A Descriptive Model of the Growth of Cucumber Fruit under Salinity at Low Oxygen Supply Levels in the Nutrient Solution

Abstract

In order to provide further information on the relationship between the occurrence of“sakibosori” fruit disorder and the fruit growth activity, a descriptive model of the growth of cucumber fruit under increasing levels of salinity at low oxygen supply levels in the nutrient solution was developed. Assumptions of the model were as follows : (i) the upper limit of the growth rate in volume of a fruit (GR_max) is determined by the following equation : GR_max=A/ (1+exp (B (x-C+De) ) ) +E, where A, B, C, D and E are constants, x is NaCl concentration (mM) and e is a standard Gaussian noise with mean 0 and variance 1; (ii) a fruit grows exponentially until its growth rate reaches GR_max, thereafter linearly. The model reproduced fairly well the all-or-none probabilistic patterns of the response of the relative growth rate of fruits to salinity at low oxygen supply levels in the nutrient solution in spring culture, which had been measured in earlier experiments. It was also suggested that there can be a seasonal difference in the parameters of above equation.