Quantifying the genetic contribution to the variability of count traits

Abstract

Heritability is a important concept in animal and plant breeding, as it is in human biological applications. It is quantified based on fitting a model to hierarchical data. For data where linear models can be used, this attribute is conveniently defined as a ratio of variance components. Matters are less simple for non-Gaussian outcomes. The focus here is on count outcomes where extensions of the Poisson model are used to describe the data. Expressions for heritability of count traits are derived using the so-called Poisson combined model, which combines a Poisson outcome distribution with normal as well as gamma random effects, to capture both correlation among repeated observations as well as overdispersion, and admits closed-form expressions for the mean, variances and, hence, ratio of variances. It thus flexibly accommodates overdispersion and within-unit correlation. The proposed methodology is illustrated using maize data from a plant breeding program and compared with the usual, but questionable analysis using linear mixed models.