Methodology for choosing a model for wheat kernel growth

A methodology for choosing a model describing the wheat kernel growth of 16 wheat cultivars, grown in nine environments, is presented. Indeed, it was a preliminary and essential step before comparing the cultivars for their rates and durations of grain filling. Four current growth functions, i.e. logistic with three parameters assuming that the lower asymptote equals 0, logistic with four parameters estimating the lower asymptote, Weibull and Gompertz functions, were compared. In a first step the parameters of the curve were estimated assuming that the variance of the observed kernel weight was constant. Examining the graphs of absolute values of standardized residuals against predicted values of kernel weight highlighted that the variance of errors in the regression model was not constant and suggested modelling the variance using a power function. In a second step, modelling of the variance was added to the model. The models were compared using the likelihood ratio tests, the graphs of residuals, Akaike's criterion and the biological meaning of the estimated final kernel weight. Significant likelihood ratio tests indicated that, for all functions except Weibull, the assumption of homogeneous variances had to be rejected; thus, it was necessary to model the variance. Comparisons of the four functions using Akaike's criterion led to keeping the logistic function with four parameters and modelling of the variance. Comparing the estimates of the final kernel weight (95 % of the upper asymptote) obtained with this model with observed kernel weights revealed that some of the estimates were not realistic from a biological point of view. Finally, we chose to model the kernel growth using the logistic curve with three parameters for modelling the growth curve and the power function for modelling the heterogeneity of variance. In addition, a modification of the sampling protocol is also presented. ((C) Inra/Elsevier, Paris.)