Selection and phenotypic plasticity in evolutionary biology and animal breeding

This paper reviews models for phenotypic plasticity in evolutionary genetics and animal breeding and shows how those models are connected. Environmental differences often lead to systematic phenotypic differences: phenotypic plasticity. Genetic differences in phenotypic plasticity among individuals or populations surface as genotype-by-environment interaction in the analysis of data. The presence of a genotype-by-environment interaction variance indicates the possibility to select on the sensitivity of a genotype to environmental differences. All models of selection on quantitative traits in evolutionary biology use the general description of selection by the covariance between phenotype and fitness. In this approach, the vector of selection responses equals the genetic variance covariance matrix times the selection gradient vector-the vector of partial regression of mean fitness on mean phenotype. Models of selection on phenotypically plastic traits are special cases of the general model of simultaneous selection on a set of quantitative traits. Several variants of models of selection on phenotypic plasticity exist in evolutionary biology: the character state model, the infinite-dimensional model and the reaction norm model, corresponding to the multitrait model, the covariance function model and the random regression model in animal breeding. Index selection directly connects to the selection gradient model. The selection gradient vector directly connects to the vector of weights b and the selection intensity . The selection gradient approach allows the construction of a selection index in a very general way, including separate selection on overall performance and on sensitivity to the environment. In animal breeding, models of phenotypic plasticity may be an aid to select for robust animals, or to optimise breeding programs that develop stock for multiple environments