Abstract
A mathematical model was presented to evaluate the efficiency of low temperature and photoperiod on flower stalk development in Chinese cabbage. Flower stalk development was found in plants treated with low temperature and longer day length and not observed in any plants untreated with low temperature. The pattern of flower stalk development was fitted to the logistic curve on time after the low temperature treatment. This curve of higher order lag can be estimated by using the asymptote and time of delay in its rise. The equation of asymptote was given by the function of treating duration with low temperature and day length after low temperature treatment. In order to evaluate the delay, equation of the logistic curve was approximated to that of the first order lag having the same asymptote and the same differential coefficient at 63.20 (1-1/e, e is napier's number) of asymptote as those of the logistic curve. The sum of the time constant and dead time of the first order lag curve was used to estimate the time of delay in rise of flower stalk development. The time of delay was given by the function of treating temperature, treating duration with low temperature and day length. Thus, the mathematical model of flower stalk development was represented by an equation of the first order lag as a function of treating parameters of low temperature and photoperiod. From this model, it became clear that log10 PΔT1/2td2 is useful as a treating parameter for evaluating the combined effect of the temperature and photoperiod on plant response to those factors, where P, ΔT and td are the function of day length, a degree of the subtraction of treating temperature from untreating temperature of 20°C and treating duration with low temperature, respectively.
