day treatments with respect to initial stern length and elongation
rate during the lag phase were then incorporated in the model. a was assigned the value of
the observed stem length at transplant. Each short day treatment was assigned a separate 0
pararneterto represent elongation during the lag phase (0,3, 026, and 0,. for the SD 13, SD
26, and SD 54 treatments respectively). The remaining parameters (7, VBPLA, and 6) were
assumed independent of treatment. Results of the statistical fittings were tabulated and

graphed against the observed data.

RESULTS

Elongation of the three short day treatments followed a sigmoid pattern (Figure 2a). Visible
bud occurred 18-20 days after SD for the three short day treatments (Table l) and both the-
time from SD to VB and from SD to anthesis were not significantly difl‘erent between
treatments. The average number of days from SD to VB for the three short day treatments
(SDI/B) was 19.1116 (:t 95%) days, and fiom SD to anthesis was 542:2.5 days. Elongation
rate after VB was similar for the three short day treatments, and elongation after anthesis was
less than 10 mm (Figure 2a). Elongation before VB was more rapid for the SD 26 treatment

than the other two treatments.

The longer the period between transplant and the start of short days, the longer the final stern

length. This difl‘erence in final stern length was primarily due to an increase in intemode

44
number with increasing duration of the vegetative period (Table 1, Figure 2b). There was no
difference in the initial leaf number between treatments (9.6:b0.5 leaves). After an initial lag,
leaf unfolding rate was approximately linear until VB, afier which four further leaves unfolded
on the main stem. The SD 26 treatment unfolded leaves more rapidly than the other
treatments. Final intemode length (Figure 3) for the short day treatments exhibited a
consistent pattern Length declined fi'om internodes one to eight (counting upward fi'om the
soil), which were expanding at the time the cuttings were either on the vegetative stock plant
or were being meted as transplants. Intemodes nine to fourteen, which were expanding alter
transplant and during the initial lag period of elongation, were successively longer. The
following internodes were approximately equal in length until the final 8-11 internodes which
were progressively shorter. One source of variability in intemode lengths was that although
nodes were alternate, occasionally two successive nodes were almost opposite, resulting in

particularly short and long internodes at that point.

Leafunfolding rate of poinsettia increases with increasing average temperature below 25C,
and shoot elongation increases as DIF temperature increases (Berghage and Heins, 1991).
Average temperature declined by over one degree C during the experiment (Figure 2c,

P<0.01), however there was no significant trend in DIF temperature.

When the fm model was fit separately to each photoperiod treatment, the R’ was over 0.99
in each case (Table 2). Initial cutting length was shorter for the SD 26 plants than other
treatments (Table l), which was reflected in a lower estimate for 0:. Plants in the SD 54

treatment had slow initial elongation, with the lowest estimate of [3 and latest estimate of 1,.

45

The SD 26 plants elongated more quickly during the linear phase than the other treatments,
withthehighest estimateofy. t, forthe SD13, SD 26, and SD 54 treatrnentswas estimated
to occur 28, 24, and 33 days after transplant. From to to r,, the model predicted 23, 23, and
29 mm of elongation and plants were observed to unfold 5, 5, and 8 leaves for the SD 13, SD
26, and SD 54 respectively. The period represented by VBPLA ranged fi'om 23 to 26 days,
and asymptotic 95% confidence intervals overlapped for all treatments. Estimates of 6 had
large coeficients of variation, and although the SD 54 treatment had the highest estimate of

6, the asymptotic 95% confidence intervals overlapped in all cases.

Whn the model was fit to all data using non-linear regression, assuming a, B, y, t,, and 6
were independent of short day treatment (analysis not displayed), the resulting R’ was 0.99.
However, the model predictions tended to be out-of-phase with observed data, i.e. the
predicted height was consistently taller or shorter than observed because of difi‘erences in
initialstemlengthandearlyelongationrate. t,was estimatedinthisfitto occur28 days after
transplant, a was estimated at 50i2 mm (iasymptotic standard error), and B was estimated

at 0.116d:0.003.

The model resulted in a closer fit to data when difl‘erences between short day treatments with
respect to initial stem length and elongation rate during the lag phase were incorporated. a
was assigned the value of the observed stern length at transplan, separate estimates of B by
treatments represented elongation during the lag phase (0 ,3, 02,, and 0,, for the SD 13, SD
26, and SD 54 treatments respectively) and remaining parameters (7, VBPLA, and 6) were

assumed independent of treatment. Fit of this ‘ all treatrnents' model to the combined data set

46

resulted in an r’ of 0.994 (Table 3). In this analysis, 1, was linked to observed VB in the same
manner as in the previous model fit. Standard errors for parameter estimates were generally
smaller than when the model was fit individually by photoperiod treatment. The estimates of
0,, and 0,, were very similar and were significantly lower than the estimate of 02,. As a
result, timing oft, was predicted to occur later for the SD 13 and SD 54 treatments than the
SD 26 treatments, with correspondingly greater elongation between transplant and 1,. The
coefficient of variation was greatest for the estimate of 6. The predicted final height was
within 10 mm of the observed final height for all treatments, with deviations of 8, 7, and -2

mm for the SD 13, SD 26, and SD 54 treatments respectively.

DISCUSSION

The f3,,,,,,,, function fit closely to observed data and explained over 99% of the variation,
however initial elongation varied baween transplant batches. The overall model predicted that
1, would occur 20-33 days after transplant. Timing of 1, was not closely correlated to a
particular leaf number, but consistently occurred when the plants had elongated 19 to 29 mm.
The SD 26 treatment was more vigorous than the other treatments in terms of elongation rate
and leaf unfolding rate during the PLA phase, and the SD 13 and SD 54 treatments were
similar. The slight trend in decreasing average temperature was not suficient to explain
difi‘erences between initial elongation rate of treatments. The SD 26 cuttings were shorter

than other treatments and may have experienced less transplant stress. Factors afl‘ecting

47
variability between transplant batches, particularly in the LAG and LIN phases, and the efl‘ect

of temperature need to be addressed by firrther research.

1, was predicted to occur about 42 days (SDVB + VBPLA) afier SD. Assuming a starting
length of 50 mm, and 0 equal to 0.116 (the average of all treatments), the model predicted
a pattern (Fig. 6) where varying the short day date assumption afl‘ected final height because
of the efl‘ect of SD on 1,. Although the model assumed that 6 was independent of the
duration of the LIN phase where SD + SDVB, the parameter estimates in Table 2 indicated
that 6 may increase as time fi'om transplant to SD increases. This result may have been
caused by experimental error, or may have arisen because fewer internodes were elongating
at the time of1,in the SD13 treatment than in the SD 26 and SD 54 treatments. In addltion,
the model does not quantify elongation during the plateau phase when plants are never

exposed to short days.

The use of a model which explicitly separates the growth period into three phases yielded
useful biological information about the timing of phenological events. For poinsettia stem
elongation, 1, (the transition fiom the lag to linear phases) represents the point when a period
of maximum and constant absolute elongation rate begins, with regular development and
elongation of internodes. At 1,, the shoot is fuo(1,) in length. The parameters a and 0
represent the initial transplant size and rate of increase in elongation during the LAG phase
respectively. Time 1,, the change fi'om LIN to PLA, represents the point when the change to
reproductive development under short days begins to impact on stem elongation rate. Where

the start of short days is known, 1, could be predicted because VB consistently occurred 19

48

(SD VB) days after the start of short days. The elongation remaining at the end of the LIN
phase for reproductive plants, represented by 6 , was approximately 30 mm. The rate at
which plants reach the asymptote was represented by km. H, the asymptotic final height,

increases the later 1, occurs.

The multi—phasic modeling approach could be readily modified for other horticultural
applications. We chose to estimate a, B, y, 1,, and 6 by non-linear regression, and to
calculate other parameters. However, Equations 6 to 14 could be readily rearranged to alter
which parameters are estimated or calculated. For example, 1, could be estimated and 7
calculated if the asymptotic standard error of 1, was of interest. In addition, the number of
phases could be altered (for example where a lag phase does not occur or data are missing).
Finally, the choice of equations within each stage could be changed. For example, if the initial
size was hypothesized to afi‘ect subsequent growth rate, the lag phase could be reformulated

as

rm, - u‘” (15)

The model assumes that elongation rate is determined by a combination of growth stage and
plant size. During the lag phase, relative elongation rate is dependent on current plant height
in an exponential function and is not afi‘ected by the other two phases that have yet to occur.
During the linear phase, relative elongation rate is independent of plant size -f(H) in Equation
1 equals y. During the plateau phase the monomolecular function defined by 6 and km is
independent of the duration between 1, and 1,, and hence is independent of the height at 1,.

In contrast, the Richards function assumes that growth rate is always dependent on a

49
continuous firnction that is a function of plant size (Equation 2). If 1, and 1, are linked to
observable phenological events, the ability to utilize separate firnctions at difi‘erent growth

stages provides a powerful biological tool.

Dynamic simulation requires the use of rate equations, which can be calculated for each
component of the fm model, and consequently for the entire model. From a mathematical
standpoint, the f,,,,,,,, model could be readily adapted to incorporate other variables, for
example average temperature or growth retardant applications. During the LIN stage, linear
elongation is assumed to occur based on regular intemode development and elongation rates.
Increased elongation rate would be expected at higher temperatures based on the leaf
unfolding rate response to average temperature. A leaf unfolding rate model would be a
useful addition to a f,,,,,,, model: by linking 1,, 1,, and the entire time axis to thermal time,
average temperature could be incorporated. An advantage of the incremental nature of the
model, with phase changes linked to observable events, is that 1, and 1, could be readily
calibrated during simulation if observed height, SD, or VB were difi‘erent from their predicted
values. One example where this feature would be useful is in the case of plants grown under
natural photoperiods, where SD can not be precisely identified. In this case, observed visible
bud date could be used to calibrate the model and predict 1,. Factors that afi‘ect stem length,
for example growth retardant applications, could be incorporated by multiplying the first
derivative by a perturbation function or scalar using the methodology described by Lieth and

Reynolds (1986) and Larsen and Lieth (1993).

50
The model described here would, however, require validation with independent data before

being used for simulation or being applied commercially. The elongation curve is likely to
vary depending on cultivar, transplanting of rooted or unrooted cuttings, temperature, and

pinching.

A finther use ofthe model would be in graphical tracking, 5. technique described by Karlsson
and Heins (1994) where a stem elongation model is used to develop a target height curve over
time for use in a control chart. Observed height during the production season are plotted on
the chart and compared against the target curve to provide feedback on whether a crop is
elongating at the desired rate. Karlsson and Heins (1994) scaled height and time axes from
zero (minimum height and pinch date) to one. The resulting model was then scaled based on
the target final height and production dates. The f3”, could readily be sealed in height and
time fi'om zero to one. However, because timing of 1, is known to be dependent on SD, and
SD varies in commercial poinsettia production, it would be more valid to have a separate
graphical track curve based on the intended timing of SD. Because the vigor of transplant
batches may vary, afi‘ecting 1,, this factor would need to be considered when constructing a
robust graphical track model. The graphical track curve could be used after an observable
indicator that the crop has reached 1,, for example that plants have elongated at least 30 mm
above the transplant height, to avoid errors in the target curve in situations where transplant

elongation during the lag phase is faster or slower than expected.

51

CONCLUSIONS

The f3,” fimction is an empirical model designed for quantifying stem elongation of higher
plants. There were advantages in explicitly modelling each phase of growth. Parameters had
clear biological meaning. Ifthe model was used for simulation, the incremental nature of the
functions would allow the model predictions to be calibrated at intermediate points in the life
cycle, based on observed phenological or environmental events. The fw function could
be applied to other biological situations in which the identification of growth phases is an

important objective, or where phase lengths are likely to vary.

LITERATURE CITED

Berghage, RD. and RD. Heins. 1991. Quantification of temperature efl‘ects on stem
elongation in poinsettia. J.Amer.Soc.Hort.Sci. 116: 14-18.

Brody, S. 1945. Bioenergetics and growth. Reinhold Publishing, New York, NY.

Causton, DR, C.O. Elias, and P. Handley. 1978. Biometrical studies of plant growth. Plant,
Cell and Envt. 1:163-184.

Genard, M. and Bruchou, C. 1993. A functional and exploratory approach to studying
growth: the example of the peach fi'uit. J.Amer.Soc.Hort.Sci. 118:317-323.

Hunt, R. and G.C. Evans. 1980. Classical data on the growth of maize: curve fitting with
statistical analysis. New Phytol. 86:155-180.

Karlsson, M. G. and RD. Heins. 1994. A model of chrysanthemum stem elongation.
J.Amer.Soc.Hort.Sci. 119:403-407.

52

Kofianek, AM. and W.P.Hackett. 1966. The influence of daylength and night temperature
on the flowering of poinsettia, Cultivar ‘Paul Mikkelsen’. Proc.Amer.Soc.Hort.Sci. 87:515-520.

Koops, WJ. 1986. Multiphasic growth curve analysis. Growth 50:169-177.

Larsen, RU. and J.H. Lieth. 1993. Shoot elongation retardation owing to daminozide in
chrysanthemum: 1. Modeling single applications. Sci.Hort. 53:109-125.

Larson, RA and RW. Langhans. 1963. The influences of photoperiod on flower bud
initiation in poinsettia (Euphoria pulchem’ma Willd.). Proc.Amer. Soc.Hort. Sci. 82:547-551.

Lieth, J.H. and P. Carpenter. 1990. Modeling stem elongation and leaf unfolding of Easter
lily during greenhouse forcing. Sci.Hort. 44: 149-162.

Lieth, J.H. and IF Reynolds. 1986. Plant growth analysis of discontinuous growth data: a
modified Richards function. Sci.Hort. 28:301-304.

Nath, SR and FD. Moore 1111. 1992. Growth analysis by the first, second, and third
derivatives of the Richards Function. Growth, Dev. & Ag. 56:23 7-247.

Richards, F .J . 1959. A flexible growth filnction for empirical use. J. Exp. Bot. 10:290-300.
Richards, F .J. 1969. The quantitative analysis of growth. p.3-76. In F.C. Steward (ed). Plant
Physiology: A treatise. Analysis of growth: behaviour of plants and their organs. Academic
Press, New York, NY.

Robertson, T.B. 1923. The chemical basis of growth and senescence. Lippincott, Philadelphia.

Statistical Amlysis Systems Institute. 1988. SAS/STAT Users guide. Release 6.03 edn. SAS
Institute Inc, Cary, N. C.

53

 

 

 

Table l. Phenological and growth data (mean i 95%) for each photoperiod treatment.
Photoperiod treatments
SD 13 SD 26 SD 54 significance’
transplant to visible bud 33.4:t1.3 46.6:t4.3 72.4:1:4.9 "t
(VB) (daYS)
N8

short days to visible bud 20.4i1.3 18.6:b4.3 18.4:h4.9

(SDVB) (days)

transplant to anthesis 68.417 .1 81.4i7 .2 105.8il. *"
(daYS) 1

short days to anthesis 55.4:h7.1 55.4312 51.s=b1.1 "3
(daYS)

initial stem length (mm) 56d:14 32:11 51:1:6 **
final stem length (mm) 180:1:26 228:1:25 303:1:21 ***
final intemode number 19.43:] .5 24:1:l.0 32.236 “W

 

1 NS,*,**,*" nonsignificant, or significant at P = 0.05. 0.01. or 0.001 YCSPGCfiVCIY-

 

54

 

 

 

 

 

 

Table 2. Parameter estimates for the fw model fit individually to each photoperiod
treatment.
Photoperiod treatments
Estimated parameters i SD 13 SD 26 SD 54 Units
ASE‘z

01 62312.2 37.7:h2.5 52.7d:2.2 mm
0.114i0.00 0.133i0.00 0.1021000 day’1

6 7 4
7 2.70m. 18 3.19t0.10 3.02:1:006 mm day"
VBPLA 22.7:l:4.2 24.0:I:3.7 25.9:h4.1 days
6 l7.8:l:11.6 27.9:l:13.2 34.1:t15.9 mm
Calculated factors Units
1, 27.8 23.9 33.2 days
1, 56.1 70.4 98.3 days
qu(1,) 85.0 60.6 81.3 mm
fm,(1,) 161.7 209.1 277.9 mm
km 0.152 0.114 0.089 (lay'l
H, 179.4 237.0 312.0 m

R’ 0.995 0.995 0.996

 

‘ ASE, asymptotic standard error

55

Table 3.

Analysis ofvariance and parameter estimates from fitting thefw model to
all data (‘ the all treatments model').

 

 

 

 

 

 

 

 

Source df. Sum of Squares Mean square
Regression 6 12757345 2126652
Residual 419 74179 177
Uncorrected total 425 12833554
Corrected total 424 2847055 113-0994
Estimated Estimate :1: ASE‘
parameters
0,, 0.1038i0.0019 day“
13,, o.1523w.omo day‘
0 ,4 0.1031i0.0022 day‘
7 3.089e0.053 mm day"
VBPLA 233:2.4 days
6 30.2-l:8.9 mm
Calculated factors SD 13 SD 26 SD 54
n 33 20 33
{mag-c 29 19 29 mm
km, 0. 102 0.102 0.102 day"
11,4: 133 204 253
Asymptotic correlation matrix

0,3 0,6 0 ,4 y VBPLA 6
0, 3 l 0.23 0.22 -O. 15 -0. 15 0.10
[3,6 l 0.63 0.68 0.19 -0. 13
0,4 l -0.82 0.30 -0.20
y 1 -0.50 0.32
VBPLA 1 -0.94
6 l

 

‘ ASE, asymptotic standard error

56

Table 4 List of abbreviations and parameters

 

 

[313,926, BS4

SD l3,SD 26,
SD 54

initial stem length in LAG phase of fw
rate constant in LAG phase

rate constants for the LAG phase of the SD 13, SD 26, and

SD 54 treatments respectively

gradient of LIN phase

day'l

asymptotic potential growth during PLA phase
asymptotic height parameter in the Richards firnction
three-phase stem elongation model

filnction during LAG phase

fimction during LIN phase

filnction during PLA phase

predicted stern length

initial stem length parameter in the Richards fimction
final stern length

rate parameter in the Richards function

rate parameter in PLA phase

lag elongation phase

linear elongation phase

point of inflection in the Richards function

plateau phase

days after transplant at which short (flower-initiating)
photoperiods begin

experimental treatment, short days beginning 13, 26,
and 54 days after transplant respectively

time from the start of short days to visrble bud

time variable

time when LAG phase ends and LIN begins

time when LIN phase ends and PLA begins

days after transplant at which visible bud occurs
days from VB to 1,

days

 

57

 

fLIN(t2)

Stem length

 

 

 

 

. l ,

t1 t2
Days after transplant

 

Components of the fw function elongation curve

58

 

§ ‘2’
l

(A)

250 -

 

 

Stem length (mm)
o 3 § § §
1 l l l

 

 

 

 

 

 

 

 

 

Leaf count

 

 

 

 

 

 

 

Anti=22§23nill4rieys r
a s s

, A :

24k;
24- 1.3.3

 

     

—a
m
1

Average temperature (C)
N
l

 

l
A
DIF Temperature (C)

 

 

 

 

- 0
s s s a s 2 s - -4
l l 7 l 7 1 fi
-80 -60 -40 -20 0 20 40 60 80 100
Days relative to start of short days

i (a) Mean stem length and (b) leaf count over time for the three short day
treatments (meartt95°/o confidence intervals, A: SD 13, EJ= SD 26, .= SD

54). (c) a= average temperature and 0= DIF (average day minus average
night) temperatures during the experimental period.

