GENETIC-VARIATION OF TRAITS MEASURED IN SEVERAL ENVIRONMENTS .1. ESTIMATION AND TESTING OF HOMOGENEOUS GENETIC AND INTRA-CLASS CORRELATIONSBETWEEN ENVIRONMENTS

Estimation of between family (or genotype) components of (co)variance among environments, testing of homogeneity of genetic correlations bet ween environments, and testing of homogeneity of both genetic and intr a-class correlations between environments are investigated. The testin g procedures are based on the ratio of maximized log-restricted likeli hoods for the reduced (under each hypothesis of homogeneity) and satur ated models, respectively. An expectation-maximization (EM) iterative algorithm is proposed for calculating restricted maximum likelihood (R EML) estimates of the residual and between-family components of (co)va riance. The EM formulae are applied to the multiple trait linear model for the saturated model and to the univariate linear model for the re duced models. The EM algorithm guarantees that (co)variance estimates remain within the parameter space. The procedures presented in this pa per are illustrated with the analysis of 5 vegetative and reproductive traits recorded in an experiment on 20 full-sib families of black med ic (Medicago lupulina L) tested in 3 environments.