Mathematical Model of Flower Stalk Development in Chinese Cabbage in Relation to High Temperature Effect Combined with Low Temperature Effect

Abstract

The mathematical model of flower stalk development in Chinese cabbage was developed in relation to high temperature effect combined with low temperature effect. Fifteen days old seedlings treated with 5°C for 10 days under artificial light and day length of 8 hours, were treated again with 25, 30 and 35°C for durations of 5 and 10 days under continuous lighting. After the treatments, plants were grown under 20°C and continuous lighting. The pattern of flower stalk development was fitted in time course to the logistic curve and was approximated to the first order lag curve which was used as the model.The rise of flower stalk development in the treatments with higher temperatures of 25, 30 and 35°C after the low temperature treatment was delayed much more as compared with that under 20°C (untreatment with higher temperatures) after the low temperature treatment, but the difference in rise was observed scarcely among degrees of the higher temperatures. Thus, it could be conceivable that temperatures higher than at least 25°C decreased the low temperature effect on the rise of flower stalk development. For determining the time of delay in its rise, sum of the time constant and the dead time was used as a parameter. So, log10 ΔT1/2⋅td2 obtained in previous paper to evaluate the low temperature effect on the time of delay was compensated by high temperatures of 25 to 35°C after the low temperature treatment, as denoted by log10 HΔT1/2⋅td2 on the time of delay, where ΔT, td and H are a degree of the subtraction of treating low temperature from untreating temperature (20°C), treating duration with low temperature and the function of treating duration with higher temperatures, respectively. That is, the log10HΔT1/2⋅td2 was used as a parameter evaluating the high temperature effect combined with the low temperature effect. Thus, the effect of low temperature on flower stalk development was decreased multiplicatively by higher temperatures after the low temperature treatment as expressed by the parameter (H) evaluating the effect of higher temperatures, which exists within the range of 0 to 1.0.