Theory of estimation of parameters and genetic values under mixed models

Abstract

In animal breeding, it is essential to know genetic parameters such as heritability, with the aim of being able to predict genetic values (GV) and efficiently direct selection programs. A mixed model refers to those cases where the researcher considers fixed and random factors in a statistical model. Models widely used in the area of animal genetic improvement are the reproductive model and the animal model, which consider the reproductive or animal factor as random and a group of non-genetic effects as fixed. These mixed models allow us to obtain both heritability values (h2) for a trait, as well as genetic predictions such as the expected progeny difference (EPDs) or the predicted transmission ability (PTA) for each animal. An example of birth weight (BW) in cattle was used to calculate the VG, h2 and e2 using a mixed model, with a fixed and a random factor. The ANOVA, ML and REML methods were used to calculate h2, e2 and the VG first using all the information and subsequently assuming the last lost data, under a reproductive model and an animal model. The results found using the 3 methods were the same for REML and ANOVA in balanced data and different for the 3 methods in unbalanced data, where in the unbalanced case the ANOVA estimated a negative variance component, therefore, it can be concluded that estimate genetic values and parameters using ANOVA, ML and REML, but with the risk of estimating negative variance components using ANOVA or null (or overestimated) heritabilities with likelihood-based methods when the data structure or model is not the same correct.