Prediction of breeding values and selection responses with genetic heterogeneity of environmental variance

Abstract

There is empirical evidence that genotypes differ not only in mean, but also in environmental variance of the traits they affect. Genetic heterogeneity of environmental variance may indicate genetic differences in environmental sensitivity. The aim of this study was to develop a general framework for prediction of breeding values and selection responses in mean and environmental variance with genetic heterogeneity of environmental variance. Both means and environmental variances were treated as heritable traits. Breeding values and selection responses were predicted with little bias using linear, quadratic, and cubic regression on individual phenotype or using linear regression on the mean and within-family variance of a group of relatives. A measure of heritability was proposed for environmental variance to standardize results in the literature and to facilitate comparisons to "conventional" traits. Genetic heterogeneity of environmental variance can be considered as a trait with a low heritability. Although a large amount of information is necessary to accurately estimate breeding values for environmental variance, response in environmental variance can be substantial, even with mass selection. The methods developed allow use of the well-known selection index framework to evaluate breeding strategies and effects of natural selection that simultaneously change the mean and the variance.

Figure 1.—

Expected (A) and (B) as a function of P and P², respectively (; ; ; ; ).

Figure 2.—

Expected (MC) and predicted breeding values (A) and (B) based on a single phenotype as a function of phenotype using the full model with multiple regression on P, P², and P³ (MR3) or the reduced model with multiple regression on P and P² (MR2) (; ; ; ; ).

Figure 3.—

Expected (MC) and predicted as a function of the standardized mean phenotype of half-sib progeny (A) and expected and predicted as a function of (B) using either (MR linear) or (MR log) in multiple regression (; ; ; ; ; number of half-sib progeny/sire = 100).