Fitting A Regression Model for Genotype‐By‐Environment Data on Heading Dates in Grasses by Methods for Nonlinear Mixed Models

Abstract

Summary. The analysis of agricultural crop variety trials is usually complicated by the presence of genotype‐by‐environment interaction. A number of methods and models have been proposed to tackle this problem. One of the most common methods is the regression approach due to Yates and Cochran (1938, Journal of Agricultural Science28, 556–580), in which performances of genotypes in the environments are regressed onto environmental means. The underlying regression model contains a multiplicative term with two unknown parameters (one for genotypes and one for environments). In the present paper, the model is modified by exchanging the role of genotypes and environments. Various diagnostic plots show that this modified model is adequate for a data set on heading dates in the grass species Dactylis glomerata. If environments are considered as a random factor while genotypes are taken as fixed, the model falls into the class of nonlinear mixed models. Recently, a number of procedures have been suggested for this class of models, which are based on first‐order Taylor series expansion. Alternatively, the model can be estimated by maximum likelihood. This paper discusses the application of these methods for estimating parameters of the model.