The quantitative genetic consequences of pleiotropy under stabilizing and directional selection.

The independence of two phenotypic characters affected by both pleiotropic and nonpleiotropic mutations is investigated using a generalization of M. Slatkin's stepwise mutation model of 1987. The model is used to determine whether predictions of either the multivariate normal model introduced in 1980 by R. Lande or the house-of-cards model introduced in 1985 by M. Turelli can be regarded as typical of models that are intermediate between them. We found that, under stabilizing selection, the variance of one character at equilibrium may depend on the strength of stabilizing selection on the other character (as in the house-of-cards model) or not (as in the multivariate normal model) depending on the types of mutations that can occur. Similarly, under directional selection, the genetic covariance between two characters may increase substantially (as in the house-of-cards model) or not (as in the multivariate normal model) depending on the kinds of mutations that are assumed to occur. Hence, even for the simple model we consider, neither the house-of-cards nor the multivariate normal model can be used to make predictions, making it unlikely that either could be used to draw general conclusions about more complex and realistic models.