Intemode length (mm)

.s.
O)

.s
A

.A
N

.s
O

(D

59

 

 

 

 

 

 

 

 

0 5 10 15 20 25 30 35 4o
Intemode number (counting up from soil)

Final intemode lengths (average of five plants) for the short day treatments

( A: SD 13, ‘3: SD 26. O= SD 54).

60

 

350
300 -

 

250 -l
200 -

 

 

150
100 -

 

Stem length (mm)

50—

 

 

350
300 -
250 -
200 -
150 -
100 -

Stem length (mm)

50-

 

0
350

 

300 -
250 -
200 -
150 -
100 -

50 ~-

 

 

Stem length (mm)

 

 

 

 

o i i i a 4 .5 i
-60 -40 -20 0 20 40 60 80 100
Days relative to the start of short days

Fitting the f, pm firnction (solid line) separately to each observed mean data
(0) fiom short day treatment (a) SD 54, (b) SD 26, and (c) SD 13.

Stem length (mm)

Stem length (mm)

Stem length (mm)

61

 

350
300 -
250 -
200 -

150 --

100-

50 -~

 

 

 

 

 

350

 

300 -
250 -
200 -
150 -
100 -
50 -

 

 

 

 

 

 

350

 

300 —
250 e
200 ~
150 —
100 -
50 J

 

 

 

0

 

 

 

 

 

-60 -40 -20 0 20 40 60 80 100
Days relative to the start of short days

Fit of the overall fw model (solid line) to observed mean data (0). (a) SD
54, (b) SD 26, and (c) SD 13.

62

300

 

250

'é’

 

150

Stem length

100

 

50

 

 

 

o 20 4o 60 80 100 120
Days after transplant

Model predictions for three short day date (SD) assumptions (short days 15,

30, and 45 days after transplant), a starting height of 50 mm, and 0 equal to
0.116. Arrows represent SD, and 1, occurs 42 days after SD.

SECTION 3

3. MODELING THE DOSE RESPONSE OF POINSETTIA TO A CHLORMEQUAT

GROWTH RETARDANT APPLICATION

P.R Fisher‘, RD. Heins‘, and J. H. Lieth2

1. Department of Horticulture, Michigan State University, East Lansing,
Michigan 48824-1345, USA
2. Department of Environmental Horticulture, University of California, Davis,

California 95616-8587, USA

To be submitted to the Journal of the American Society of Horticultural Science

ACKNOWLEDGEMENTS. We would like to thank University Outreach at Michigan State

University for providing firnding for this project.

ADDITIONAL INDEX WORDS
stem elongation, Euphorbia pulcherrima Klotz., plant growth, height control, Richards

function, simulation

63

64

ABSTRACT. The dose response to a single foliar application of the growth retardant
chlormequat for poinsettia (Euphorbia pulchen'ima Klotz.) was quantified. The dose
response firnction assumed that the initial retarding efl‘ect was independent of concentration
between 500 and 4000 ppm and that concentration primarily afi‘ected the duration of growth-
retarding activity. The dose response firnction was incorporated into a three-phase
mathematical fimction of stem elongation of single-stem poinsettia. The model was calibrated
using a data set fiom plants receiving 0, 500, 1000, 1500, 2000, 3000, and 4000 ppm, with
a resulting R2 of 0.99. Validation of the dose response model against an independent data set

resulted in an r2 of 0.99, and predicted final stem length was within 12 mm of observed final

height.

INTRODUCTION

A three-phase mathematical fimction has been used to model shoot elongation of single-stem
poinsettia (Euphorbia pulcherrima Klotz.) (Fisher et al., 1995). In calibrating the model,
aside fiom photoperiod and minor greenhouse temperature fluctuations, environmental factors
were constant throughout the experiment. For a stem elongation model to be usefirl for
simulation and practical application, however, it is necessary to incorporate the effect of
environmental perturbations such as growth retardant applications and temperature efi‘ects.
Growth retardant chemicals are used widely in the commercial production of poinsettia and

other flowering potted plants for height control (Ecke et al., 1990). A simulation model may

65

be a useful horticultural tool because there is increasing pressure to minimize the use of

growth retardants (Ludolph, 1992) and maximize their eficacy.

Although many researchers have examined the impact of growth retardant applications on
poinsettia final height and flowering (for example, Larson (1967), McDaniel (1986),
McDaniel and Wilson (1990), Holcomb et al. (1992), Holcomb and Rose (1992)), published
data are not suitable for predicting short term changes in stem elongation rate. These data
provide a broad database for determining the effects of growth retardant type and
concentration on final plant height. It is difiicult to generalize results, however, because
growth retardant efiicacy can be afi‘ected by a range of environmental conditions, including
soil media composition (Barrett, 1982), timing (Gilbert; 1992), nutrient status, application

technique and fi'equency, chemical type, concentration, and temperature (Larson, 1967).

The objectives of this project were to quantify the dose response of poinsettia to a single
foliar application of chlormequat growth retardant ((2-chloroethyl) trimethylarnmonium
chloride) and incorporate the dose response into a three-phase model of stem elongation

(1'3”, , Fisher et al. (1995)). Separate data sets were collected for model calibration and
validation. A methodology developed by Lieth and Reynolds (1986) for modifying the
Richards fimction (RF) (Richards, 1959) to incorporate the efi‘ect of darninozide applications
on chrysanthemum (Dendranthema grandrflora (Ramat) Kitamura) was adapted to model
a different chemical (chlormequat), species (poinsettia), and base function (the f,_,,,,,,,

function).

66

MATERIALS AND METHODS

M lin vir nmen ' n
In the Lieth and Reynolds (1986) approach, the Richards equation (Eq. 1)

an, wyhab
1* ' (M')

 

 

(l)
with the solution (Eq. 2) commonly termed the Richards fimction

”c4

H, - n
([11:44 "-rro'). 4'

 

(2)

 

was fitted to data fi'om plants grown in constant conditions. In the RF, 1 represents time, A
defines the upper asymptote of untreated plant height H,, and parameters H, n, and I:
determine the lower asymptote and shape of the growth curve with respect to A. The
estimated values of A, H, n, and k described the asymptotic growth characteristics of H, in

the absence of environmental change.

The RF was modified by Lieth and Reynolds (1986) to simulate the response to an
environmental perturbation. The response function was termed g(t), and the modified

Richards equation was written as

 

a!
% - “g(t) (3)

i
W

here g(t) is a firnction that has a value >= 0. Ifg(1) = 0, there is no growth, a g(t) of 1

67

means that the treated plant grows at the same rate as a control plant, and a g(t) <1 or >1

would indicate that the treated plant is growing slower or firster than the control, respectively.

Larsen and Lieth (1993) modeled the dose response to daminozide by formulating two
alternative g(t) functions (Fig. 1, Eq. 4 and 5). A foliar spray application at time 1,, was
assumed to immediately reach a maximum efl‘ect, or amplitude, that declined over time.
Before the spray application (1 < 1,,), g(t) had a value of 1 (no efl‘ect). After 1,,, g(t) was a
function that had a value less than 1. When a linear decay function (g,(1)) was used, the
chemical was assumed to have no effect alter a period termed persistence, P, at time 1",. The
slope of the decay curve, C,, was calculated fi'om the immediate amplitude, M, and P. The

linear model is represented below (Eq. 4), and is represented graphically in Figure 1a:

1 ............................................ for 1st"
ha) . ML.((1-M,)IP)(1-r,) ............. for 1.51:1", (4)
l ............................................ far 1m<1

In the exponential decay curve (g(t), Eq. 5 and Fig. lb), M ,- referred to the amplitude of the

response and C, represented the rate of decay.

l .................................. for 1st"
23(1) ' 141.11,). “4“” ..... for or, (S)

Larsen and Lieth (1993) obtained estimates of A, n, H, and I: in the Richards function by
fitting Eq. 2 to data from untreated plants. The modified RF (Eq. 3) was then fitted to data
fiom the growth retardant-treated plants, requiring only the estimation of the g(t) parameters,

because the parameter estimates of A, 11, H0, and It were fixed based on the untreated plants.

68

Thr m h l

The f ,.,,,,,,,, poinsettia stem elongation model for modeling elongation under constant
temperature conditions and variable flower initiation dates is described in detail by Fisher et
al. (1995). Equations were chosen (Eq. 6) that provided the empirical qualities desired to
develop a sigmoid curve. Increasing growth rate during the initial lag phase was described
withanexponentialfirnctionvuc), inwhich a istheobserved startinglengthand 0 isarate
constant. Constant growth rate during the linear phase was described with a linear function
(IUN) with elongation rate 7. A monomolecular fimction (fpu) was used to describe
decreasing growth rate during the plateau phase, where the proportion of growth remaining

when the plateau phase begins is represented by 6, and It,“ represents the rate at which the

crop reaches the asymptote.
e-l o e a: ........................... for 1st,
[3 , m . Imus . vr- -- for ‘1‘“‘2 (6)

 

1,311,) . 6(1-0 W”) ..... for or,

where

facal) ' fLM‘l)
furK‘z) ' 51.102)
fl’Ad‘l) ' 1101(5) (7)
W5) ' M12)

and

69

00 W .............................. for 1:1,

{#1) . r ..... I" 11““: (3)
km“: 4NW) ........ for or,

 

In the elongation model described by Fisher et al. (1995), 1, was assumed to occur some
number of days, VBPLA, after the visible bud date (VB), because at VB the apical flower bud
is visible and all internodes on the stem have begun to elongate. VB was assumed to occur
SDVB days after the start of short days (SD). The model was therefore assigned parameters

to estimate VBPLA and calculate 1, based on the visible bud date:

‘2 0 VB 9 VBPLA (9)

thereby incorporating the effect of timing of SD on elongation.

The f,,,,,,,,, function (Eq. 6) was fit to control (untreated) plant data to obtain a curve for
elongation in the absence of a growth retardant application. The resulting model was then

modified to incorporate the effect of a dose response function g(t) on plant height H by

H - [3,4020% (10)

and

43’- -1;,.....(r) :0) (11)

70

The exponential dose response function g,,(1) (Eq. 5) was reparameterized to create a new

variable D that was the inverse of CE:
I .................................. ,far 131"
3110' 0,1304») (12)
141-11,): ........ jar or,

By reparameterizing g,(1), high values of P (Eq. 4) and D both indicated a slower recovery

from the growth retardant (i.e. a greater duration of effect).

Experimgnal design

Calibration data 3g. Rooted cuttings of 'Annette Hegg Dark Red' poinsettia were
transplanted 17 August, 1994 into lS-cm-diameter (2570 cm’) pots. Plants were grown in
a Michigan State University greenhouse at setpoint temperatures of constant 21C, with an
actual average daily temperature of 21.4 :L- 0.2C (means are displayed :1: 95% unless otherwise
stated) and an average DIF (day minus night) temperature of 0.91:0.2 C. Night-interruption
lighting was supplied from 10 PM to 2 AM until 27 September. Black cloth was pulled fi'om
5.30 PM until 8 AM from 27 September until 25 October after which plants were exposed
to natural photoperiods. A foliar spray of chlormequat was applied with a hand sprayer to
four sides of the plant at 10 ml/plant to achieve thorough coverage. Chlormequat was applied
on 20 September, 34 days after transplant, at six rates: 500, 1000, 1500, 2000, 3000, and
4000 ppm plus an unsprayed control. Five plants per treatment were positioned randomly

on a single subirrigated bench at 35 x 35 cm spacing and were surrounded by untreated and

7 l
unmeasured boundary plants. Plants were grown as a single stem and lateral shoots were

removed every two weeks. Height fi'om the pot rim to the stem apex was measured twice
weekly from transplant until one week before application, daily fi'om one week before
application until two weeks afier application, and twice weekly fi'om two weeks afier
application until two weeks after anthesis. Leafnumber was recorded weekly. Incidence of
first interveinal red bract color (first color), externally visible flower buds (visible bud), and

anthesis was recorded daily for each plant.

W. In a second experiment at a Michigan State University greenhouse during
1993, 40 meted cuttings of 'Annette Hegg Dark Red' were planted into lS-cm-diameter pots
on 20 August, and groups of 10 plants received chlormequat spray applications of 0, 1000,
2000, or 3000 ppm at 10 ml/plant 24 days after planting Plants were not pinched, and lateral
shoots were removed 15, 30, and 68 days after pinching to leave a single stem. Night-
interruption lighting was supplied until 36 days after pinching, and was followed by 10-h
photoperiods until anthesis. Setpoirrt temperature was a constant 21C, with an actual average
temperature of 21.5 i 0.2 C and an average DIF temperature of -0.2 :1: 0.2C. Plants were
subirrigated and grown in an MSU greenhouse at 35 x 35 cm spacing in a completely
randomized design Plant height to the stem apex and leaf count were recorded several times

each week until anthesis. Dates of first color, visible bud, and anthesis also were recorded.

72
m
The fw model (Eq. 6) was fit to the control plants in the calibration experiment to obtain
untreated estimates for 0, y, VBPLA, and 6 using PROC NLIN, the non-linear regression
procedure of SAS (SAS Institute, 1988). a was assigned the value of the observed transplant

height for each plant.

Final plant heights for all treatments were compared using ANOVA to confirm that the
treatments had reduced elongation compared with the control. The assumption that there was
an immediate growth retardant efi‘ect afier 1,, was tested using AN OVA to compare the
growth rates of the treated and control plants between 1,, and the first measurement date on
1,, + l. Efi‘ects of the chlormequat application on leaf unfolding rate and the time to first
color, visible bud, and anthesis were compared by AN OVA to investigate whether

development rate was afi‘ected in addition to stem elongation rate.

Variation in initial elongation rate of growth retardant treatments was accounted for before
fitting the dose response model. We found that the g(t) models were highly sensitive to even
slight difi‘erences in absolute height at 1,,. To account for random variation in the initial
elongation rate of plant groups before 1,,, the fw function was fit separately to data from
each treatment between 1,, and 1,,. Parameters y, VBPLA, and 6 were assumed to be equal
to the parameter estimates for untreated control plants, and these estimates were entered as
constants in the model. The initial rate parameter, 0, was estimated separately for each

growth retardant treatment by using SAS PROC NLIN to fit Eq. 6.

73

Computation of H using Eq. 10 required a numerical simulation procedure that used a
rectilinear integration method with an integration interval of 0.5 days. The resulting data set
of predicted H, using parameters for y, VBPLA, and 6 fi'om control plants and the estimates
of 0 by treatment, was used to estimate g(t) parameters for each concentration. The SAS
program is included in Appendix B. The g(t) parameter estimates were graphed and a
firnction was fit to these data to estimate the dose response as a function of concentration.
The fw control parameters were combined with the gL(1) and g,,(1) dose response functions
to derive complete models, termed G, and GE respectively, for the elongation of single-stem
poinsettia beginning at time of transplant (1,,). A simulation program with a time step of 0.5
days was used to generate data sets of predicted heights fiom both models. Goodness of fit
of the predicted heights against the entire observed data set including treated and untreated

plants was then quantified.

Finally, the model was validated against the 1993 data set. The fm, model (Eq. 6) was fit
to the control plants in the validation experiment to obtain untreated estimates for 0, y,
VBPLA, and 6 using PROC NLIN, and a was assigned the value of the observed transplant
height for each plant. Predicted heights were obtained by simulation of the g(t) models from
the calibration experiment combined with the untreated elongation curve to form G, and G,
models for the validation data set. Predicted heights fi'om the G, and GB model were then

compared for goodness of fit against the observed height.

74

RESULTS

'on n l
Elongan'on followed a three-phase pattern (Fig. 2), with an initial lag in elongation followed
by a near-linear period of growth and a final plateau stage. Average transplant height was 43
i 6 mm above the pot rim, and elongation increased by an additional 383 mm by the end of
the experiment. Leafunfolding late did not exhibit an initial lag and was approximately linear
from 1,, until 80 days after transplant (day 80), after which no further leaves unfolded on the

main stem.

Fitting the f Mm function to the height of untreated control plants resulted in an 12 of 0.996
(Fig. 2, Table 1). Final height (H) including the transplant height (a) was predicted to be 426
mm, compared with an observed final height of 427 :1: 43 mm. Plants were predicted to begin
the linear phase of elongation 23 days after transplant, when they were 78 (fua(11)) mm in
length, at over 5 mm day‘1 (7). The linear phase was predicted to end 15 (VBPLA) days after
visible bud (or 35 days after SD) at a height of 365 (f,_,,,(12)) mm, after which an additional

63 mm of elongation (6) was predicted during the plateau phase.

wth r trnen
There was a statistically significant effect (P = 0.011) of growth retardant concentration on
elongation between 1,, and the end of the experiment, with a trend of decreasing height with
increasing chlormequat concentration (Table 2). However, because of variability in initial

elongation before 1,,, the difi‘erence between transplant height at 1,, and final height was not

75

statistically significant (P = 0.136) between treatments. Plants fiom the 4000 ppm treatment
had the greatest variability in elongation after 1,,, followed by those final the 3000 ppm and

untreated plants.

Growth retardant treatments had a rapid efi‘ect on elongation rate, and the initial efi‘ect was
similar at all concentrations between 500 and 4000 ppm. The null hypothesis that, compared
with the control, the growth retardant concentrations between 500 and 4000 ppm did not
affect elongation during the first day after application was rejected after a significant t-test
comparison (P = 0.027) between elongation of the control plants (6.5 :t 3.5 mm) and all
growth retardant concentrations combined (3.5 :1: 0.8 mm). However, the null hypothesis that
the initial effect on elongation was the same for all growth retardant concentrations (excluding
the control) was not rejected — there was no significant difl‘erence in an ANOVA comparison
of the initial elongation between 1,, and 1,, +1 between 500 and 4000 ppm. Elongation
between 1,, and 1,,+l was similar between treatments and was highly variable (Fig. 3).
ANOVA of elongation fi'om 1,, until the first two and three days after 1,, also was not

significantly different between 500 and 4000 ppm.

Growth retardant applications did not afl'ect timing of visible bud, first color, or anthesis
(which averaged 20.1 :1: 0.2, 16.1 i 0.7, and 50.7 :1: 1.1 days, respectively, alter the start of
short days on day 41). Final leaf count (average 25.7 :h 0.4 leaves) also was not afi‘ected by

growth retardant concentration.

76

F i ' 1 m

The estimates of 0, the rate parameter for the lag phase, ranged from 0.141 day" for the 500
ppm-treated plants, which were shorter than the control plants at 1,,, to 0.176 day" for the
3000 ppm-treated plants which initially elongated more rapidly than the control plants (Table

2). In all cases, 1,, the start of the linear phase, was estimated to occur before 1,,.

