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Tomasz Anisko, Cynthia L. Haynes and Orville M. Lindstrom

Freeze tests were performed on stem sections of Fraxinus americana, Lagerstroemia indica Magnolia gradiflora, Rhododendron `Red Ruffle', Zelkova serrata, and leaves of Magnolia grandiflora and Rhododendron `Red Ruffle' in the tinter and summer of 1993. Freeze injury was quantified using electrolyte and phenolic leakage techniques and compared to the lethal temperature range determined by visual method assisted by differential thermal analysis. Richards function was fitted to the electrolyte and phenolic leakage data by the modified Gauss-Newton method. The inflection point of the Richards function coincided with the lethal injury range for non-acclimated leaves, but overestimated the freeze tolerance for acclimated leaves and for both acclimated and non-acclimated stems. A proposed interception point of the lower asymptote and a line tangential to the curve inflection point provided an improved estimate of the lethal injury range in most of the species.

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Chon C. Lim, Rajeev Arora and Edwin C. Townsend

Seasonal patterns in freezing tolerance of five Rhododendron cultivars that vary in feezing tolerance were estimated. Electrolyte leakage was used, and raw leakage data were transformed to percent leakage, percent injury, and percent adjusted injury. These data were compared with visual estimates of injury. Percent adjusted injury was highly correlated (0.753) to visual estimates. Two asymmetric sigmoid functions—Richards and Gompertz—were fitted to the seasonal percent adjusted injury data for all cultivars. Two quantitative measures of leaf freezing tolerance—Lt50 and Tmax (temperature at maximum rate of injury)—were estimated from the fitted sigmoidal curves. When compared to the General Linear Model, the Gompertz function had a better fit (lower mean error sum of squares) than Richards function. Correlation analysis of all freezing tolerance estimates made by Gompertz and Richards functions with visual LT50 revealed similar closeness (0.77 to 0.79). However, the Gompertz function and Tmax were selected as the criteria for comparing relative freezing tolerance among cultivars due to the better data fitting of Gompertz function (than Richards) and more descriptive physiological representation of Tmax (than LT50). Based on the Tmax (°C) values at maximum cold acclimation of respective cultivars, we ranked `Autumn Gold' and `Grumpy Yellow' in the relatively tender group, `Vulcan's Flame' in intermediate group, and `Chionoides' and `Roseum Elegans' in the hardy group. These relative rankings are consistent with midwinter bud hardiness values reported by nurseries.

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Douglas A. Hopper

Height data were collected three times weekly between pinch and flowering to represent `Royalty' rose (Rosa hybrida L.) response to 15 unique treatment combinations of irradiation as photosynthetic photon flux (PPF: 50 to 300 μmol·m-2·s-1), day temperature (DT: 12 to 22 °C), and night temperature (NT: 15 to 25 °C) under constant growth chamber conditions. Combinations were determined according to the rotatable central composite design. A previous full quadratic model approach was compared with a revised approach using a nonlinear Richards function derivative form. This allowed a dynamic change of parameter values for each daily growth iteration by computer. The Richards function assumes nonconstant daily growth rates are proportional to current size; Euler integration enabled additive accumulation of these values. Ratios of the growth constant (k) to the theoretical catabolic constant (m = v+1) caused flexible changes in the growth curve, which were compared with the previous quadratic approach.

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A. Maaike Wubs, Yun T. Ma, Ep Heuvelink, Lia Hemerik and Leo F.M. Marcelis

follows a sigmoid growth curve ( Adams et al., 2001 ; Marcelis and Baan Hofman-Eijer, 1995 ). The logistic, Gompertz, and Richards functions are often used to describe fruit growth over time ( Adams et al., 2001 ; Barrera et al., 2008 ; Cuevas et al

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Robert D. Berghage and Royal D. Heins

Elongation characteristics of each internode on a lateral shoot of poinsettia (Euphorbia pulcherrima Klotz) `Annette Hegg Dark Red' were determined from pinching through anthesis for plants grown with 36 day/night temperature (DT/NT) combinations between 16 and 30C. The Richards function was used to describe the elongation of each internode. The first internode developing on a lateral shoot was longer and matured faster than subsequent internodes. The length of the first internode was a function of the difference between day and night temperatures (DIF = DT - NT). Subsequent internodes elongated uniformly in the absence of flower initiation. In the absence of flower initiation, the length of an internode, after the first, was a function of DIF. Internodes were shorter as proximity to the inflorescence increased. Internode length after the start of short days was a function of DIF and the visible bud index where visible bud index = [(days from pinching to the day an internode began to elongate - days from pinching to the day of the start of flower initiation)/the number of days from pinching to visible bud]. A poinsettia lateral shoot elongation model was developed based on the derived functions for internode elongation. The model predicted lateral shoot length within one standard deviation of the mean for plants grown in a separate validation study with 16 combinations of DT/NT. The model allows the prediction of lateral shoot length on any day from pinching through anthesis based on temperature, the number of nodes on the lateral shoot, the time each internode on the lateral shoot began elongating, and the visible bud index at the start of elongation of each node.

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K.G.V. Davidson, F.D. Moore III, E.E. Roos, S. Nath and S. Sowa

Five seed-quality indices based on individual seed electrolyte leakage tests were evaluated. Zea mays L. seeds were soaked for 6 hours, and individual seed leachate conductivity values were obtained. A total of 100 cells were scanned, one seed per cell, at 5-minute intervals for the first 30 minutes, followed by 15-minute intervals for the remaining 330 minutes. Seeds were allowed to dry for 5 to 7 days at room temperature and then were tested for germinability at 25C for 7 days. Radicle lengths were measured after 72 hours. The Richards function was fitted to cumulative frequency distributions of μAmps to obtain internal slope (IS), mean μAmp, and median μAmp values for each scan. Initial leach rate (ILR) was estimated after fitting hyperbolic functions to μAmp vs. soak time data. Average leach rate (ALR) was also derived from fitting the Richards function to μAmp vs. soak time data. Linear regression of seed quality on IS, mean, and median μAmp values after 5 hours of imbibition yielded r2 values of 0.91, 0.81, and 0.86 for predicting viability and 0.56, 0.46, 0.52 for predicting radicle length. Thus, IS was the best seed quality predictor, followed closely by median and mean μAmp values. ILR and ALR were not correlated with seed quality.

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J.G. Carew, K. Mahmood, J. Darby, P. Hadley and N.H. Battey

The effects of temperature, photosynthetic photon flux density (PPFD) and photoperiod on vegetative growth and flowering of the raspberry (Rubus idaeus L.) `Autumn Bliss' were investigated. Increased temperature resulted in an increased rate of vegetative growth and a greater rate of progress to flowering. Optimum temperatures lay in the low to mid 20°C range. Above this the rate of plant development declined. Increased PPFD also advanced flowering. While photoperiod did not significantly affect the rate of vegetative growth, flowering occurred earliest at intermediate photoperiods and was delayed by extreme photoperiods. These responses suggest that there is potential for adjusting cropping times of raspberry grown under protection by manipulating the environment, especially temperature.

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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.

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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.

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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.