RESTRICTED MAXIMUM LIKELIHOOD ESTIMATION OF VARIANCE AND COVARIANCE COMPONENTS OF MULTIPLE TRAITS UNDER DESIGNS I AND II OF NORTH CAROLINA

Abstract

A method for estimating variance and covariance components by restricted maximum likelihood (REML) under Designs I and II of North Carolina when two or more variables are observed on each experimental unit, is described in this study. Even though REML requires a large amount of computational resources, it can be implemented given the current availability in modern equipments. REML is based on the mixed models development for multiple trait situations for both mating designs, considering the same matrix design for all traits and balanced data. In addition to the restricted maximum likelihood equations and the variance-covariance matrices, the REML estimators of the phenotypic and genotypic correlations, and their approximated variances by the Delta method are developed. The models described in this study are part of the theoretical basis for the multiple trait REML estimation in plant breeding.