The SAS PROC NLIN procedure was used to simulate the g(t) dose response fimctions,
using the untreated estimates of 0, y, VBPLA, and 6, and estimating either P or D for Eqs.
4 and 12 respectively. When fitting the g(t) functions to the treated plants allowing both the
amplitude and recovery parameters to be estimated by non-linear regression, we found a high
degree of correlation between amplitude (M, and M,) and duration parameters P and D
(which was also reported by Larsen and Leith (1993)). Treated plants elongated an average
of 47% more slowly during the first day after application compared with the control, and
there was no significant difl‘erence in the initial elongation rate of plants treated with 500 to
4000 ppm, regardless of concentration (Frg. 3). Therefore, the amplitude parameters (M, and

M,) were set to 0.53 for the remainder of the analysis.

Both g(t) models were fit to each concentration to obtain a data set of estimates of P and D
(Fig. 4). Both P and D increased with increasing chlormequat concentration between 500 and
4000 ppm. For example, the growth retardant application was predicted to persist for 16
days at 500 ppm and 47 days at 4000 ppm by the linear g,(1) model. Parameters P and D

were modeled as a linear firnction of concentration using the equation

77

IcaeboCanc (13)

where X represents P or D for the g,(1) and g,(1) models respectively, and Conc was the

chlormequat concentration in ppm a and b have units of days and days ppm“ respectively

Initialestimatesofparametersaand binEq. 13 were calculated fi'om linear regression ofthe
estimated P and D parameters versus concentration (Fig. 4). The resulting estimates were
used as starting values for fitting the g,(1) and g,(1) models separately to the entire data set
of treated plants in order to estimate a and b by non-linear regression. Of the remaining
parameters in the complete G, and G, models, the amplitude parameters (M, and M,) were
set to 0.53, based on observed elongation rate between 1,, and 1,,-+1; the [w model
parameters 7, VBPLA, and 6 were set to the estimates for the untreated control plants (Table

1); and estimates of 0 (Table 2) were entered for each treatment.

The resulting two g(t) models (Table 3) had a similar 12 of 0.989, and the coeficient of
variation of parameter estimates was also similar. At 1500 ppm, the g,(1) model predicted
greater growth-retarding efl‘ect than the g,(1) model during the first 18 days after 1,, (Fig. 5a),
whereas the g,(1) model predicted greater growth retarding effect as the g,(1) model neared
1. The relative growth-retarding (g(t)) efl’ect predicted by the models never difl‘ered by more
than 0.1 for all concentrations between 500 and 4000 ppm and all days after application (Fig. 1
5a). The g,(1) model predicted that a 500 ppm growth retardant applied 34 days afier
transplant would persist for 15 days and reduce height by 6% compared with an untreated

plant (Fig. 5b); at 4000 ppm there would be 44 days of persistence and 15% height reduction.

78
There was little difl‘erence between the predictions of the G, model and those of the 6,,

model, and at a given chlormequat concentration the difi‘erence in the final height predicted
by both models was within 3 mm, or 1%, of final height (the G, model predicting slightly
more elongation). Predictions by both models were within 9 mm of the average final height

for each treatment, with the greatest deviation for the 2000 ppm treatment (Figs. 6 and 7).

Meielxaflatign

The f3,“ fimction was fit to the untreated control plants (Table 4, Fig. 8a) in the validation
experiment. The control plants elongated more rapidly during the lag phase compared with
the control plants in the calibration experiment, with a significantly higher estimate of 0 and
an earlier estimate of 1,.. Elongation of the untreated validation plants was 26% slower
during the linear phase compared with the calibration experiment. However, validation
experiment transplants were 7 cm longer than the calibration cuttings. Therefore, although
total predicted final height (H,) of the control plants was only 3 cm shorter in the validation
experiment compared with the the calibration experiment, validation plants were 10 cm
shorter when only elongation alter transplant was considered. The estimate of 6 (21 :1: 19
mm) had a high asymptotic standard error, which was probably because few data points were
collected fiom the plateau phase. The 6 parameter for the validation plants was estimated to
be only one-third of the length of the plateau in the calibration experiment, in part because the

estimate of VBPLA was nine days later than that in the calibration experiment.

79
Heights were predicted for the growth retardant-treated plants using the g(t) models (Table
3) from the calibration experiment combined with the f,_,,,,_,, parameters fi'om the untreated
validation plants (Table 4), sinnrlating with a 0.5-day time step. The estimates of 0 were not
significantly different between growth retardant treatments, and the estimate of 0 for
untreated control plants was used in all cases. The predicted height of G, (not displayed) and
G, models (Fig. 8) closely tracked the observed height (12 = 0.967) and was always within the
95% confidence intervals. However, both models overpredicted final height of the grth
retardant-treated plants, by 3, 9, and 8 mm in the G, model for the 1000, 2000, and 3000

ppm, respectively, and by 6, 12, and 11 mm for the G, model.

DISCUSSION

The untreated control plants exhibited a three-phase elongation pattern in both experiments.
However, between years thee were difl‘erences in the length of each phase and the elongation
rate. Validation control plants elongated 10 cm less after transplant than the calibration
plants. Flower-initiating short days were begun five days earlier in the validation experiment
than in the calibration experiment and the fw model would predict z 26 mm less elongation
in the validation experiment, based on the effect of short-day date described by Fisher et al.
(1995). DIF temperature was 1C lower during the validation experiment, which would also
have slightly reduced elongation (Berghage and Heins, 1991). Difi‘erences in transplant size
and vigor also may have been significant. Few data were collected during the plateau phase

in the validation experiment, and plants may have elongated more than predicted.

80
The dose response g(t) models are highly empirical. In the equation describing the efl‘ect of
chlormequat concentration on duration of efi‘ect (Eq. 13), a represents the intercept or
duration when concentration Cone = 0, and 6 represents the efl'ect on duration of increasing
Cone. Because a does not equal zero duration at Conc = 0, the model should not be
extrapolated beyond concentrations of 500 to 4000 ppm. The model predicts that initial
retarding efi‘ect is independent of concentration between 500 to 4000 ppm. No matter how
high the chlormequat concentration, the model predicts that the maximum growth retarding

effect is 53% of the untreated control.

This type of experiment and methodology does not efl'ectively identify the most biologically
valid or mechanistic formulation ofg(1). In Larsen and Lieth’s (1993) research on darninozide
applications to chrysanthemum, g,(1) and g,(1) equations resulted in a close fit to observed
chrysanthemum data. The researchers noted close correlation of amplitude and recovery
factors, a similar effect on absolute growth rate of the two g(t) models, variability in data, and
a lack of knowledge of the physiology of darninozide activity. As a result, although their
methodology was an efl‘ecfive empirical model, Larsen and Lieth (1993) noted that it was less
effective at selecting the most biologically valid form ofg(1). The most appropriate form of
g(t) is likely to vary depending on chemical type, translocation pathway, and plant species.
Either Larsen and Lieth (1993) g(t) model may be appropriate for darninozide on
chrysanthemum, because translocation and activity are rapid (Dicks, 1972) and the efl‘ect
declines over time (Dicks, 1972; Dicks and Charles-Edwards, 1973; Tayama and Carver,

1992)

8 1
Increased knowledge of growth retardant physiology would be necessary to develop a more
mechanistic model. Chlormequat primarily retards height by inhibiting intemode elongation
(Stefl‘ens, 1980), although the chemical inhibited subapical cell expansion and division in
chrysanthermm, and promoted transverse stem growth, resulting in short, thick stems (Sachs
and Kofianelg 1963). The principal mechanism of action for chlormequat has been associated
with the inhibition of gibberellin biosynthesis resulting in a reduction in the endogenous
content of gibberellins (Grossman, 1992). Efl‘ects on gibberellin activity, IAA metabolism,

ethylene production, and sterol synthesis also may be involved, however (Stefi'ens, 1980).

Chlormequat is absorbed rapidly, with over 90% of “C-labeled chemical applied to a wheat
leaf being taken up within 24 h (Arissian et al., 1991). Rapid absorption supports the g(t)
assumption of immediate growth-retarding effect after1,,. Chlormequat has been described
as readily translocated in the xylem and phloem and is highly water-soluble (Krishnamoorthy,
1981; Smith et al., 1982). However, Arissian et al. (1991) found that over 85% of the
chemical remained in a treated wheat leaf 10 days after a foliar application. This result
suggests that as a plant elongates over time, the zones of cell division and elongation may
become physically distant from the original application sites that contain the highest

concentration of chlormequat.

Smith et al. (1982) reviewed research on the rate of degradation of chlormequat chloride and
found contradictory evidence, with some research suggesting rapid degradation (20% to 30%
metabolism within 24 h in barley and chrysanthemum shoots (Schneider, 1967)) and other

reports indicating that the compound may be stable in wheat plants for four or more weeks

82
after application. Decomposition rate of chlormequat is afi‘ected by temperature, with little
decomposition below 4C or above 40C, and the chemical is broken down by soil
microorganisms if applied as a drench (Stefl‘ens, 1980). Growth-retarding activity may not
simply decline as metabolism of chlormequat increases. Smith et al. (1982) suggested the
possibility that the growth effects attributed to the parent compound may occur as a result of

a combination or balance of parent compound and metabolites.

We chose the g(t) models based on achieving the desired empirical qualities for the intended
use of the model. The initial amplitude M, or M, can be observed as the reduction in
elongation immediately after 1,,, whereas P and D must be estimated by non-linear regression.
Data were highly variable within growth retardant treatments when examined over short
periods; for example, the first one to three days after 1,,. However, a statistical comparison
of initial elongation did not indicate that initial elongation rate was afl‘ected by concentrations
between 500 and 4000 ppm. When we used non-linear regression to estimate M, or M, in
addition to the duration equation (Eq. 13), the amplitude estimates were 0.75 :1: 0.01 (:1:
asymptotic standard error) and 0.71 i 0.02 for the G, and G, models respectively. Although
the resulting models overall had a slightly higher R2 (0.990) than the G, and G, models in
Table 3, the predicted heights during the first 10 days after application did not fit as well to
observed data, especially in the validation experiment. Using non-linear regression to
estimate amplitude therefore less efl‘ectively predicted short-term efl‘ects of chlormequat,
which was our primary intended use of the model, than assuming a 47% initial reduction.

Although the linear estimate ofgrowth retardant duration (Eq. 13) should not be extrapolated

83

beyond 500 to 4000 ppm. label and recommended rates of chlormequat applications for

poinsettia fall within this range (Ecke et al., 1990).

The resulting model closely fit the observed data during calibration and validation trials.
Further validation of this model would be necessary to incorporate variables that are
important in commercial horticulture. Efi‘ect of plant pinching; cultivar, average and DIF
temperatures; date and method of application; and number of applications should be
considered. Several other growth retardants are applied to poinsettia (Ecke et al., 1990),
including ancymidol, daminozide (applied in combination with chlormequat), paclobutrazol,
and uniconazole. Therefore, a comprehensive growth retardant dose response model would
need to make considerable simplifying assumptions to accommodate this large combination
of possible situations. The model could be used to aid height-control decisions, by predicting
the final effect of a single foliar application of chlormequat on percent height reduction (Fig.
8b) and dynamically simulating the efl‘ect of a proposed or actual application on elongation

over time.

84

LITERATURE CITED

Arissian, M., D. Perrissin-Fabert, A Blouet, J. Morel, and A Guckert. 1991. Efi‘ect of
imazaquin on absorption, translocation, and pattern of distribution of chlormequat chloride
in winter wheat. J. Plant Growth Reg. 10: 1-4.

Barrett, J.E. 1982. Chrysanthemum height control by ancymidol, PP333, and EL-500
dependent on medium composition. HortScience 17 2896-897 .

Berghage, RD. and RD. Heins. 1991. Quantification of temperature efi'ects on stem
elongation in poinsettia. J. Amer. Soc. Hort. Sci. 116:14-18.

Dicks, J.W. 1972. Uptake and distribution of the growth retardant, arninozide, in relation to
control of lateral shoot elongation in Cinysanthemum morifolium. Ann. Appl. Biol. 72: 313-
326.

Dicks, J.W. and DA Charles-Edwards. 1973. A quantitative description of inhibition of stem
growth in vegetative lateral shoots of Chryswuhemum monfolium by N-
Dimethylaminosuccinarnic Acid (Daminozide). Planta 112:71-82.

Ecke, P., O.A Matkin, and DE. Hartley. 1990. The poinsettia manual, 3rd ed. Paul Ecke
Publications, Encinitas, Calif.

Fisher, P.R, RD. Heins, and J.H. Lieth. 1995. Modeling the efi‘ect of short day date on stem
elongation of poinsettia with a three-phase mathematical function. J. Amer. Soc. Hort. Sci.
(in press).

Gilbertz, DA 1992. Chrysanthemum response to timing of Paclobutrazol and Uniconazole
sprays. HortScience 27:322-323.

Grossman, K. 1992. Plant growth retardants: Their mode of action and benefit for
physiological research, p 788-797. In: C.M. Karssen, L.C. von Loon, and D. Vreugdenhil
(eds). Progress in Plant Growth Regulation, Kluwer, Netherlands.

Holcomb, E.J., L. Gohn, and 1C. Shliver. 1992. 1991 poinsettia trials: fertigation and growth
retardant trials. Pennsylvania Flower Growers Bul. 411.

Holcomb, E]. and M Rose. 1992. Poinsettia height reduction using multiple applications of
Sumagic. Pennsylvania Flower Growers Bul. 413.

Krishnamoorthy, H.N. 1981. Plant growth substances, Tata McGraw-Hill, New Delhi.

Larsen, RU. and J.H. Lieth. 1993. Shoot elongation retardation owing to daminozide in
chrysanthemum: 1. Modeling single applications Scientia Hort. 53: 109-125.

85

Larson, RA 1967. Chemical growth regulators and their efl‘ects 0n poinsettia height control.
North Carolina Agr. Expt. Sta. Tech. Bul. 180.

Lieth, J.H. and JP. Reynolds. 1986. Plant growth analysis of discontinuous growth data: a
modified Richards function. Scientia Hort. 28:301-304.

Ludolph, D. 1992. Height control of ornamental plants without chemical growth retardants.
Ohio Florists Assn. Bul. 748: 1-4.

McDaniel, G.L. 1986. Comparison of paclobutrazol, flurprimidol, and tetcyclasis for
controlling poinsettia height. HortScience 21:1161-1163.

McDaniel, G.L. and S. Wilson. 1990. Comparison of split application vs. single rate
application of Uniconazole on poinsettia. Tennessee Farm Home Sci. 155:11-15.

Richards, F]. 1959. A flexible function for experimental use. J. Expt. Bot. 10: 290-300.

Sachs, RM. and AM. Kofranek. 1963. Comparative cytohistological studies on inhibition
and promotion of stem growth in Chrysanthemum monfoliran. Amer. J. Bot. 50:772-779.

SAS [Statistical Analysis Systems] Institute. 1988. SAS/STAT users guide, version 6.03.
SAS Institute, Inc., Cary, NC.

Schneider, ER 1967. Conversion of the plant growth retardant (2-chloroethyl)t1i-methyl
ammonium chloride to choline in shoots of chrysanthemum and barley. Can J. Biochemistry
45 :395-400.

Smith, AR, T.H. Thomas, and IF Garrod. 1982. Specificity and mode of action of BTS
44584 and chlormequat chloride in wheat and soybeans: II. Distribution and persistence.
Ann. Applied Biol. 101:349-357.

Stefi‘ens, G.L. 1980. Applied uses of growth substances - Growth inhibitors, p. 397-408. In:
F. Skoog (ed.). Plant growth substances 1979. Springer-Verlag, Berlin.

Tayama, HK. and SA. Carver. 1992. Residual eficacy of Uniconazole and Daminozide on
potted 'Bright Golden Anne' chrysanthemum. HortScience 27: 124-125.

86

Table 1. Analysis of variance and parameter estimates from fitting the fwgnodel to
the untreated control data fi'om the calibration experiment.

 

 

 

 

 

 

 

 

 

.___Smm Lmaw
Regression 4 13103843 3275961
Residual 200 57586 288
Uncorrected total 204 13161429
Corrected total 203 3208912 R’=0.996
Estimated Estimate 3: ASE‘ Units
parameters
0 0. 154:1:0.003 day"
7 5.36:h0.10 mm day"
VBPLA 15.4:h3.l days
6 63:1:20 mm
Observed factors
a 43:14 mm
Calculated factors
1, 23.1 days
1, 76.5 days
fu0(1,) 78 mm
fm,(1,) 365 mm
1:,“ 0.0852 day"
H, 427 mm
Asymptotic correlation matrix

0 y VBPLA 6
0 1 -0.844 0.350 -0.223
7 1 -0.551 0.345
VBPLA 1 -0.945
6 1

 

: ASE, asymptotic standard error

87
Table 2. Increase in height before and after the growth retardant application at time 1,,,

and estimates of the initial rate parameter (0) by growth retardant treatment.

 

treatment elongation elongation elongation 0:1:ASE' (day")

 

 

fi'om 1, to 1,, after 1,, after 1, estimated by non-

(mm) (mm) (mm) linear regression
control 94:1:17 289:1:36a 383:1:43 01541-0003
500 ppm 76i18 277$:23ab 353129 014110.001
1000 ppm 95:? 265:1:4lab 3603:40 0.156ct0.002
1500 ppm 96116 259:1:24ab 355134 0.164zh0.002
2000 ppm 90:18] 246:1:19ab 336d:26 0. 155:1:0.003
3000 ppm 110:1:35 244:1:30ab 354:1:46 0.176d:0.004
4000 ppm 88:1:23 236d:41b 33:69 0. 1531-0003

, , Ns NS

slgnrficance *

(P=0.104) (P=0.136)

- 0.011

Ni‘Nonsignificant or significant at P = 0.05, respectively

Table 3. Estimates of a and b used to calculate persistence P and duration D

parameters in the g,(1) and g,(1) models respectively.

 

 

g,(1) (linear model) g,(1) (exponential model)
Amplitude M, = 0.53 M, = 0.53
a 10.558:tl.278 days 5.523:I:O.784 days
b 0.00824:l:0.0006 days ppm'l 0.00493:l:0.0004 days ppm’1

r2 0.989 0.989

 

88

Table 4. Analysis of variance and parameter estimates from fitting the fw model to

the untreated control data fiom the validation experiment.

