Calculation of Population Parameters using Richards Function and Application of Indices of Growth and Seed Vigor to Rice Plants
Yoshitaka Hara
The Richards function, an asymmetric growth function, was fitted to germination data for several rice varieties, and functional parameters were transformed into stable population parameters that comprehensively characterize germination (viability Vi, time Me, dispersion Qu and skewness Sk). For practical purposes, the population parameters calculated using a symmetric logistic function were similar to those calculated using the asymmetric Richards function for the germination of rice plants. The reproducibility of the calculated population parameters was so high that germination data can be measured at one-day intervals without replication. Therefore, population parameters can be applied as indices of the germination properties of a seed lot. Me was especially highly correlated with the establishment percentage, which indicates that it can be applied as a useful index of seed vigor. Although the emergence data could also be fitted to a logistic function, those for establishment should be fitted to the Richards function because the skewness becomes so large that population parameters can not be calculated exactly using logistic functions. Population parameters that show the properties of seedling growth are also available. For example, Qu of emergence shows the effect of seed soaking on the uniformity of emergence. In fields with fluctuating temperatures, the measured data fit better with the cumulative temperature than with time.
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