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Keywords:

  • Phenotypic plasticity;
  • environmental dependence;
  • genetic (co)variance;
  • pleiotropy;
  • developmental constraint

Abstract

A model of the quantitative genetics of phenotypically plastic characters is developed. When genotype-environment interaction is present, and the allelic effects contributing to any two traits are linear functions of the environment, the additive genetic variances of, and additive genetic covariance between, traits become quadratic functions of the environmental variable. The additive genetic covariance will in general change sign over some range of the environmental variable. The conditions of the mathematically special case, where additive genetic covariance has the same sign in all environments, imply structure in the pleiotropic effects of any alleles, i.e. developmental constraints can prevent additive genetic covariance changing sign. Mathematical independence of polygenic effects between traits represents in this model a lack of developmental constraints and leads to sign change in the additive genetic covariance over environments.