 

 

 

 

 

 

 

Source d.f. Sum of Squares Mean square
Regression 4 17817477 4454369
Residual 320 40502 127
Uncorrected 324 17857979

total

Corrected total 323 2138957 R’=0.997
Estimated Estimate :1: ASE‘ Units
parameters

(3 0169:0003 day"
7 3.95:1:044 mm day"
VBPLA 24.4:l:3.6 days
6 21:1:19 mm
Observed factors

a 1 10:1 1 mm
Calculated factors

1, 18.6 days
1, 79.9 days
f,_,6(1,) 133 mm
f,,,,,(1,) 375 mm
It,“ 0.186 day‘l
H, 396 mm

 

‘ ASE, asymptotic standard error

 

89

 

 

 

Table 5 List of abbreviations and parameters
symbol description tmits
a initialstemlengthinthelagphaseoffw mm
0 rate constant in lag phase day'
7 gradient of linear phase mm
day-1
6 asymptotic potential growth during plateau phase mm
a parameterusedtoestimatedurationorpersistenceofgfl) days
A asymptotic height parameterintheRichards fimction mm
b parameteruscdtoestimatedmationorpersistenceofg(1) ppm'
1
days
C, recovery parameter in exponential g,(1) dose response frmcticn day'
D duration parameter in exponential g,(1) dose response function
(inverse of C ,)
DIF average day minus average night temperature C
g,(1) exponential dose response fimction
81(1) linear dose response function
G, complete stem elongation model incorporating f”... and g,(1)
G, complete stem elongation model incorporating f,” and g,(1)
g(t) environmental perturbation fimction
f,” three-phase stem elongation model
f“, function drning lag phase
f,,, fimction dining linear phase
f,“ fimction during plateau phase
H predicted stern length mm
H, initial stern length parameter in the Richards function mm
H, predicted final stem length mm
H, predicted stem length of untreated plant m
k rate parameter in the Richards fimction dayl
km rate parameter in plateau phase day"
M, initial amplitude effect of exponential g,(1) dose response function
M, initial amplitude effect of linear g,(1) dose response fimction
11 point of inflection in the Richards function
P persistence parameter in linear g,(1) dose response fimction
SD days after transplant at which short (flower-initiating)
photoperiods begin days
SDVB time fi'om the start of short days to visible bud days
1 time variable days
1, time of transplant days
1, timewhenlagphaseendsandlinearphasebegins days
1, time when linear phase ends and plateau phase begins days
1,, time of growth retardant application days
1,,, time at which plant recovers from linear g,(1) dose response days
VB days after transplant at which visible bud occurs days
VBPLA days from VB to 1, days

 

g,(t)

9O

 

 

 

0.6 -
0.4 ~

0.2 -

 

0.0

 

 

 

 

1.0
0.8.-
0.6 -
0.4 i

0.2 -

 

0.0

 

 

l ' l ' 7 1 I ‘ I ' l

20 4o 60 - 80 100 120
Days after transplant

Alternative g(t) dose response models proposed by Larsen and Lieth (1993).
(a) a linear g,(1) model where the initial efl‘ect of a growth retardant
application at time 1,, is represented byML, and the declining growth retardant
effect persists for P days. (b) an exponential dose response model with
declining growth retardant efi‘ect after an initial amplitude ofM,. ’

91

500

 

.‘OCCOCCOOOO‘...0.......‘C"............a............“........... .‘C .O- 0.. OOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOO
.C....O....."CO..0...‘....°’.I.......... OOOOOOOO

. COOOCOC0.0...‘..‘......... ..............

N m w A A
VI 0 Ur o Ui
O O O O O
l I I I I

0.00....COCO‘.O......I.....'...... ':’ ‘0...........‘.OOOCOOOOOOOOO;OOOOCOOOOOOO ..............

I C O I O I
I I I I I I
I I .‘. I I o o
I I o“ I I I I
—l ............................ "_"' IIQOIOIIIIooooo-IIOI ooooooooooooooooooooooooooooooooooooooo
I C I. O I I O
I ' I I I I
I I I I I
I [I I I o o
I '. I I I I
I ,‘w I I I I
150 — ICC-IOIIIIOO‘. OOOOOOOOOO I" ;.......O....;...........O‘. OOOOOOOOOOOOO ;....l’......‘. .............
I " v I I I I I
I , I I I I a I
I r ’ I I I I I
I I" I I I I I
I ', I I I I I
I ’1 I I I I I
-I 0000000000000000 ,IIIIIooowooooI-IIIIIIIIIIIIIIOIIII- OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
O ' O O I O C
I I I n I I
I I I I I
I I I I I
I I n I I I
' O O O I C
50 I - - 1’. oooooooooooooo ’OOOOOOOOOCOO; ..... 'IIIIIII‘IIona...cocoo;oo-IIIIIIIII‘. 000000000000 1
v " v I I I I I I
I I I I I I
O O O C I I
I I ~ I I I I
I I I I I I

Stem length (mm)

 

 

 

O 20 4O 60 80 100 120 140
Days after transplant

Plot of observed and predicted average stem length over time for the
untreatedplantsduringthecalibiationexperiment: 0=meanobservedheight
t 95% confidence intervals, solid line= fit of the fw fiinction

92

12

 

 

 

 

 

 

 

 

Elongation from tW to tw+1 (mm)

 

 

 

O 1000 2000 3000 4000

Chlormequat concentration (ppm)

Observed average elongation during the first day after application (i.e.
between r“, and n+1) during the calibration experiment for difi‘erent growth
retardant treatments (mean :1: 95% for five plants per treatment).

93

 

 
    

50 r
45 _. .(é). ............ .................... ..............................
40 _................P...1:"1.9.9.2..Tt.Q.QQ§fi.9..f§9Il.C. ..........

0..0.0.6.0...O00.0.0,0..0.0..0.0....COCO-$0....CII000...0.. .IOCOOOIOCOIOOOOOCOC OOOOOOOOOOO

P (days)

 

R (days)

 

 

 

O 1000 2000 3000 4000
Chlormequat concentration (ppm)

Parameter estimates (0) for (a) the persistence P in the linear g(t) model and
(b) the duration parameterD in the exponential g(t) models respectively. The
solid lines represent the linear regression (Eq. 13) fit to the parameter
estimates where the y-intercept constant represents the parameter a and the
gradient constant represents b.

94

 

 

 

 

 

 

 

 

 

0.20
0.16
0.12
0.08 ‘0
9°
0.04 9::
Co
0.00
0.2 — UV — -o.04
r -0.08
0.0
-20 0 20 4O . 6Q 80 100
Days after application
50 = z : z 100
(B)
45 — - . ..
4O — 90 f3
’5; b .C
5.. 35 - '8
3 3o — .6
9
g 25 - - 80 g
.g 20 — :0:
o 15 — c
D“ — 7o 8
10 “ a
n.
5 .—
0 60

 

 

 

0 1000 2000 3000 4000
Chlormequat concentration (ppm)

(a) Comparison of g,(1) (dashed line) and g,(1) (solid line) dose response
models assuming a 1500 ppm chlormequat application, O=difi’erence between '
models (g,(1) minus g,(1)). (b) The percentage height of chlormequat-treated
plants with respect to the final height of untreated plants for a growth
retardant applied 1,,=34 days after transplant (0), and growth retardant
persistence for various concentrations (Cone) using the g,(t) model (B).

Stem length (mm)

(a)-(t) Plot of observed average stem length (0) for growth retardant
treatrnents over time during the calibration experiment and predicted height
from the exponential g,(1) model (solid line). The dashed line represents
heights predicted by the fan- model in the absence of a growth retardant

500 -
450
400 -
350 -
300 -
250 -
200 -
150 —

95

“(13) 590 ppm :(D) 2000 ppm

 
 
 
 
 
 

 

 

 

 

 

 

”iiiiri.i.irlin

: (C) 1500 ppm

   

 

 

.ifiiriiniir

I (F) 40,00 ppm

 

    

 

 

  

.1J1.1.1.i.iig

 

.i.3i.L.iii.1rg

0 20 40 60 80100120 0 20 40 60 80100120

Days afier transplant

application.

96

3A) 590 ppm

 

 

 

O 411:1411111111]

Stem length (mm)

 

 

 

 

.1.:L.1.4.i.1.

(F) 4090 ppm

0151444111112] J

: (C) l§00tppm

l_l

l

    

    

L11

1

 

 

T'l'IlliJlllllllllllllzlllllllllll

O 20 40 60 80100120 0 20 40 60 80 100120
Days afier transplant

(a)-(t) Plot of observed average stem length for growth retardant treatments
overfimediuingthecahbrafionarpahnern(0) and predicted heightfiomthe
linear g,(1) model (solid line). The dashed line represents heights predicted by
the fw model in the absence of a growth retardant application.

97

:(A) Untreated control :(c) gooo ppm

 

 

 

 

 

 

g) 0 lllLllllllJlll‘llsllllllllllll
3 500- -

a 450 _ (B) 1000 ppm __ (D) 3000 ppm

8 : 3

m 400% " '

   

 

 

O iliilililrlilil ljslllllllllllI
O 20 40 60 80100120 0 20 40 60 80 100120
Days after transplant

 

(a)-(d). Plot of the validation data set showing observed average stem length
for control and growth retardant treatments over time (0) and predicted
height fiom the exponential g(t) model combined with the fw fimction fit
to the untreated validation control plants (solid line).

SECTION 4
4. A DECISION-SUPPORT SYSTEM FOR REAL-TIME MANAGEMENT OF

EASTER LILY (Lilium longiflorum Thunb.) SCHEDULING AND HEIGHT. 1.
SYSTEM DESCRIPTION

Paul R Fisher‘, Royal D. Heins‘, Niels Ehler’, J. Heinrich Lieth3

1. Department of Horticulture, Michigan State University, East Lansing, MI
48824, USA

2. Horticulture Section, Department of Agricultural Science, Royal Veterinary
and Agricultural University, Rolighedqu' 23, 1958 Frederiksberg C, Denmark

3. Department of Environmental Horticulture, University of California, Davis,

CA 95616-8587, USA

Submitted to Agricultural Systems.

ACKNOWLEDGEMENTS: We would like to thank University Outreach at Michigan State
University for providing funding for this project, and the cooperation of Bordines Better
Blooms, Andy Mast Greenhouses, Henry Mast Greenhouses, Neal Mast Greenhouses,
Meiring Greenhouses, and Post Gardens in testing and developing this model.
ADDITIONAL INDEX WORDS. environmental computer, expert system, height control,
knowledge-based system, process control, stem elongation

98

99

ABSTRACT. There is considerable economic potential for greenhouse control systems that
combine biological models and expert recommendations to improve productivity. A decision-
support system was deve10ped for recommending night and day temperature setpoints to
control the timing and height of Easter lily. Existing biological models and qualitative rules
were combined into an overall model of the response of plant development rate to
temperature. A process control algorithm was used to determine appropriate height control
actions based on a graphical control chart of plant height over time. A knowledge-based
system checked the feasibility of output from the development and height control models and
generated a text report. This model was implemented on a personal computer in a program
called The Greenhouse CARE System and has been linked directly with an environmental
computer to control greenhouse temperatures. A companion article describes validation of

this model.

INTRODUCTION

Increasing research effort is being directed toward developing systems to control the
greenhouse environment based on models that link plant performance with environmental
variables. Examples of these systems include an automated misting system (Jones, 1989), a
plant nutrition-based fertigation system (Fynn et al., 1989; Fynn et al., 1994), and CO,
Optimization linked with an environmental computer (Ehler and Karisen, 1993). Using
plant/environment models for greenhouse control potentially optimizes resource use,

minimizes agrichemical applications, and increases crop quality.

100
The goal of this study was to develop a decision-support system to control flowering and
height of Easter lily, a major greenhouse potted plant crop in the United States. System
recommendations were based on existing models that quantify plant developmental rate
responsetoairtemperanueandontherecommendations ofextensionbulletins and an expert
in Easter lily production. To develop the system, four objectives were formulated: l)
integrate existing plant development models into an overall model fiom emergence to flower,
2) develop a process control model for controlling plant height, 3) develop a knowledge base
that recommended day and night air-temperature settings based on output from the
development and height control models, and 4) program the system on an IBM-compatible
personal computer to run in real time. The approach taken to meet these four objectives is
described here, and validation of the system is discussed in a companion article (Fisher et al.,

199?).

101

METHODS AND MATERIALS

A r ' of exi ' er lil in

Commercial production of Easter lily requires precise temperature control to bring the crop
to flower in time for Easter sales, and there is considerable financial loss if the target flower
date is not achieved. Temperature control strategies differ substantially fi'om year to year
because Easter falls on difl‘erent dates and bulbs vary, depending on the field conditions in
which they were grown. Markets also specify the final desired plant height (usually 50-55
cm), and the optimum temperatures for height control and development rate can conflict. In
the United States, bulbs are field-harvested fi'om September to October and are vernalized at
4-7C for a six-week period. In November and December, plants are moved into the
greenhouse and are forced until approximately Palm Sunday (late March to late April), when

they are shipped (lvfiller, 1992).

Easter lily development rate and stem elongation rate (SER) responses to temperature have
been well quantified (Healy & Wilkins, 1984; Karlsson et al., 1988; Erwin et al., 1989; Erwin
& Heins, 1990; Lieth & Carpenter, 1990). Phenological stages of Easter lily development
provide a fiamework for using these models during the production cycle (Fig. I). We defined
each stage in terms of an observable event for a plant population. The start of greenhouse
forcing (SF) was defined as the point at which the potted or unpotted bulbs were removed
from vernalization conditions and placed in pots on the greenhouse bench. Leaf-tip
emergence (EML) for a crop was defined as 50% of a plant population having emerged from

the soil surface. Emergence of the shoot meristem (EMM) was defined as the point at which

l 02
the uppermost leaf tip was at least 7.5 cm above the soil for 50% of the population. After an
average 25 leaves unfolded, commercial growers dissect the terminal shoot of several plants
twice per week to check for difl‘erentiation of flower bud primordia Flower bud initiation
(FBI) for a plant population was defined as the point at which flower-bud primordia were
visible on at least 50% of a sample of ten dissected plants. The next stage, visible bud (VB),
was defined as the point at which flower buds were visible (without removing leaves) on 50%
of a plant population. Flowering (FL) was defined as the point at which bud petals split open

on at least one flower per plant in 50% of the population.

The relationship between leaf unfolding rate (LUR) and average daily temperature (ADT) for
Easter lily was linear according to Karlsson et al. (1988) and Lieth and Carpenter (1990),

allowing computation of the ADT required to achieve a desired LUR by

ADT - LUR . 10.64 . 1.12 (1)

where 10.6 degree-days above a base temperature of 1.lC is required to unfold each leaf. An
Easter lily leaf is defined as unfolded when it forms an angle of 45° with the plant stem. All
but approximately five upper leaves unfold by the visible bud stage, at which time flower buds
are visible and are approximately 2 cm in length For a given mrmber of days to flower (DTF)

fiom VB to FL, the required ADT was quantified by Erwin and Heins (1990) as

103

1
0.00209 .DIF

 

. 3.55 (2)

After VB, the relationship between ADT, flower bud length (BL), and DTF was quantified
by Healy and Wilkins (1984). They considered bud development rate biphasic, quantifying

the development of buds less than 6 cm as

DIF - 37.97 - 8.95 . ln(BL) - 0.45 . ADT (3)

and describing bud development for buds longer than 6 cm as

DIF-33.26-2.04.3L-o.74.aor.o.o44.(BL.Am') (4)

The stem elongation response of Easter lily to day temperature (DT) and night temperature
(NT) was quantified by Erwin et al. (1989) in terms of the difi‘erence between day and night
temperature (DIF). Easter lilies grown under warmer DT than NT (positive DIF) elongate
more rapidly and have greater final height than plants grown under cooler DT than NT
(negative DIF). The relationship between final plant height (H) and DIF, DT, NT, and ADT

was quantified as

H.25.66.1.49.DIF-0.042 .(Dr.Nr)-r.9r.ADr (5)

The DIF term alone in Eq. (5) accounted for 78% of the height variability in plants grown
under 25 day/night temperature treatments. Lieth and Carpenter (1990) modeled stem

elongation of Easter lily over time under difi‘erent ADT treatments using the Richards (1959)

104

function The main efi'ect on the sigmoid elongation curve with increasing ADT between 16.5
to 23.1C was increased elongation rate, although final plant height was not significantly

afl‘ected.

Tools based on these temperature response models have been widely adopted by Commercial
growers in Easter lily production (Miller, 1993). The LUR model is used to help select
greenhousetemperaturesettingsbetweenFBIandVBtoachieveatarget VB date 30-35 days
before flowering. Erwin et al. (1987) presented the LUR model in an isopleth graph of
day/night temperature versus LUR At FBI, growers dissect several plants and record the
final leaf count, which is obtained by adding the number of folded and unfolded leaves.
Unfolded leaf count may also be ascertained at other periods between FBI and VB. Given
the date of leaf counting and the desired VB date, a target LUR can be calculated and the
appropriate day/night temperature combination can be selected from the isopleth graph. The
flower bud elongation model developed by Healy and Wilkins (1984) is used in a bud meter,
which is a cardboard ruler that indicates the days to flower at difi'erent temperatures for a

given flower bud length.

A control chart for graphical tracking of plant height was developed by Heins et al. (1987)
usingtheleafernergencedate, thetargetVB date(30daysbeforeFL), and thetargetFLdate
onthex-axis, andaheightrangeonthey—axis betweenthe pot height and thefinal maximum
height specifications (Fig. 2). Lines running from the initial pot height to the minimum and
maximum final heights provide a target window for the entire production season. Visible bud

provides an intermediate development and height target because VB generally occurs 30-35

105
days before flowering at commercial temperatures, and height approximately doubles fiom
VB to FL (Carlson & Heins, 1990). Although the elongation curve of Easter lily is sigmoidal
(Lieth & Carpenter, 1990), the linear control chart is easily reproduced on paper by growers
and has functioned adequately in practice. Growers record the average height of several
plants per crop on the graph twice each week and compare actual to target height. If the
height exceeds the target height, steps may be taken to reduce stem elongation rate, including
a negative DIF temperature (warmer night than day temperature) or application of a growth
retardant. Conversely, positive DIF temperatures may be used to increase elongation rate

when plant height is below the target height.

Ob'ective 1: Devel ment of an verall lant el ment m 1

Although research-based tools and recommendations are available to guide temperature-
setting decisions at each stage of Easter lily production, existing knowledge has not been
integrated into an overall model with consistent assumptions and smooth transitions between
phases. We developed an overall plant model that incorporated existing models, published
data, and extension bulletin recommendations in model development fi'om emergence until
flower. From the start of greenhouse forcing to flower, plant development is divided into
several phenological stages, with different submodels applying at each stage. Inputs into the
model include EML, EMM, FBI, observed VB, total leaf count at FBI, unfolded leaf count
twice weekly fiom FBI to VB, and bud length measurement twice weekly from VB to FL.
Target VB and FL dates are also entered, and the model calculates an average temperature
required to achieve the target dates. The following section describes the submodels used at

each growth stage.

. .05] Quantitative models have

 

not been developed for data fiom SF to FBI; therefore ‘if..then' production rules (Stock,
1987) were formulated to recommend temperatures based on standard recommendations
(Erwin et al., 1987; Miller, 1992) and their clarification by Dr. Heins, one of the Erwin et al.
(1987) authors. We used Miller's (1992) definition of early, medium, and late Easters as
March 22 to April 2, April 3 to April 15, and April 15 to April 25, respectively. Standard
recommendations are for higher temperatures and, hence, more rapid development rate when
Easter is early rather than late. The development model recommends an average temperature
of 18, 17, or 16C, depending on an early, mid-, or late Easter, respectively, based on
temperatures suitable for root development, flower bud development, and rate of emergence
(Erwin et al., 1987; Miller, 1992). Recommendations refer to soil temperature fiom SF to

EML and to air temperature after plants have emerged.

