Timing of Easter lily (Lilium longiflorum Thunb.) for sales is complex because the date of Easter and the number of leaves formed on plants before flower bud initiation vary from year to year. A process control chart was developed that uses a leaf unfolding rate model of Easter lily to control development rate towards flowering. The technique allows observed and target leaf count to be tracked on a graph and compared visually over time. The optimum leaf unfolding rate and average temperature can be read directly from the chart without the need for mathematical calculation. The approach provides an intuitive method for transferring quantitative models to growers and can be applied to other management problem areas.
P.R. Fisher and R.D. Heins
P.R. Fisher and R.D. Heins
A graphical control chart was developed to monitor leaf count of Easter lily (Lilium longiflorum Thunb.) and make temperature recommendations based on predictions of a leaf unfolding rate (LUR) model. The graph allows observed and target leaf count to be compared visually over time. Timing of the visible bud stage, when flower buds are visible externally on the plant, is important to time flowering for the Easter sales period. The optimum LUR and average daily temperature required to achieve a target visible bud date can be read directly from the chart. The approach provides an intuitive method for transferring quantitative models to growers.
Paul R. Fisher and Royal D. Heins
A methodology based on process-control approaches used in industrial production is introduced to control the height of poinsettia (Euphorbia pulcherrima L.). Graphical control charts of actual vs. 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 stemelongation 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.
J.H. Lieth, P.R. Fisher, and R.D. Heins
A growth function was developed for describing the progression of shoot elongation over time. While existing functions, such as the logistic function or Richards function, can be fitted to most sigmoid data, we observed situations where distinct lag, linear, and saturation phases were observed but not well represented by these traditional functions. A function was developed that explicitly models three phases of growth as a curvilinear (exponential) phase, followed by a linear phase, and terminating in a saturation phase. This function was found to be as flexible as the Richards function and can be used for virtually any sigmoid data. The model behavior was an improvement over the Richards function in cases where distinct transitions between the three growth phases are evident. The model also lends itself well to simulation of growth using the differential equation approximation for the function.
P.R. Fisher, J.H. Lieth, and R.D. Heins
Stem elongation of commercially produced flowering poinsettia (Euphorbia pulcherrima L.) is often sigmoid. However, sigmoid mathematical functions traditionally used for representing plant growth fail to adequately describe poinsettia stem elongation when a shoot has a long vegetative growth period. A model was developed that explicitly described three phases of poinsettia stem elongation: 1) the initial lag phase, where stem length increases approximately exponentially; 2) a period when elongation is linear; and 3) a plateau phase, where elongation rate declines to zero and stem length reaches an asymptotic maximum length. The timing of the plateau phase was linked to flower initiation date. Fit of the resulting model to data from single stem `Freedom' poinsettia grown with different periods between transplant and flower initiation had an R2 of 0.99. Model parameters had clear biological meaning, and the poinsettia model has horticultural application for simulation and graphical tracking of crop height.
P.R. Fisher, J.H. Lieth, and R.D. Heins
A model was developed to quantify the response of Easter lily (`Nellie White') flower bud elongation to average air temperature. Plants were grown in greenhouses set at 15, 18, 21, 24, or 27C after they had reached the visible bud stage. An exponential model fit the data with an R 2 of 0.996. The number of days until open flowering could be predicted using the model because buds consistently opened when they were 16 cm long. The model was validated against data sets of plants grown under constant and varying greenhouse temperatures at three locations, and it was more accurate and mathematically simpler than a previous bud elongation model. Bud length can be used by lily growers to predict the average temperature required to achieve a target flowering date, or the flowering date at a given average temperature. The model can be implemented in a computer decision-support system or in a tool termed a bud development meter.
