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 reacti on norms allowing for S=spatial and/or temporal variation in the environmen ts 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 g enetic variances in height and slope of a linear reaction norm, and their c ovariance, are predicted to decrease with the variation in the environment. Non-pleiotropic loci influencing either height or slope are expected to de crease the genetic variance in slope relative to that in height. Decrease i n the ratio of genetic variance in slope to genetic variance in height with increasing variation in the environment presents a test for the presence o f loci that only influence the slope, and not the height. We use data on Dr osophila to test the theory. In seven of eight pair-wise comparisons geneti c 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 predict ions.