Flower bud initiation to visible bud (FBI to VB) Leafunfolding rate (Eq. (1)) was used to
recommend ADT between FBI and VB. A leaf-count control chart was developed (Fig. 3),
with date on the x-axis, leaf count on the y-axis, and a line fi'om the leaf count at FBI to the
final leaf count at VB indicating the target leaf count. The desired LUR and ADT to achieve
the target leaf count are calculated using the LUR model. Data fi'om a commercial Michigan
Easter lily crop are shown in Figure 3, in which an average of 17 leaves had unfolded at FBI
21 daysafteremergence, andanestimated 73 leaveswererequiredto unfoldbythetargetVB
date on day 56. An average of 48 leaves fi'om ten plants had unfolded 42 days after
emergence, and the target leaf count on day 42 was 51 leaves. The desired LUR on day 42

would therefore be 1.8 leaves per day, and the model would recommend an ADT of 20C.

107
WELL) Equation (2) is used to recommend the ADT once VB occurs. Alter
flower buds are 4 cm long approximately 10 days after VB, bud length can be measured
nondestructively, and a bud elongation model is used dynamically to recommend an ADT.
Data fi'om Healy and Wilkins (1984) were reanalyzed to quantify the relationship between

BL, ADT, and DTF in a single equation, expressed as

our . (so . b, . ADT) . (b, . b, . ADT) - MEL) (6)

ThisequationassumwthatD'I’Fislinearlyrelated to ADT and the natural log ofBL and that
the intercept and slope of this relationship vary with ADT. The nonlinear regression
procedure in SAS (Statistical Analysis Systems Institute, 1988) was used to estimate
parameter values (Table 1). The resulting R2 of 0.993 indicated a close fit to data, and the
estimates of DTF were always within two days of those fiom the Healy and Wilkins (1984)
bud meter. Using parameter estimates from Table 1, recommended ADT can be calculated

as

DIF - 57.16 . 19.43 . ln(BL) 7
-1.26 . 0.42 . roast.) ( )

 

ADT-

for a given DTF and BL.

Compromise between alternative model recormnendations during the transition between
models was necessary to avoid rapid ADT recommendation changes that may have been
caused by sampling error or model bias. For example, when approaching VB, Eq. (1) was
highly sensitive to errors in the unfolded leaf count or the estimate of final leaf count. As the

crop matured to fewer than 10 days before the target VB date, the recommended ADT was

108

obtained by averaging ADT recommendations fi'om Eqs. (1) and (2). From VB until the
average bud length developed to 4 cm, Eq. (2) alone was used. During the period when bud
length was 4-10 cm, an average of ADT values fiom Eqs. (2) and (4) was employed, and afier
this period, ADT was calculated solely by Eq. (4). This approach made maximum use of the

degree of certainty associated with each of these models.

Objective 2: A height control mflel
The goal of the height control model was to mimic the DIF temperature and growth retardant

recommendations of an expert consultant based on graphical tracking plots of plant height.
Dr. Royal D. Heins (RDH) was used as the expert for this model. In a quality control
application for plywood manufacturing, Cook et al. (1992) used eight production rules to
identify and interpret out-of-control situations for a statistical quality control chart. For
example, if six consecutive points were outside statistical limits, then an out-of-control had
occurred and remedial action was required. Further rules were used by Cook et al. (1992)
to recommend remedial action based on interviews with production experts. In contrast, we
used a process control algorithm, rather than rules, to interpret a height control chart because
the maximum and minimum guidelines for lily height graphical tracking are approximate and
are not based on statistical limits. We also defined a range of DIF and growth retardant
control options in an action table based on interviews with the expert and linked the output

from the control algorithm with the appropriate cell in the action table.

The action table represented the range of DIF temperature recommendations and growth

retardant applications the expert would suggest in different production situations. To provide

109
data for the action table, the expert was presented with hypothetical control charts showing

various graphical tracking situations. Expert responses, phrased in terms of the growth
retardant applications and change in DIF temperatures he would recommend, were
characterized as seven discrete situations (Table 2). For example, if the current day
temperamreinagreenhousewasZZCandnighttemper-ann'ewas 18C (aDIF of+4C)andthe
expert recommended an adjustment of -2C, the corresponding control index (CI) would be
-1, a day/night temperature recommendation of 21/ 19C, and a growth retardant application
recommendation. Recommended relative changes in DIF temperature take into account
actual plant response to the greenhouse environment and may be more robust than

recommended absolute temperature changes.

The CI in the action table reflects the direction (sign) and magnitude (absolute value) of a
desired change in SER: a CI of -3 represents a strong need to reduce SER and a highly
negative DIF plus growth retardant, whereas a value of +1 represents a slight need to
promote SER (a slightly positive DIF and no growth retardant). When the CI equals zero,
the SER is accurate; i.e., the grower's current practices are maintaining height in the desired

range and no corrective change is necessary.

A control algorithm was used to link specific graphical tracking situations with the CI in the

action table:

dc
CI - K’CU) 9 rd: (8)

where K, and K, are constants assigned to proportional (e(1)) and derivative error (dc/d1)

l 10
components at time 1, respectively. Proportional error represents the deviation between the
actual controlled variable (plant height) and the target value (the center of the graphical track
curve), whereas derivative error represents the rate ofchange in error over time. The desired
CI could therefore be estimated using Eq. (5) for any combination of actual and desired

performance over time.

In order to estimate K, and K4, the domain expert (RDH) was presented with a random
selection of 48 hypothetical graphical tracking graphs with an e(1) that ranged fi'om +10 to
-10 cm above and below the graphical track window, and four relative growth rates (dc/d1)
that ranged from -0.27 to 1.19 cm/day. In each situation, the domain expert indicated which
CI from Table 2 best matched his recommendation. Data were then fitted using linear
regression to Eq. (5), with an r’ of 0.89 (Table 3), indicating that the model mimicked the
expert responses reasonably well. The equation to calculate integer CI values by using the

parameter estimates fi'om Table 3 was

do
(:1 . rand(-0.25 . 0(1) - 1.33 7), -3 s 111(1) 5 3 (9)

which results in the example control indexes shown in Figure 4.

 

tern re

A knowledge-based system was necessary to ensure that recommendations based on the
output fiom the developmental and height control models were feasible. A knowledge-based

system of this type, also called an expert system, is a computer program that attempts to

111

capture human problem-solving ability (Stock, 1987). The knowledge-based system uses
production rules to check and interpret model output before presenting recommendations to
the user. There are 70 rules in our knowledge base, and forward-chaining (Stock, 1987) is
usedastheprimaryinferencemechanism Theuserinteractswiththe knowledgebase, which
activates the appropriate parts of the development and height control models, rather than

interacting with the models directly.

The basic tasks in the knowledge base correspond to the steps a grower takes to decide
greenhouse temperature settings for an Easter lily crop (Fig. 5). The top part of each box in
Figure 5 represents an action by a human decision maker, and the bottom part of each box
shows how that action was represented in the knowledge base. The optimum average
temperature (Fig. 5, Step 1) is determined by the goal to flower on the target date, which is
in turn determined by the relationship between temperature and development rate. The
knowledge base selects which component of the overall development model (for example, leaf
unfolding rate, Eq. (1)) is relevant based on the growth stage of the crop. Concern over
deviation in plant height from the target height is quantified using the height control model
(Step 2), and the knowledge base then determines the DIF and growth retardant actions fiom
the action table (Step 3). Given the average and DIF temperatures, simple arithmetic is

required to calculate the day and night temperatures (Step 4).

“nth any control system, it is essential to check that model recommendations are technically
and biologically feasible. A ‘ constraint table' was developed for all growth stages (Table 4),

based on data fi'om Erwin et al. (1987) and interviews with the expert (RDH). Maximum and

112
Mummacceptablevfluesnewmaimdmflwwnsuaimmbleuweflasdefatmmesused

when there are insuficient data available to run the development model. The knowledge base
checksthatdayandnightternperaturesfi'omStep4arewithinthe constraint tablelimits (Step
5). Model recommendations are bounded by the constraints in Table 4, and where it is not
possible to achieve target ADT and DIF temperatures (development and SER goals,
respectively), ADT has priority in Step 6 because timing has overriding importance for Easter
lily (O'Rourke & Branch, 1987). The knowledge base also checks whether current
greenhouse temperatures are above or below the recommended limits for the current growth
stage and displays a warning message if the threshold temperatures are exceeded. The final

step (7), to implement greenhouse temperature settings, is discussed in the next section.

The knowledge base creates a brief text report that is constructed using a template with a set
paragraph layout and is filled with specific text, depending on the control index and growth
stage. An example report for the crop with the height in Figure 2 and leaf count in Figure 3

would be as follows:

113

CROP REPORT FOR AESSICK C T?“ BLOCK 4 02/04/94

This report should only be used as a second opinion.
Crop decisions we solely your responsibility

CURRENT SITUA TTON: CROP Conaol index: -1
Actual height: 31. 7 cm. Target: 29.2 cm.

48. 0 leaves have unfolded 14 days before visible bud
25 leaves have yet to unfold
We sugest a leaf unfolding rate of 1.8 leaves/day.

CURRENT WERA TURES:

Daily temperature since 1/28 has averaged 18 C
and DIF since [/28 has averaged -3 C.
SUGGESTED TWERA TURES:

We suggest a new average temperature of 20 C
and a DIF temperature of -4 C.

FOR THIS CROP ONLY, recommended night: 22 C
and the recommended day: 18 C.

GRO WTH RE T ARDANTS
Consider applying a low rate growth retardant
e. g., 2.5 ppm Sumagic spray, or
0.125 mg/pot A-Rest (bench, or
25 ppm A-Rest spray

In the first part of the report, the ‘CURRENT SITUATION is described in terms of current
height and development. ‘CURRENT TEMPERATURES’ are summarized in terms of
average and DIF temperatures, and if current temperatures exceed recommended limits (from
Table 4), the user is alerted with warning messages. The ‘ SUGGESTED TEMPERATURES

Section contains the actual recommendation, first in terms of the average and DIF

1 14
temperatures and finally in terms of the night and day settings required to meet those
temperatures. The number of leaves unfolded is less than desired (Fig. 3), and an increase in
ADT fiom 18 to 20C is recommended. Because the crop is taller than the target height (Fig.
2) and has a negative control index, a negative DIF is recommended. In order to achieve the
target ADT and remain within the maximum NT of 22C for the FBI to VB stage (Table 4),
an optimum DIF of -5C (the current -3C DIF minus 2C fiom the action table) cannot be
achieved. The DIF recommendation is therefore constrained to -4C. ‘FOR THIS CROP
ONLY‘ refers to the fact that this recommendation disregards the optimum temperatures for
other cr0ps that would be afi‘ected by these settings and are in the greenhouse zone: a zone
report that recommends temperatures settings optimized for all crops in the zone can be
obtained by the user. A growth retardant is recommended because the control index is less

than one, the crop has not reached VB, and no other chemicals have been applied in the last

seven days.

Objective 4: Implementation on a 2mm] oomouter
The models and knowledge base were implemented in a program called The Greenhouse

CARE System (CARE). CARE was designed with several desired features: a modular
structure connected by a central shell program, a consistent graphical user interface, a
common database shared by all modules, and the ability to run the program in real-time and
off-line modes. The resulting structure (Fig. 6) is described in the following section and uses

data fiom commercial crops grown in Michigan.

All modules including the central shell are executable files written in Turbo Pascal version 6.0

115

(Borland International, 1990) and run in graphics mode, with icons and mouse control.
Considerable efi‘ort (1.75 years) was expended in developing the user interface and testing
prototype versions with a group of beta test growers. Graphical tracking modules for Easter
lily, poinsettia, and chrysanthemum are commercially available for CARE. Interface features
important to the users have been 1) minimum input time, 2) case of use, 3) graphical or
concise table output, 4) consistency, and 5) maximum computational speed, in that order.
Although the development time for the interface was a major investment, science-based
programs need to have the same professional presentation as other software if they are to be
successful. Once the basic graphical user interface was completed, developing new modules
became more rapid: the lily module required three months of knowledge acquisition and

coding, whereas a previous poinsettia module required 1.5 years of development.

(1) The central shell is a combination of Turbo Pascal procedures for handling the graphical
user interface, database communications, and graphical and model output. These procedures
are compiled in a central module that is the first screen entered in the CARE program. The
other modules (Zones And Crops, Data, View, and Second Opinion) allow the user to
organize cr0ps into greenhouse zones; manually enter height, leaf count, and temperature
data; view control charts; and obtain recommendations, respectively. Species icons in the
central shell give the user access to modules for lily, chrysanthemum, and poinsettia. Modules
for these crops have the same layout and difi'er only in the plant models, rule bases, and shape

0f the height control curve.

(2) In the Zones And Crops module, an entry form is used for creating crop control charts.

1 l6
Fields in the form inchrde crop name, pot height, minimum and maximum heights, production
dates, cultivar, plant number, grower name, and greenhouse zone. This information is used
to update a database that organizes crops into greenhouse zones; a zone refers to a section
of greenhouse that has common temperature and lighting management. Multiple crops that

may be separated by variety or emergence date can be contained within one greenhouse zone.

(3) Crop information that changes during the season is entered into a spreadsheet in the Data
module, including plant height, leaf count, growth retardant applications, and plant spacing.
These data are usually entered by the grower twice each week. Greenhouse data needed to
calculate ADT and DIF (night and day temperatures; sunrise and sunset times) can be
manually entered in the Data module when the system is run ofi‘ line. Data are stored in a
relational database linked by crop or zone name, with separate files for the zone and crop
organization, the crop data, the climate data for a particular zone, and crops produced during

previous seasons.

(4) Any combination of height, leaf count, and temperature graphs can be displayed in the
View module. Height data can be viewed overlaid on the same graph or as multiple small
graphs. In the example screen (Fig. 7), the DIF temperature and height graphs are displayed
for the same crop shown in Figures 2 and 3. Because the system stores data fiom previous

years, former and current crops can be compared easily.

(5) Plant models and the knowledge-based system are combined in the Second Opinion

module (Fig. 8). The user selects the desired greenhouse zone fiom a menu by using the

117

Zoneiconattheright ofthe screen. Inthe example inFigure 8, there are four crops located
in difi‘erent sections of a greenhouse zone called ‘RA'. Each crop is associated with a height
graph (on the left in Fig. 8), and either a leafcount graph or bud size icon (on the right ofthe
height graph) depending on stage of development, and a ‘ crop report' icon. Activating the
‘crop report' icon next to a graph leads to a text report for the associated crop. In contrast,
the ‘zone temps' icon at the right of the screen averages the control indices for each crop to
recommend a compromise temperature for the entire zone. The temperature form at the
bottom of the screen contains the current greenhouse temperatures. Once a zone temperature
recommendation is obtained by activating the ‘zone temp' icon, the temperature form is
updated with the recommended temperatures. Alternatively, the grower can activate the

temperature form and enter temperatures directly to override the model recommendation.

(6) CAREcanberunofi‘line,withmanualentryoftemperaturedataandmanual
implementation of settings recommended by the grower, or run on line using an automated
link program. Climate data are stored in a temporary database file by the link program, an
executable file that is called every 15 minutes by the environmental control software
(commercial products produced by several companies independent of CARE). After sunset
each day, the link program converts the accumulated 15-minute temperatures into a daily
record that contains night and day temperatures and updates the main CARE climate
database. Theadvantageoftheclimatestoragelinkisthat manual entryofclimate data is not

required, and this essential model input is handled in the background.

Downloading settings fi‘orn CARE to the environmental computer enables the model directly

l 18
to manipulate the greenhouse climate for validation or automation purposes. When the Send
icon (in the lower right of Fig. 8) in the Second Opinion module is activated, a settings file
that contains the latest recommended temperatures fi'om the temperature form is written. At
every lS-minute interval when the link program is called by the environmental control
software, the link program reads the setting file and modifies the greenhouse temperature

settings.

The link between plant models and the environmental computer is largely company-specific
and is essentially an engineering problem. Although the link would require a minor effort for
most companies, until now there have been few applications (and little financial incentive) to
use this facility. Reading climate data into plant models is more easily implemented than
downloading settings. Whereas the former task has been implemented in CARE on four
environmental computer systems, only one system (the DGT-Volmatic Corporation system,

Ehler [1991]) is currently linked with the latter pathway.

(7) Temperature settings decisions based on grower experience and CARE recommendations
are implemented on the environmental computer. A degree of multitasking is necessary to
run the environmental computer and plant models on the same computer, and it is essential
that the environmental computer run continuously to control the greenhouse environment.
The ability to link plant models to different environmental computer products varies. DGT-
Volmatic, for example, provides easy linkage with plant models by allowing external
programs to be executed at any desired frequency. A Turbo Pascal (Borland International,

1990) program unit includes procedures for retrieving or downloading data to the

119

environmental computer in the DGT-Volmatic system and can be readily incorporated into
plant model sofiware (Ehler, 1991). Alternative approaches would be to run the plant models
and environmental computer in a true multitasking environment; for example, DESQView

(QuarterDeck Ofice Systems, 1991) or Windows (Microsoft, 1991).

DISCUSSION .

To be commercially usefirl, models need to be packaged into decision-support tools of some
form, whether a graph on paper, a piece of equipment, or computer software. The major
benefits are that research is used commercially, becomes more integrated, and can be
validated in the field. A considerable effort is required by developers to achieve a realistic and
easy-to—use computer decision-support system, and such projects involve a mix of quantitative

science, programming, and knowledge engineering skills.

The Easter lily application has features that apply to many control situations and provides a
model of one approach for developing a real-time decision-support system for greenhouse
control. General tasks in the application included 1) identifying ultimate production goals
(flowering and height targets), 2) identifying intermediate milestones or reference values
(emergence and visible bud dates, leaf count, and height-control charts), 3) monitoring
production variables (leaf count, bud length, height, temperatures, and phenological stages)
and storing these data, 4) comparing actual and target performance using control charts, 5)
quantifying the need for management changes (using the control index algorithm), 6)
identifying management options and- checking for feasibility using models and a knowledge

base, and 7) implementing the recommendations in either manual or on-line modes.

120
LITERATURE CITED

Borland International, Inc. 1990. Turbo Pascal version 6.0 user’s guide. Borland International,
Scotts Valley, California.

Carlson, W.H. and RD.Heins. 1990. Get the plant height you want with graphical tracking.
GrowerTalks 53:62-68.

Cook, D.F., J .G.Massey, and C.McKinney. 1992. A knowledge-based approach to statistical
process control. Computers Electronics Agr. 7:13-22.

Ehler, N. 1991. Interfacing crop models to standard software for greenhouse climate control.
Ecological Modelling 56:245-257.

Ehler, N. and P.Karlsen. 1993. OPTICO - A model based real-time expert system for
dynamical optinrization of CO2 enrichment of greenhouse vegetable crops. J.Hort.Sci. 68:485-
494.

Erwin, J .E. & RD.Heins. 1990. Temperature efi‘ects on lily development rate and
morphology fi'om the visible bud stage until thesis. J. Amer. Soc.Hort. Sci. 115:644-646.