P.R. Fisher, J.H. Lieth, and R.D. Heins
The objective was to predict the distribution (mean and variance) of flower opening for an Easter lily (Lilium longiflorum Thunb.) population based on the variability in an earlier phenological stage and the expected average temperature from that state until flowering. The thermal time from the visible bud stage until anthesis was calculated using published data. `Nellie White' grade 8/9 Easter lilies were grown in five research and commercial greenhouse locations during 1995, 1996, and 1997 under a variety of temperature and bulb-cooling regimes. Distributions of visible bud and anthesis were normally distributed for a population growing in a greenhouse with spatially homogenous temperatures. The variance at anthesis was positively correlated with variance at visible bud. The mean and variance at visible bud could therefore be used to predict the distribution of the occurrence of anthesis in the crop. The relationship between bud elongation, harvest, and temperature was also incorporated into the model. After visible bud, flower bud length measurements from a random sample of plants could be used to predict the harvest distribution. A computer decision-support system was developed to package the model for grower use.
P.R. Fisher, R.D. Heins, and J.H. Lieth
Stem elongation response to a single foliar application of the growth retardant chlormequat chloride [(2-chloroethyl) trimethylammonium chloride] for poinsettia (Euphorbia pulcherrima Klotz.) was quantified. Growth retardant applications did not affect final leaf count or timing of visible bud, first bract color, or anthesis. There was a statistically significant effect of growth retardant concentration on stem elongation, with a range from 289 ± 15 mm (mean 95% confidence intervals) for the control plants to 236 ± 17 mm at 4000 ppm. The growth-retarding effect during the first day after the application was not significantly different between 500 and 4000 ppm, and concentration primarily affected the duration of growth-retarding activity. A dose response function was incorporated into a three-phase mathematical function of stem elongation of single-stem poinsettia to predict elongation of treated and untreated plants. The model was calibrated using a data set from plants receiving 0, 500, 1000, 1500, 2000, 3000, and 4000 ppm, with a resulting R 2 of 0.99. Validation of the dose response model against an independent data set resulted in an r 2 of 0.99, and predicted final stem length was within 12 mm of observed final length.
M.K. Hausbeck, C.T. Stephens, and R.D. Heins
Two fungicides registered for the control of Pythium spp. were evaluated for their effects on size and time to flowering of seed-propagated geraniums (Pelargonium × hortorum L.H. Bailey). Fungicide drenches of fenaminosulf and metalaxyl were applied to geraniums grown in soilless root medium: 1) at seeding (S); 2) at seeding and transplanting (ST); 3) at seeding, transplanting, and 1 week after transplanting (ST + 1); 4) at transplanting (T); and 5) 1 week after transplanting (T + 1). Metalaxyl drenching schedules did not significantly influence plant size or time to flowering. Fenaminosulf drenching schedules 3 and 4 significantly reduced plant size, and drenching schedule 3 significantly increased days to flowering in comparison to control plants. Although fenaminosulf is used infrequently because of limited availability, the detrimental effects of this fungicide on plant size and time to flowering warrant similar investigations with additional fungicides and crops. Chemical names used: sodium[4-(dimethylamino) phenyl]diazenesulfonate (fenaminosulf); N-(2,6-dimethylphenyl) -N-(methoxyacetyl) -dl-alanine methyl ester (metalaxyl).
Paul R. Fisher, Royal D. Heins, and J. Heinrich Lieth
Stem elongation of poinsettia (Euphorbia pulcherrima Klotz.) was quantified using an approach that explicitly modelled the three phases of a sigmoidal growth curve: 1) an initial lag phase characterized by an exponentially increasing stem length, 2) a phase in which elongation is nearly linear, and 3) a plateau phase in which elongation rate declines as stem length reaches an asymptotic maximum. For each growth phase, suitable mathematical functions were selected for smooth height and slope transitions between phases. The three growth phases were linked to developmental events, particularly flower initiation and the first observation of a visible flower bud. The model was fit to a data set of single-stemmed poinsettia grown with vegetative periods of 13, 26, or 54 days, resulting in excellent conformance (R 2 = 0.99). The model was validated against two independent data sets, and the elongation pattern was similar to that predicted by the model, particularly during the linear and plateau phases. The model was formulated to allow dynamic simulation or adaptation in a graphical control chart. Model parameters in the three-phase function have clear biological meaning. The function is particularly suited to situations in which identification of growth phases in relation to developmental and horticultural variables is an important objective. Further validation under a range of conditions is required before the model can be applied to horticultural situations.