Analyzing Genotype-Environment Data by Mixed Models with Multiplicative Terms

where Yij mean yield of ith genotype in jth environment, , = general mean, gi = effect of ith genotype, ej = effect of jth environment, (ge)ij = interaction of ith genotype and jth environment, Eij random error associated with means Yij, assumed to be distributed as N(O, ac2). This model is appropriate for the analysis of means from equally replicated data with homoscedastic errors. In an analysis of G x E data, it may be useful to fit a more specific model describing the interaction. The most common of such models is the regression model first suggested by Yates and Cochran (1938), which was further elaborated by Finlay and Wilkinson (1963) and Eberhart and Russell (1966). It may be written as