Erwin, J .E., RD.Heins, and KGKarlsson. 1989. Thermomorphogenesis in Lilium
longiflorum. Amer.J.Bot. 76:42-52.

Erwin, J.E., RDHeins, MG.Karlsson, W.Carlson, and J.Biernbaum. 1987. Producing Easter
lilies. Coop. Ext. Serv. Michigan State Univ. Ext. Bul. E—1406 (revised), November 1987.

Fisher, PR, RDHeins, N.Ehler, J .H.Lieth, P.Karlsen, and M.Brogaard. A decision-support
system for real-time management of Easter lily (Lilium longrflorum) scheduling and height.
2. Validation. Agr. Systems. (In Review.)

Fynn, RP, W.L.Bauerle, and W.L.Roller. 1994. Implementing a decision and expert system
model for individual nutrition selection. Agr. Systems 44:125-142.

Fynn, RP., W.L.Roller, and HMKeener. 1989. A decision model for nutrition management
in controlled environment agriculture. Agr. Systems 3 1 :3 5-53.

Healy, W.E. & H.F.Wilkins. 1984. Temperature efl‘ects on ‘Nellie White' flower bud
development. HortScience 19:843-844.

Heins, RD., J..EErwin, MG.Karlsson, RD.Berghage, W.Carlson, and J .Biembaum. 1987.
Tracking Easter lily height with graphs. Easter lily response to temperature during forcing,
Part 2. GrowerTalks 51:64-68.

Jones, P. 1989. Agricultural applications of expert systems concepts. Agr.Systems 3023-18.

121

Karlsson, M.G., RD.Heins, and J.E.Erwin. 1988. Quantifying temperature-controlled leaf
unfolding rates in 'Nellie White' Easter lily. J .Amer. Soc.Hort.Sci. 113170-74.

Lieth, J .H. and P.Carpenter. 1990. Modeling stem elongation and leaf unfolding of Easter lily
during greenhouse forcing. Scientia Hort. 44:149-162.

Microsoft Corporation. 1991. User‘s guide, Microsoft Windows operating system 3.1.
Microsoft Corporation.

Miller, W.B. 1992. Easter and hybrid lily production: Principles and practice. Timber Press,
Portland.

Miller, W.B. 1993. Lilium longrflorunr, p 391-422. In: A De Hertogh and M. Le Nard (eds).
The Physiology of Flower Bulbs. Elsevier, London.

O'Rourke, EN. & P.C.Branch. 1987. Observations on the relationship between degree-day
summations and timing of Easter lilies. HortScience 22:709-710.

QuarterDeck Office Systems. 1991. User's guide, DESQView version 2. Quarterdeck, Santa
Monica, CA.

Richards, El 1959. A flexible growth function for empirical use. J .Expt.Bot. 10:290-300.

Statistical Analysis Systems Institute. 1988. SAS/STAT user‘s guide. Release 6.03. SAS
Institute, Inc., Cary, NC.

Stock, M. 1987. AI and expert systems: An overview. AI Applications 129-17.

122

 

 

 

 

Table 1 Parameter estimates for Equation (6).
Source DF DF
Regression 4 9414
Residual 95 68.7
Uncorrected total 99 9483
Parameter Estimate :1: asymptotic Units

standard error

b0 57.158i2.166 d
b, -1.258:h0.093 dC“
b2 -19.484 :1: 1.027 d cm'l
b 0.417 a: 0.044 0 (cm (3"

 

123

 

 

 

Table 2 Action table for DIF recommendations
Control index Recommended DIF Growth retardant recommendation
(CI) temperature adjustment (°C)
-3 -6 apply1
-2 -4 apply‘
-1 -2 apply‘
0 0 do not apply
1 2 do not apply
2 4 do not apply
3 6 do not apply

 

1‘ Apply' means a recommendation to apply a foliar spray of 2.5 ppm uniconazole, 0.125
mg/pot ancymidol drench, or 25 ppm ancymidol spray if it is more than one week prior to VB

and it has been at least seven days since the last application.

Table 3 Parameter estimates for K, and deased on linear regression of interview data

 

 

 

Source DF Sum of squares

 

 

Regression 2 9414.5
Residual 46 68.7
Uncorrected total 48 9483.2
Parameter Estimate i standard error

K -0.247:l:0.016 cm'l

P

K, -l.383:l:0.094 cm"day

124
Table 4 Constraints for temperature recommendations (°C) during Easter lily
production stages. From SF to EML, values represent soil temperatures, and

afier EML, values represent air temperature settings.

 

1

 

 

Feature (°C) SF to EMM EMM to FBI FBI to VB VB to FL
Minimum ADT . 13 13 10 10
Maximum ADT 20 20 27 27
Default ADT 18 18 20 20
Minimum NT l3 13 10 10
Maximum NT 20 20 22 27
Minimum DT 13 13 10 10
Maximum DT 20 20 27 27
Most positive DIF 6 6 12 12
Most negative DIF -4 -4 -8 -8

Default DIF 0 0 O 0

 

125

 

 

Table 5 Variables, abbreviations, and parameters used in this study
Abbreviation Description Units
ADT average daily temperature °C
bo parameter for flower bud length model d
bl parameter for flower bud length model (I C“
b2 parameter for flower bud length model (1 cm’1
b3 parameter for flower bud length model d (cm C)‘l
BL flower bud length cm
CARE The Greenhouse CARE System, Version 2.0 -
CI height control index calculated by a process control
de/dt algorithm -
DIF derivative error in stem elongation rate cm (1'1
DSS day minus night temperature °C
DT decision-support system -
DTF average daytime temperature °C
e(t) days to flower (FL) d
EML proportional error in elongation rate cm
the point in time at which 50% of a crop has emerged
EMM above the soil line (I
the point in time at which the leaf tips of 50% of a crop are
FBI at least 7.5 cm above the soil line (1
the point in time at which flower buds are visible on at least
FL 50% of a sample of ten dissected lilies d
the point in time at which 50% of a crop of lilies has at least
H one open flower d
Kd final plant height cm
Kp derivative error parameter cm’l d
LUR proportional error parameter cm"
NT leaf unfolding rate leaves (1‘1
SER average night temperature °C
SF stem elongation rate cm (1'1
start of greenhouse forcing; the point in time at which
VB plants are first moved into the greenhouse afier
vernalization d

the point in time at which flower buds are visible on at least
50% of a crop, without removing leaves d

126

‘
r

 

 

 

 

 

 

 

 

 

Time
Leaf unfolding rate Days from Bud length
(Karlsson et al., 1988; VB to FL (Healy and
Lieth and Carpenter, 1990) (Erwin and Wilkins, 1984)
Heins, 1990)
......... 3: 19E". 919299920 9391910. 55919.?! 91.11.9931- . - - - - - - - - - - - - - - -,
r, 09 e b ~o\° 49$
9° (9 «$9 9° 4’ O
Q} 9 '3 \° Q\ 9° {1‘
Q \ $ \ \¢ \9 e 0 Q
" $23 é‘i 1’ e“ at" é‘"
05$ (0‘? Q 9° 3 ob
4? e99 49‘ Q
\l é «\0

Easter lily models and phenological stages used in the DSS.

127

60

 

Maximum height

 

Minimum height
50‘

 

 

 

 

 

 

 

A 40 -<
g Target
:1 Measured heights .
E, 30 _ heights
0)
.C
E
O
EIZO‘
Poi height
10 e Visible Flower
bud date
date
0 I I I I I ‘17 T T
0 10 20 30 40 50 60 70 80 90

Days after emergence

An example graphical tracking control chart for Easter lily height.

Leaf number

128

 

 

 

 

 

 

 

 

80
Estimated final leaf number
70- Target
60- leaf
number
50-
40" Actual
’ _ leaf
3° . number
Initial leaf

20‘ number at FBI

_ Flower Visible
1° bud bud

0 initiation
O 10 20 30 40 50

Days after emergence

An example graphical tracking control chart for Easter lily leaf count.

60

Plant height (cm)

129

   

 

 

/
55 /
/
50 / x / ’
45 ’ ’ /
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SECTION 5

5. A DECISION-SUPPORT SYSTEM FOR REAL-TIME MANAGEMENT or
EASTER LILY (LILIUM LONGIFLORUM THUNB.) SCHEDULING AND HEIGHT.
2. VALIDATION

Paul R. Fisher‘, Royal D. Heins‘, Niels Ehlerz, J. Heinrich Lieth’, Michael Brogaardz, and

Poul Karlsen2

1. Department of Horticulture, Michigan State University, East Lansing, MI
48824, USA.
2. Horticulture Section, Department of Agricultural Sciences, Royal

Veterinary and Agricultural University, Rolighedsvej 23, 1958
Frederiksberg C, Denmark. ,

3. Department of Environmental Horticulture, University of California, Davis,
CA 95616-8587, USA.

Submitted to Agricultural Systems

ADDITIONAL KEYWORDS. decision support, Easter lily, expert system, height
control, knowledge-based system, Lilium Ionnglorum, scheduling, validation

134

135
ABSTRACT. Computer decision-support systems (DSS) are interactive programs that
provide model recommendations in a problem area. An experiment was conducted to validate
a DSS for scheduling and height control of Easter lily (Lilium Iongrflorum Thunb.) called Dre
Greenhouse CARE System. The DSS was used to recommend temperature setpoints in three
locations (Michigan, California, and Copenhagen, Denmark) with the goal of producing
Easter lilies at predefined flowering and visible bud dates, and at plant height targets. Day
and night temperature settings recommended by the DSS were the sole method used to
control timing and, secondarily, plant height. Flowering of 50% of plants occurred on the
specific target date in two locations and was one day early in the third location. The DSS was
less able to achieve a target visible bud date, and information fi'om commercial crops grown
with the DSS indicated changes needed to implement a leaf unfolding rate model. Plant
height was consistently taller than desired, indicating that growth retardants need to be
included in future model recommendations. DSS temperature recommendations were similar

to those made by experienced Easter lily consultants.

INTRODUCTION

Validation is essential in the development of decision-support systems (DSS) to eliminate ‘
model and programming errors, check feasibility of recommendations, and increase user
acceptance. Decision-support systems are interactive computer programs that typically
combine quantitative models and knowledge-based systems to provide feedback or

recommendations on a problem area. A knowledge-based system of this type, also called an

136
expert system, is a computer program that attempts to capture human expertise usually in a
narrow field (Stock, 1987). The validation of an agricultural DSS determines whether the
biologicaL physical, or economic models correctly predict observed behavior in the field and
whether knowledge-based system recommendations are feasible and similar to those of a

human expert.

Whereas quantitative models are usually validated by statistical comparison between the
model predictions and an independent data set (Reynolds and Cunningham, 1981), validation
of knowledge-based systems is a complex and evolving area of artificial intelligence research
(Nazareth and Kennedy, 1993) that as yet lacks an established methodology (Harrison, 1991).
Knowledge-based systems designed to mimic a human expert are generally validated by
comparing recommendations of human experts with those of the knowledge-based systems
over a set of test cases (Harrison, 1991; Hochman and Pearson, 1991; Huime et al., 1991;
O'Keefe et al., 1987). DSS designed to manage a production process have also been used as
the controller in a test situation in which model recommendations are implemented directly
and the resulting production performance is measured (Fynn et al., 1989; Jacobson et al.,

1989)

The objective of this project was to develop and implement a methodology for validating a
DSS for scheduling and height control of Easter lily, called Ihe Greenhouse CARE System
(Fisher et al., 1995). In this article, we describe validation of three aspects of the DSS: 1) the
possibility of achieving visible bud and flowering target dates via program use, 2) agreement

between plant development model predictions and observed plant behavior, and 3) agreement

137

between DSS and human expert recommendations of average temperature. The methodology
for validating the DSS is presented in the next section. Results are presented and discussed
in order of the three elements (production goals, development models, and DSS

recommendations).

MATERIALS AND METHODS

W. Three data sources were used for validation: 1) experiment in which
the DSS was used to control greenhouse temperatures in real time, 2) a comparison of
recommendations of the DSS and human consultants, and 3) a database of commercially
produced crops.

1. DSS real-time control. In an experiment at three locations (Michigan State University
(MSU), University of California, Davis (UCD), and the Royal Veterinary and Agricultural
University in Copenhagen Denmark (KVL)), recommendations from the DSS were used to
grow ‘Nellie White' Easter lilies. In each location, 50 case-cooled bulbs 20 to 22.5 cm in
circumference (size 8/9) bulbs were grown in 15-cm-diameter pots. Bulbs for UCD were case
cooled in redwood sawdust in a growth chamber at 4C for 48 days, then were removed and
immediately planted in UCD mix (1:12] by volume of peat, redwood sawdust, and sand) on
17 Dec. 1993 and placed in a greenhouse. At MSU, bulbs were case cooled in sawdust for
six weeks by a commercial supplier (Gloeckner and Co., Harrison, New York) and were
planted on arrival on 21 Dec. 1993 into Metro Mix 510 medium (Scotts, Marysville, OH).

Bulbs from the same batch of lilies as those used at MSU were packed in sawdust and air

138

shipped to KVL. The KVL bulbs were in transit for nine days (at unknown storage
temperature) after which they were planted in Pindstrup peat mixture number 2 (Pinde

Mosebrug NS, 8550 Ryomgérd, Denmark) on 29 Dec.

In the greenhouses, plants were placed at 25-x-25-cm spacing in 16C root medium until 90%
emergence. The date at which leaf tips emerged above the soil line for 50% of the plant
group (EML) occurred on 1 Jan. 1994 at UCD, 4 Jan. at MSU, and 7 Ian. at KVL. Plants
were top watered at UCD and subirrigated at MSU and KVL. Nutrients were supplied with

the irrigation water at standard recommended levels (Erwin et al., 1987).

After 90% of the plants emerged, the first and last 10% emerged were used as boundary
plants around the outside of the bench. Fifteen of the remaining plants were chosen randomly
for observation, and the rest of the plants were either used as boundary plants, unused or

dissected.

Once EML occurred, target dates were entered into the DSS for visible bud (VB), defined
as the point at which buds were visible on 50% of the observed plants, and for flowering (FL),
defined as the date when 50% of the observed plants had at least one open flower. Target
dates were 1, 7, and 7 Mar. 1994 for VB and l, 7, and 7 Apr. 1994 for FL at UCD, MSU,
and KVL, respectively. Target dates for VB and FL for MSU and KVL were selected at
emergence because of the bulbs' delayed delivery to KVL and our intention to use the same

target dates at MSU and KVL.

139

The only control variable used to meet production goals was air temperature. The highest
priority was to meet the target VB and FL dates, and a second priority was to obtain a final
plant height of 50-55 cm, including a pot height of 12 cm at KVL and 14 cm at UCD and
MSU. Average temperatures recommended for plant development goals were therefore not
compromised by selection of day/night temperature settings needed for height control.
Growth retardant chemicals are usually applied in commercial Easter lily production to
control plant height (Miller, 1993). In this experiment, growth retardants were not applied
because some of these chemicals can delay development of Easter lily (Heins, 1993 ), and this
effect was not considered in the DSS. In addition, growth retardant use is becoming
increasingly restricted, and this project was part of a wider research effort to manage plant

production by nonchemical methods.

Newly unfolded leaves (those with an angle equal to at least 45° to the plant stem at the
center of the leaf) were counted twice each week between EML and VB . A wire loop 3 cm
in diameter was placed around the stem on the last unfolded leaf to mark leaves already
counted. The loop was moved carefully up the plant after each measurement to avoid
damaging the plant or restricting the opening of new leaves. Near VB, unfolded leaves were

marked with a dot of typist's correction fluid rather than the loop.

Total leaf count was obtained by dissecting four plants twice weekly starting when 30 leaves
had unfolded and ending at flower bud initiation (FBI), which was defined as the date when
flower bud primordia were first visible on 50% of a sample of ten plants under a x10 hand

lens. Because no firrther leaves are produced after FBI, total leaf counts were obtained at that

140

time. FBI date and total leaf count were entered into the DSS when FBI occurred.

Visrble bud date was recorded for each plant, and the median VB date was entered into the
DSS. After VB, flower bud length from base to apex was measured twice each week using
a flexible plastic ruler. Flowering date, defined as the date when the first bud began to open,
was recorded for each plant. Plant height was measured with a ruler fi'om the pot rim to the
top of the plant twice each week between EML and FL and was added to the pot height to

give the total plant height.

Plants were grown under natural lighting at MSU and UCD, with photoperiods ranging from
9 to 13.5 hours during the experimental period. Three 400-W high-pressure sodium lamps
were suspended 1 m above the canopy at KVL to supply supplemental lighting for a 12-hour

photoperiod.

Air temperatures were recorded using aspirated G-type thermocouples at MSU and KVL and
an aspirated solid State thermometer at UCD. At KVL and UCD, soil temperatures were
logged using a thermocouple and a solid state thermometer, respectively. A hand-held soil
thermometer was used at MSU. Average temperatures were recorded every 15 mimrtes by
a PRIVA environmental computer (Priva Agro B.V., De Lier, Holland) at MSU, a datalogger
and a Q-Com environmental computer (Q-Com, Irvine, California) at UCD, and a DGT-
Volmatic environmental computer at KVL (DGT-Volmatic AIS, Vejlesvinget 2-4, 2660,
Brondby Strand, Denmark). At KVL, the greenhouse computer was programmed to store

temperatures directly in the DSS database and automatically to implement DSS-recommended

141
temperature settings. At MSU and UCD, greenhouse temperatures from the greenhouse
control computer were read into the DSS, and an operator manually implemented temperature
settings.

2. Consultant recommendgtions. Three experienced Easter lily growers (referred to as the
consultants) in the United States were selected to provide recommendations on the KVL
experiment, against which the DSS recommendations could be compared. These consultants
were not completely independent of the DSS because they were part of a beta test user group.
The consultants were chosen because they were highly innovative, were among the first
producers to use graphical tracking of plant height, had a known level of expertise and
experience (between 10 and 20 years of experience growing ISO-250,000 Easter lilies

annually), and were willing to commit time to the project.

Information on the crop at KVL (current temperatures, height, leaf count, or bud length, but
excluding model output and recommendations) was sent to the consultants by facsimile during
the growing period. Using only their expertise, the consultants then developed
recommendations for temperature and growth retardants for the KVL crop. The consultants'
opinions, based on and limited to the same data used in the DSS, were recorded but not
implemented. After the production season, the consultants were visited for a two-hour

follow-up interview to discuss their recommendations.

3. Grower Database. Leaf count data fi'om 49 crops grown with the DSS in three

 

commercial greenhouses in Michigan during 1994 were used to validate the leaf unfolding

142

rate (LUR) model (Karlsson et al., 1988) in the DSS. Each of these crops consisted of a
group of plants from a single bulb supplier and was planted on the same date and located in
a single greenhouse temperature zone. Air temperatures were recorded for all crops by using
aspirated thermistor temperature sensors located 30-60 cm above bench height. Between FBI
and VB, average night, dawn (first two hours after sunrise), and day temperatures were
obtained for each crop every day by calculating the means of 15-minute average temperatures.
Leaves in the grower database were counted as unfolded when the leaf tip was bent back (in
contrast to the real-time control experiment were a leaf was considered unfolded when the
center of the leaf was bent 45" away from the stern axis). The average leaf counts fi'om at
least four plants per crop were recorded twice weekly fi'om FBI to VB. The occurrence of
FBI for each crop was determined by dissecting a representative sample of bulbs at regular

intervals until 50% of the plants in the sample had visible flower bud primordia.

