Maintenance of genetic variation in phenotypic plasticity: the role of environmental variation

We study genetic variation in phenotypic plasticity maintained by a balance between mutation and weak stabilizing selection. We consider lineal reaction norms allowing for S=spatial and/or temporal variation in the environments of development and selection. We show that the overall genetic variation maintained does not depend on M:whether the trait is plastic or not. The genetic variances in height and slope of a linear reaction norm, and their covariance, are predicted to decrease with the variation in the environment. Non-pleiotropic loci influencing either height or slope are expected to decrease the genetic variance in slope relative to that in height. Decrease in the ratio of genetic variance in slope to genetic variance in height with increasing variation in the environment presents a test for the presence of loci that only influence the slope, and not the height. We use data on Drosophila to test the theory. In seven of eight pair-wise comparisons genetic variation in reaction norm is higher in a less variable environment than in a more variable environment, which is in accord with the model's predictions.