Validation goals

Production objectives. The hypothesis that adhering to DSS temperature recommendations
would allow the crop scheduling targets to be met was tested with the real-time control
experiment. The median and distribution of observed VB and FL dates at each location were
recorded and compared with the objective of 50% of the plants achieving VB or FL stage by
the specific target dates.

Developmental models. The hypothesis that the development models in the DSS correctly
predicted Easter lily development was tested using statistical comparisons of predicted and

observed plant behavior. Using regression analysis, the LUR model was compared with

143

observed leaf count over thermal time for the three locations in the real-time control
experiment, and with data fi'om the grower database. The first 20 leaves to unfold are
dificult to measure on Easter lily, and Lieth and Carpenter (1990) noted that the first 20-35
leaves of Easter lily tend to unfold rapidly before a linear leaf unfolding pattern begins.

Therefore, only leaf counts after the 20th leaf were analyzed.

After VB occurred, two separate submodels were used in the DSS to recommend ADT - a
model developed by Erwin and Heins (1990) for the thermal time required between VB and
FL, and a bud length model adapted from Healy and Wilkins (1984). The former model
resulted in a Single ADT estimate, whereas the latter computed a new ADT setting each time
bud length was measured. Observed rates of development were compared with those
predicted by both models. Several plants were dissected at VB and bud length was measured,
with an average length ofl.9 cm (range 1.8 to 2.1 cm). Assuming a bud length of 1.9 cm at
VB meant that the Erwin and Heins (1990) model and bud length model could be compared
directly. The ADT predicted by the two models was plotted against days to flower for each

location and the observed average ADT.

DSS recommendations. Average temperatures recommended by the DSS and those
recommended by the consultants were compared graphically over time. Interviews with
consultants and internal analysis of the DSS were used to identify the causes for any

differences.

144

RESULTS

Muctign objectives. Implementation of the DSS temperature recommendations allowed
the target flowering dates to be met within a range that was acceptable by commercial
standards. Flowering date of individual plants relative to the target date of 1, 7, and 7 Apr.
for UCD, KVL, and MSU, respectively, ranged from six days earlier to four days later (Fig.
1a). The median flowering date was on target at KVL and UCD and one day early at MSU.
The FL date at MSU was more variable (range 10 days) than at UCD (seven days) or KVL

(three days).

Temperature setting recommendations by the DSS were less successful at leading to the VB
date goal (Fig. 1b). The median VB date was on target at UCD, four days early at KVL, and
five days early at MSU. The VB date distribution was bell shaped at UCD, but was bimodal
at MSU, with a range of nine days between the earliest and latest plant. At KVL, the VB date

of each plant was not recorded.

Between FBI and VB, the observed leaf count was within eight leaves of the target number
at all locations (Fig. 2). The DSS reacted to higher-than-expected leaf count by reducing the
temperature setting (e. g., day 28 at MSU) or increasing LUR by increasing ADT (e. 3., day
48 at KVL). An increase in ADT near the VB date promoted LUR and contributed to the

early VB dates at KVL and MSU.

Developmental models. Counts of unfolded leaves over time for the three locations were

145

similar to those predicted by the LUR model for leaves 20 to 60 (Fig. 3a). The LUR slowed
consistently after approximately 60 leaves had unfolded. VB occurred when 65, 68, and 67
leaves had unfolded at KVL, MSU, and UCD, respectively, which was on average six leaves

fewer than the total final leaf count at the end of the experiment.

Further validation of the LUR model with data from the grower database showed a close
correlation with the LUR model predictions. The r2 comparing grower data as the dependent
variable against the model predictions was 0.97, with the intercept estimate not significantly
difl‘erent from zero (-l.88:h5.83, estimate :1: 95% confidence limits) and the gradient slightly
greater than one (10221-0015). There was no decline in LUR at high leaf counts, although

the leaf-count trajectories of individual crops became more variable.

A total thermal time of 478 degree days from VB to FL was predicted by the Erwin and Heins
(1990) model using a base temperature of 3.5C. The predicted thermal time was within 13%
of the observed duration, overestirnating the period for KVL (429 degree days) and UCD
(459 degree days), and underestimating for MSU (543 degree days). When results were
averaged over the three locations, the average (477 degree days) and predicted thermal time
were within 1 degree day, which at an 18C average temperature, for example, represents two

hours.

At VB, the thermal time model was closer to the observed ADT than the bud length model
prediction in all locations (Fig. 4). The thermal time model predicted that an average 17 to

19C was required to reach the desired FL target, whereas the bud length model predicted ll

146
to 14C. In comparison, observed ADT fi'om VB to FL averaged 16 to 20C. The thermal

time model predictions were within 2.4C of the observed average ADT fi'om VB to FL in all
three locations. There was a bias in the bud length model: near VB the predicted ADT was
lower than observed average ADT, and near FL the model predictions increased up to or

above the observed ADT.

DSS recommendations. At KVL, average temperature recommendations by the DSS
generally fell within the highest and lowest consultants' recommendations (Fig. 5). One
exception occurred at FBI, 21 days after EML; the development model changed fi'om the
EM to FBI phase, in which a simple rule is used to recommend temperature (see companion
article), to the FBI to VB phase, in which temperatures are recommended based on leaf
unfolding rate. Consultants' recommendations changed more gradually during this transition
phase. Another deviation occurred on day 44 because the LUR model reacted more strongly
to a high leaf count than did the consultants. Around VB, consultants tended to recommend
higher temperatures than the DSS. During interviews, it became apparent that consultants
based their temperature recommendations around VB on their local experience of the ADT
needed for a given number of days fiom VB to FL. During the final 14 days, the temperature
settings recommended by the DSS were lower than those the consultants recommended and
were based on the bud length model. Data fi'om only one consultant were available on days
80 and 83 because during this period, commercial crops were packed and shipped and

consultants were unable to participate in the experiment.

There were considerable differences (up to SC) among the ADT recommendations made by

147
consultants for any given date (Fig. 5). Averaged over the entire season, difi‘erences in
consultants' recommendations were not statistically significant (Table 1) float each other or

fi'om the DSS recommendations.

The plant height goal. The secondary goal in this experiment was to control plant height
using DIF. At all three locations, final plant height was taller than the 50- to 55-cm target-
height range (59.4:t1.6 cm at KVL, 60.0d:l.7 cm at MSU, and 67.3:t2.4 cm at UCD). Warm
outside temperatures at UCD meant that DIF targets were fiequently not achieved. DIF
temperatures recommended by the DSS throughout the KVL experiment were generally
within the minimum and maximum range recommended by consultants, and the average DIF
recommended over the production season was not significantly difi‘erent between the DSS and
the consultants (Table 1). All consultants recommended growth retardant applications to the

KVL crop.

DISCUSSION

Production goals. The DSS successfully led to the flowering date goal in the real-time control
experiment, although several concerns were noted. An important aspect not addressed by the
development model was variation in development rate across an entire crop. In the real-time
control experiment, only a single bench of homogeneous plants was grown at each location,
whereas in commercial production, plants may be spread across several greenhouses, with

bulb material from several suppliers. Mean leaf count and bud length data were used as

148
modelinputs, andinthereal-time control experiment, the median flowering datewasused as
a target. In contrast, objectives for a commercial crop would be to have all crops in flower
by the marketing date, with minimum variation between plants to avoid the need for cool
storage, multiple handling of plants, and multiple shipments. The final height goal was not
achieved using DIF temperature alone, and more extreme negative DIF conditions and/or

growth retardants were needed to achieve height specifications.

Development model. In the real-time control experiment, the leaf unfolding rate model
predictions were closely correlated with observed data from the 20th to 60th unfolded leaves,
after which they exceeded observed LUR. In contrast, data fi'om the grower database were
closely correlated with LUR model predictions for all leaves after leaf 20, without a reduction
in LUR after the 60th leaf. Slight difi‘erences in the definition of an unfolded leaf were
probably the cause for these discrepancies - leaves were counted as unfolded earlier when the
grower database method was used than in the real-time control experiment. This difl‘erence
became significant near VB when internodes and leaves became compacted. The consultants
considered that approximately five leaves remained to unfold at VB if a 45° leaf tip angle was
used as the criterion and that leaf counting for the last five days before VB needed to be

completed cautiously because it became more subjective.

The thermal time model (Erwin and Heins, 1990) was within 2.4C of observed ADT and was
more accurate than the bud length model. The maximum deviation between the predicted
(478 degree days) and observed (543 degree days) thermal time occurred at MSU (where a

65 degree days difi‘erence represented 4.5 days at 18C). The difl‘erence between the thermal

149

time observed for the KVL and MSU crops is considerable, given that the bulbs originated
from the same case. The Erwin and Heins (1990) model was based on temperatures between
14 and 22C-the relationship between ADT and development rate for temperatures outside
this range was not linear. Temperatures above 22C at MSU for a five-day period (Fig. 2)
therefore contributed to a thermal-time calculation error. The difi‘erence between thermal
time at KVL and MSU (114 degree days, or almost eight days at 18C) may also been'caused
by the difi‘erence between air (measured) and bud (not measured) temperatures under artificial
and natural lighting, bench heating that was only used at KVL, and some residual effect from
transporting bulbs to KVL. In comparison to the Erwin and Heins (1990) model, thermal
time from VB to FL analyzed by O'Rourke and Branch (1987) was an average 515 degree
days using a base temperature of 3.7°C (which equals 519C at a 35°C base and 18C ADT)
for several experiments with ‘ Ace' Easter lily, with a coeflicient of variation of 15% across
experiments. Variability in the thermal time estimates in the real-time control experiment and
results fiom O'Rourke and Branch (1987) therefore indicate that a flower bud length model

is an essential tool to consistently achieve a flower date within three days of the target.

The bud length model was strongly biased and requires calibration using data obtained fiom
greenhouse plants. Observed bud length at VB was 1.9 cm, and part of the model error near
VB may have been because buds shorter than 2.5 cm were not measured by Healy and
Wilkins (1984). In addition, their data were obtained from a growth chamber study, and
radiant heating from the lamps in the growth chambers may have caused bud temperatures
to differ from greenhouse bud temperatures at the same air temperatures. One consultant had

developed his own bud meter based on his own crops, and other consultants may have

150

compensated for biases in the bud meter by using their local experience. These results
indicate the need to develop a new bud length model based on plants grown in greenhouses,
and it may be desirable to design a model that could accept air or flower bud temperatures

as inputs.

DSS flmmendations. Consultant recommendations provided a benchmark against which
the feasibility of the DSS recommendations could be tested. Because of the absence of
independent experts in the field and the time investment required to send facsimile responses
on the KVL trial, it was more practical to use beta test users familiar with The Greenhouse
CARE System as experts, rather than truly independent consultants. Bias in consultants'
responses therefore means that comparison between the DSS and the consultants must be
treated with caution. Another potential source of bias was that all consultants were located
in Michigan, and recommendations are likely to differ in warmer areas. The heuristics used
by an individual grower may differ from rules that would be appropriate for a wide range of
locations, and differences in strategy were indeed found between consultants. These biases
meant that differences between consultant and model recommendations did not necessarily
mean that the DSS was wrong, but instead indicate difi‘erences in the processes or criteria by

which they made recommendations.

151
LITERATURE CITED

Erwin, J .E., RD. Heins, M.G. Karlsson, W. Carlson, and J. Biembaum. 1987. Producing
Easter lilies. Coop. Ext. Serv., Michigan State Univ. Ext. Bul. E-l406 (revised), November
1987.

Erwin, J.E. and RD. Heins. 1990. Temperature efi‘ects on lily development rate and
morphology item the visrble bud stage until anthesis. J .Amer.Soc.Hort.Sci. 115(4):644-646.

Fisher, PR, RD. Heins, N. Ehler, and J.H. Lieth. A decision-support system for real-time
management of Easter lily (Lilium longrflorum Thunb.) scheduling and height. 1. System
description. Agr. Systems. (In press.)

Fynn, RP., W.L. Roller, and HM. Keener. 1989. A decision model for nutrition management
in controlled environment agriculture. Agr. Systems 31:35-53.

Harrison, SR. 1991. Validation of agricultural expert systems. Agr. Systems 35:265-285.

Healy, W.B. and HF. Wilkins. 1984. Temperature efi‘ects on ‘Nellie White' flower bud
development. HortScience 19(6):843-844.

Heins, RD. 1993. Sumagic's effect on Easter lilies. Greenhouse Grower (F ebruary):46-48.

Hochman, Z. and C .J . Pearson. 1991. Evaluation of an expert system on crossbreeding beef
cattle. Agr. Systems 37:259-274.

Huime, R.B.M., A.A. Dijkhuizen, and G.B.C. Backus. 1991. Validation of an integrated
decision support and expert system for analysis of individual sow-herd performance.
Computers Electronics Agr. 6:71-86.

Jacobson, B.K., P.K. Jones, J.W. Jones, and IA Paramore. 1989. Real-time greenhouse
monitoring and control with an expert system. Computers Electronics Agr. 3 2273-285.

Karlsson, MG, RD. Heins, and IE. Erwin. 1988. Quantifying temperature-controlled leaf
unfolding rates in 'Nellie White' Easter lily. J. Amer. Soc. Hort. Sci. 113270-74.

Lieth, J.H. and P. Carpenter. 1990. Modeling stem elongation and leaf unfolding of Easter
lily during greenhouse forcing. Scientia Hort. 44:149-162.

Miller, W.B. 1993. Lilium Iongrflorum, p. 391-422. In: A. De Hertogh and M. Le Nard
(eds). The physiology of flower bulbs. Elsevier, London.

Nazareth, D.L. and M.H. Kennedy. 1993. Knowledge-based system verification, validation,
and testing: The evolution of a discipline. Intl. J. Expert Systems 6(2): 143-163.

152

O'Keefe, RM, 0. Balci, and ER Smith 1987. Validating expert system performance. IEEE
Expert 2(4):81-90.

O'Rourke, E.N. and RC. Branch 1987. Observations on the relationship between degree-day
summations and timing of Easter lilies. HortScience 22(5):709-710.

Reynolds, IF. and G.L. Cunningham 1981. Validation of a primary production model of the
desert shrub Larrea tridentata using soil-moisture augmentation experiments. Oecologia
5 1 2357-3 63.

Stock, M. 1987. AI and expert systems: An overview. AI Applications 1(1):9-17.

153

 

 

 

Table 1. Comparison of consultant and CARE temperature recommendations.
CARE Grower l Grower 2 Grower 3
Average temperature (‘C)
Mean :1: 95% 14.9:h2.2 15.9:12 16.0:hl.6 15.5:h1.3
Minimum to 10-18 11-21 13-20 11-20
maximum
DIF temperature (°C)

Mean :1: 95% -6. 1:1:1.7 -5.7:i:1.5 -7.0i1.8 -6.3il.l
Minimum to -13 to 0 -11 to 0 -8.5 to -3.5 -10 to -2

maximum

154

Table 2 Variables, abbreviations, and parameters used in this study

 

Abbreviation

 

Description Units
ADT average daily temperature °C
DIF day minus night temperature °C
DSS decision-support system d
EML the point in time at which leaf tips emerge above

the soil line for 50% of a crop d
EMM the date at which the leaf tip is at least 7 .5 cm

above the soil line for 50% of a crop d
FBI the date at which flower buds are visible on 50%

of a sample of ten dissected plants (1
FL the date at which 50% of a crop of lilies has at

least one open flower (1
KVL Royal Veterinary and Agricultural University,

Copenhagen, Denmark -
LUR leaf unfolding rate leaves d'
MSU Michigan State University, East Lansing, l
UCD Michigan -
v13 University ofCalifornia, Davis, California '

the date at which flower buds are visible on 50%

d

of a crop

155

 

 

l
(A) l
‘ I
10 ~ KVL : d
{5’ 8 - MSU 2
a UCD
.5 6 _ -
h 2:2
at 2V8
2: "‘
_ 2 2 ‘
a 4 2i2
z 5?
232
2 — i _
0 . E $2 2.2% i
(B)
10 — I

e
_-———————————_———-

   
 

Number of plants
¢\

 

 

-8-6-4-20 2 4 6

Deviation from targetid)

Distribution of (a) flower date (FL) and (b) visible bud date (VB) in the real-
time control experiment at three locations (KVL, MSU, and UCD). Visible
bud date for each plant was not recorded at KVL.

156

 

A
:p
v
:1
HHNNCD
omomo

 

HHNNCO
OCJ‘OUIO

Leaf number
Average temperature (C)

 

 

(C) :

HHNNCO
OU‘OU‘O

70 -

60 -

50 ~

40 - FBI

30 - l

20 - ’

10 - e; p

O l l 1 r
o 20 40 60 so 100

Days after emergence

 

 

 

Leafcountand averagedailytemperamreinthe real-time experiment atthrce
locations ((a) KVL, (b) MSU, and (c) UCD). v = observed ADT, Cl = ADT
setting, A = observed leaf count, :1: 95% confidence intervals.

157

 

 

(A) -
100 - _
VB
UCD
is 80 - VB l ..
.o KV
E
i3
,H 60 — A _
3 VB
.4 / MSU
4O — ..
20 i i i l g I 4' l
(B)
100 ~ .0 . _
8' a)"
r- 00:;°' {a e
vs" , '-
s 80 ‘- 5 q, ' ..
'0 V
g .
”t . .
‘3 60 ~ 2 _
Q—u 00
cc . ° .°‘
Q) 0 O
'4 . "t'
or ~g '
4O — ' _
v ' 3
20 ' 1 I i l l I i J

 

 

 

O 200 400 600 800 1000
Thermal time (Cd)

Leafcount over thermal time using a base temperature of 3.5C. (a) Data from
the real-time control experiment (0 = KVL, C] = MSU, V = UCD, :l: 95%
confidence intervals). (b) Data from the Grower Database of commercial
crops (0 = grower 1, Cl = grower 2, '= grower 3). The solid lines in (a)
and (b) are the leaf counts predicted by the LUR model.

 

24— -

20~ —

 

16

12

 

24

20,

16 - '-
12: —
r i i 2

 

 

Average temperature (C)

8

 

(C)
24 - ~

20— —
16~ —

12— ~

 

 

8 11 l 11 l
353025201510 5 0

Days before flower

Observed and predicted average daily temperature after VB in the real-time
control experiment at three locations ((a) KVL, (b) MSU, and (c) UCD). O
= the observed ADT averaged for all days between the data point and the
flower date (FL) (for example, 34 days before FL in KVL, Fig. 4(a), the
average of temperature over the next 34 days was 16.1C). V = the ADT
predictedatVBbytheErwinandHeins(l990) thermaltimemodel. Cl =the
ADT predicted by the bud length model.

 

159

 

25 r , I ,
One

20 P grower ‘
only

Temperature (C)
p—s
or

 

 

 

 

 

 

 

 

10 — l" _
FBI Visible.
bud
5 J l l l
O 20 4O 60 80 100

Days after emergence

Average daily temperatures recommended by the DSS and. the three
consultants for the crop at KVL. C = the ADT recommended by the DSS,

and the solid lines represent the maximum and minimum of the three

consultants' recommendations on each date.

SECTION 6

6. GRAPHICAL TRACKING OF LEAF NUMBER TO SUPPORT CROP TIMING

DECISIONS

Paul R. Fisher and Royal D. Heins

Department of Horticulture, Michigan State University, East Lansing, MI 48824-1325

To be submitted to HortTechnology.

ACKNOWLEDGEMENTS: We would like to thank University Outreach at Michigan State
University for providing fimding for this project and J. Heinrich Lieth at the University of
California (Davis) and Niels Ehler at the Royal Veterinary and Agricultural University in

Copenhagen, Denmark, for their cooperation.

ADDITIONAL INDEX WORDS. technology transfer, leaf unfolding rate, control chart,

process control, Lilium longrflorum Thunb., greenhouse, Ihe Greenhouse CARE System

160

161

ABSTRACT. A graphical process control chart that uses an Easter lily (Lilium Iongrflorum
Thunb.) leaf unfolding rate model to control development rate toward flowering was
developed. The technique allows observed and target leaf count to be compared visibly over
time. The Optimum leaf unfolding rate and average temperature can be read directly fi'om the
chart. The approach provides an intuitive method of describing quantitative models to

growers that could be applied to other problem areas.

Control of development rate is critical to time flowering of ornamental crops for market sales.
Easter lily (Lilium longrflorum) is a particularly challenging crop to schedule because there
is a narrow market window. Easter falls on a difl‘erent date every year and bulbs vary
depending on the field conditions in which they were grown. Development rate is controlled

by dynamically manipulating greenhouse temperature over time.

The objective of this project was to develop a graphical process control chart that provides
decision support pertaining to the optimum greenhouse temperature based on leaf unfolding
rate (LUR) of Easter lily. Karlsson et al. (1988) modeled the response of Easter lily LUR to
average temperature. A leaf was defined as unfolded when it was oriented 45° from the plant
stem, and LUR was the rate of change in leaf count per day. From 15 to 22C, LUR was
approximately a linear firnction of average temperature, allowing computation of the ADT

required to achieve a desired LUR:

162

ADT=LUR * 10.64 + 1.12 (1)

In order for research-based models to be adopted by end-users, technologies that package
complex quantitative information into intuitive formats are needed. One technique developed
for Easter lily, poinsettia, and chrysanthemum height control is the graphical tracking of plant
height over time, in which actual plant performance is compared with a target curve (Carlson
and Heins, 1990; Heins and Carlson, 1990; Heins et al., 1987; Karlsson and Heins, 1994).
We developed a similar tool for LUR where recommendations from Eq. (1) are summarized
on a control chart (Fig. l). The LUR control chart is part of a computer decision-support
system called The Greenhouse CARE System (Fisher and Heins, 1995), although the graph
can also be drawn directly on paper. The tool was tested during the 1994 Easter lily

production season and is currently being used by over 30 commercial producers.

In commercial Easter lily production, growers schedule their crops to reach visible bud (VB)
30-35 days before shipping. At VB, flower buds are visible on 50% of the crop without
removing leaves. VB provides an intermediate milestone to keep crop timing on track, and
occurs when all but about five leaves have unfolded. In the example (Fig. l) fi'om a crop of
15 plants grown in a research greenhouse at the University of California (Davis), the target

flower date was 1 Apr. 1994, and the target VB date was 1 Mar.

After 20 leaves have unfolded approximately two weeks after plants emerge, growers begin
regular plant dissections to check for flower bud initiation (FBI), the first observable presence

of flower bud primordia (\Vrlkins and Roberts, 1969). The number of leaves on a plant can

163

be counted at FBI to estimate the total number of leaves yet to unfold. The average number
of unfolded leaves at FBI and the estimated final leaf number at VB can be plotted on the
control chart (Fig. 1). The number of leaves that unfold between FBI and VB is therefore the

total number of leaves not unfolded at FBI minus five leaves remaining to unfold at VB.

There was an average of 75 leaves in the crop in Figure 1, which, subtracting the 26 unfolded
leaves at FBI, equals 49 leaves not yet unfolded at FBI, and 49-5=44 leaves to unfold

between FBI and VB.

The solid line in Figure 1 runs from FBI on 24 Jan. to VB on 1 Mar. (x-axis), and from 26
leaves at FBI to 70 leaves at VB (y-axis). This line represents a target to compare against
actual leaf number. The actual leaf number is written on the left side of the graph, working
down from the total leaf number minus five leaves at the top of the y-axis. The date is written

on the bottom of the graph, working back from VB to FBI in increments of 10 days.

The optimum LUR is calculated by the following:

optimum LUR= (leaves still to unfold by VB)/(days to VB) (2)

which in Figure 1 is 44 leaves/36 days = 1.25 leaves/day (approximately). The target line

shows the average LUR needed from FBI to VB and the desired average temperature (14C)

to achieve this LUR Working back along the diagonal dotted lines toward the bottom left,

the required LUR and temperature can be read from the chart.

164

After FBI, the number of unfolded leaves is counted on five plants per crop twice each week.

The average leaf count is plotted for each measurement date.

Warm weather, changes in light conditions, or some other factor may cause the actual leaf
number to deviate from the target, even if the environmental computer setting is at the
required average temperature (e.g., 14C). Ifactual leaf number is below the target curve, as
it was on 4 Feb. in Fig. 1, temperatures can be raised to increase leaf unfolding rate. The
required leaf unfolding rate and temperature can be read from the bottom left of the chart,
based on where the measurement point lies with respect to the diagonal dotted lines
(approximately 1.3 leaves/day and 14C, respectively, for 2 Feb.). Conversely, if actual leaf
number is above the curve, the graph can help the user decide how much to drop
temperatures to reduce leaf unfolding rate. As the crop approaches the last week before VB,
recommendations from the control chart must be treated with caution because slight errors

in leaf counting can cause large temperature recommendation errors.

Many Easter lily growers were already using the leaf-counting model (Eq. (1)) to quantify the
optimum temperature using a look-up table or a calculator, before this tool was developed.
We have had positive responses fiom growers about the LUR control chart because it
provides the required decision-making information in a visible format and clearly displays

trends over time.

The approach can be generalized (Fig. 2) to allow application to other horticultural problem

areas in which a process variable, for example, leaf count, flower bud size, or fi'uit size, is

165
tracked over time. For this method to be applicable, it would be necessary to 1) quantify a
final target value of the process variable at a specified date, 2) quantify the response of this
process variable to some input, for example, light or temperature, that can preferably be
manipulated, and 3) monitor and quantify the process variable over time. Although for
simplicity the target curve is represented in Figure 2 as linear over time, the approach could

also be applied-to nonlinear growth or development models.

166

LITERATURE CITED

Carlson, W.H and RD. Heins. 1990. Get the plant height you want with graphical tracking.
GrowerTalks 53(9):62-68.

Fisher, RR and RD. Heins (in press). A process control approach to height control of
poinsettia. HortTechnology.

Heins, RD. and W.H. Carlson. 1990. Understanding and applying graphical tracking.
Greenhouse Grower 8(5):73-80.

Heins, RD., J.E. Erwin, M.G. Karlsson, RD. Berghage, W.H. Carlson, and J. Biembaum.
1987. Tracking Easter lily height with graphs: Easter lily response to temperature during
forcing. GrowerTalks 51(8):64-65.

Karlsson, M.G., RD. Heins, and IE. Erwin. 1988. Quantifying temperature-controlled leaf
unfolding rates in ‘Nellie White' Easter lily. J. Amer. Soc. Hort. Sci. 113:70-74.

Karlsson, M.G., and RD. Heins. 1994. A model of chrysanthemum stem elongation. J.
Amer. Soc. Hort. Sci. 119(3):403-407.

Wilkins, HF. and AN. Roberts. 1969. LeafcountinguA new concept in timing Easter lilies.
Minnesota State Florists' Bul. 12:10-13.

Total unfolded leaf number

-80 -70 -60 ~50 -40 -30 -20 -10 0

70
69
50
40
30
20

10

167

Days before visible bud

 

  

 

 

r r r r l i r
.. actuaileai'number
.. .................................................................. Fm“? .................................................. _
. _ . fibufi' . .. . _

... ..... ...._,r ............ .. d‘jn‘itia‘tip‘qfv ................ ..
o 5 . ‘ -' -' "
-3? ............ r ................. i3-1.4...._....lf.1.a-}2,2 '“Wd‘y .............. l
10 .- . . e 2 s

14' firs E22’
.-12 r .- i 16 1-' 20 i- 24 l “F"‘u'fi‘q

 

1/20 1/30 2/9 2119 3/1

An example leaf count graphical control chart.

Leaves still to unfold

168

Target
process r r , r l r I r

 

<
E.
I:
a

VALUE OF PROCESS VARIABLE
«a
R»
0".
l

mirror-ids"
.- «to .o .- .-

_ ,procets ‘
Initial variable;

process J . , ,.-' . r l 1
value Isitial TIME Target

 

 

 

A generalized representation of the process control chart for horticultural

problem areas.

APPENDICES

SAS PROGRAMS FOR ESTIMATING THE THREE-PHASE STEM ELONGATION
MODEL, AND FOR QUANTIFYIN G THE DOSE RESPONSE TO A

CHLORMEQUAT APPLICATION

169

APPENDIX A. SAS program for fitting the three phase function to untreated control.

/* 3PHASE1.SAS
Paul Fisher, March 15 1995
3-phase Exponential, linear and monomolecular model, NON transformed data
Alpha = transplant height
Gamma is estimated and T1 is calculated.
T2 is linked to visible bud date.
SD 13, SD 26, and SD 54 day treatment.

Calculation of model parameters fi'om Short day experiment 1994
Freedom single stem data. */

OPTIONS PAGESIZE=60 LS=79 ERRORS=3;
LIBNAME PAUL ";
FILENAME IN 1 'FREE94E.PRN‘;

DATA PAUL.S94A;
INF ILE IN 1;
INPUT
SD /* short day date (13, 26, or 54 */
Rep /* Plant replicate 1'/
Numdate /* Days after transplant */
Starth /* Start height at transplant (mm)*/
RawHt '/* Height data (m) */
DaysVB; /* Days after transplant when visible bud occurred */
MISSING M; /* Missing data are indicated by the value M */
RUN;

/* Sort data by days after short day treatment and days after transplant"
PROC SORT DATA=Paul.S94A;

BY SD NumDate;
RUN;

/* Start non-linear regression, with a maximum 300 iterations*/

PROC NLIN DATA=Paul.SQ4A MaxIter = 300;
TITLE] 'Exponential Vegetative phase Ht=Alpha+EXP(Beta*t)-l';
TITLE2 'Linear intermediate phase Ht=tLAGTl+Gamma"‘t';
TITLE3 'Monomolecular Reproductive Phase
Ht=Delta*(l-EXP(-KPLA*t))';

RUN;

170

l‘Parameters to be estimated along with starting values for iterative regression:
Beta is rate parameter during lag phase, Gamma is gradient during linear phase,
VBPLA is the time from visible bud to T2, and Delta is the height remaining at the
beginning of the plateau phase at time T2 1'/
PARMS

Beta = 0.1

Gamma = 2.5

VBPLA= 15

Delta = 20;

Alpha = Starth; *assign the height at transplant to Alpha;

T1 = (LOG(Gamma)-LOG(Beta))/Beta; *Calculate T1;

fl..AGT1 = Alpha-1+EXP(Beta*T1); *Calculate height at T1;

T2 = DaysVB+VBPLA; *Calculate T2 as VBPLA days alter visible bud;
fl.INT2 = (fl.AGTl + Gamma*(T2-Tl)); ‘Calculate height at T2;
KPLA = Gamma/Delta; *Calculate rate parameter for plateau phase;

IF (Numdate <= Tl) then DO;
F = Alpha-1+EXP(Beta*NumDate); ‘fLAG;
END;
ELSE DO;
IF (NumDate > T1) and (Numdate < T2) then DO;
F = fLAGTl+Gamma*(NumDate—Tl); I”LIN;
END;
ELSE DO;
F = fl.INT2 + Delta*(1-EXP(-kPLA*(Numdate-T2))); *tPLA;
END;
END;
MODEL RawHt = F; *Model statement: observed height = model;
OUTPUT OUT=B P = Yhat R '= Resid;
*Output model predictions (YHAT) and residual (RESID)

PROC PLOT;

RUN;

/" Plot the observed and predicted data on a graph */

PLOT YHAT "' NumDate = 'p' RawHt "‘ NumDate = 'a' / OVERLAY;
/*Plot the residuals on a graph*/

PLOT Resid * YHat / VREF = 0;

171

APPENDIX B. SAS program for estimating the g(t) filnction by chlormequat
concentration.

/" GROWTHRI .SAS
Paul Fisher, March 15 1995
3-phase Exponential, linear and monomolecular model.
Calculation of dose response by concentration treatment, fi'om Chlormequat dose
response experiment 1994.
Annette Hegg Dark Red single stem data. ”

OPTIONS PAGESIZE=6O LS=79 ERRORS=3;
LIBNAME PAUL ”;
FILENAME IN] 'GRET94B.PRN‘;
DATA PAUL.S94A;
INFILE IN 1;
INPUT
Numdate /*Days after transplant”
Concentr /*Chlormequat concentration”

Rep /*Plant replicate (Five plants per treatment)”
RawHt I'Obscrved plant height”
Starth /*Height at transplant”
DaysVB; /*Days after transplant when visible bud occurred”
MISSING M; /*Missing data assigned the value 'M' in the data file”
DHt = RawHt-Starth; /*Elongation that occurs after transplant”
RUN;
DATA Lim;
SET Paul.S94A;
- IF (Concentr >0) THEN OUTPUT; /*Do not output the control data”
RUN;

/"‘ Sort data set by concentration, replicate, and days alter transplant”
PROC SORT DATA=Lim;

BY Concentr Rep NumDate;
RUN;

/*Begin a macro that is run for first for the exponential g(t) model, then the linear g(t)
model”
%MACRO Mrfiitg(gsel);

/*goft will hold the relevant exponential or linear g(t) equation”
%LET gofi="lNITIALLY BLANK big enough to hold complete equation";

/*Begin the non-linear regression, with a maximum of 300 iterations to attempt to fit the

g(t)”

172

PROC NLIN DATA=Lim MAXITER = 300;

BY Concentr; /*Analyzed concentrations separately. ”

%IF &gsel=1 %THEN %DO; l‘gsel is a parameter passed to the Mrfitg macro”
PARMS Recovery = 10; /*Estimate the recovery variable”
BOUNDS Recovery >= 0; /*Recovery variable estimate must be >= 0”
AmpExp = 0.53; l‘dose response amplitude set to 0.53 ”
%LET gofi = 1- (1 -AmpExp)*EXP(-(1/Recovery)*(T-TCV)); /*g(t)
equation”

%END;

%IF &gsel=2 %THEN %DO; /"'same as above, only activated if gsel = 2 for linear
g(t)”

PARMS Persis = 15;

BOUNDS Persis >= 0;

AmpLin = 0.53;

%LET goft = MIN( Amplin+ ((1-AmpLin)/Persis)"‘(T-Tev), 1);
%END;

%LET Ttl=TITLE2 "G(T)= &goft";
&Ttl; /"'Display relevant title (exponential or linear g(t))”

NumObs = 51; /"‘There are 51 observations per plant”

/" Do the following only when new plant rep is found in the data file (i.e. once
every 51 observations)”

IF ABS(( LOBS_ -1)/NumObs) - INT( (_OBS_-l) /NumObs)) < 0.001 THEN
DO;

ARRAY Ht{ 140}; /* Create height array”

RETAIN Ht 0; I“ Do not recalculate height each time”

TMax=130; I‘Maximum days to iterate = 130”

NrInc=2; l“ Two Increments per day”

dT=1/NrInc; /* Time step”

Fuzz=dT/ 100; /" Near zero value to check correct day”

Alpha = 0; /*Start predicted height at zero mm”

/*Untreated 3-phase plant parameters previously estimated from a difl‘erent

SAS program”
Gamma = 5.36095;
Reprod = 15.448;

Delta = 62.857;

173

/“'Beta estimated by treatment from another SAS program to account for
difi'erences in initial elongation between treatments”

ifConcentr = 500 then beta = 0.1412; ifConcentr = 1000 then beta =
0. 1562;

ifConcentr = 1500 then beta = 0.1643; ifConcentr = 2000 then beta =
0. 1554;

if Concentr = 3000 then beta = 0.1763; if Concentr = 4000 then beta =
0. 1 533;

T1 = (LOG(Gamma)-LOG(Beta))/Beta;
fl.AGTl = Alpha-1+EXP(Beta*Tl);

T2 = DaysVB+Reprod;

fLINT2 = (fLAGTl + Gamma"(T2-Tl));
KPLA = Gamma/Delta;

Tev = 34; /*time of spraying”
ITev = Tev-+1;

/* Initialize the array with values from the 3-phase function fit to control
plants up to the spray event at Tev, using the function.”

DO IT=1 to ITev;
/*T is the time variable. Results of the firnction are put into the Ht
array. ”
=IT-1;
IF (T <= T1) THEN DO;
Ht{IT} = Alpha-1+EXP(Beta*T);
END;
ELSE DO;
IF (T > T1) and (T < T2) then DO;
Ht{IT} = tLAGTl+Gamma*(T-Tl);
END;
ELSE DO;
Ht{IT} = tLINT 2 + Delta*( 1-EXP(-Kpla*(T -T2)));
END;
END;
END;

/*Htmp is a temporary variable, initialized here to be height at Tev”
Htmp=Ht{ITev};
=Tev;

/* Estimate plant height from Tev onward, using the difl‘erential equation
and goft ”
DO While(T <T max);

END;
END'

174

g1T=&goft; /"'g(t) firnction is inserted here by the & statement ”
/*First derivatives follow”
[F (T <= Tl) then DO;

deT = Beta‘EXP(Beta‘T);
END;
ELSE DO;

IF(T>T1) and(T<T2)thenDO;

deT = Gamma;

END;

ELSE DO;
.deT = Kpla’Delta‘EXP(-Kpla*(T-T2));
END; ‘
END; *
dH=ng I’deT *dT; /"'Calculate increment in height”
Htmp=Htmp+DH; I‘Add increment in height to cumulative height
”
T=T+dT; /*Increment time by time step”
/*If current time is a complete day, add a height to the array ”
IF ABS(Round(T, l)«T)<Fuzz THEN Ht{RoundCT, l)+1 }=Htmp;

Model DHt = (Ht{NumDate+l }); /*Model statement: observed elongation equals

height array
RUN'

*/

%MEND; /"‘End macro.”

%MRFfitg(l); I‘Run macro for exponential g(t) model”
%MRFfitg(2); /*Run macro for linear g(t) model”

nICHIGAN STATE UNIV. LIBRRRIES
WI"1|”111111111111111|”lil/11111111111111
31293014172203