Effects of migration on the genetic covariance matrix.

In 1996, Schluter showed that the direction of morphological divergence of closely related species is biased toward the line of least genetic resistance, represented by g(max), the leading eigenvector of the matrix of genetic variance-covariance (the G-matrix). G is used to predict the direction of evolutionary change in natural populations. However, this usage requires that G is sufficiently constant over time to have enough predictive significance. Here, we explore the alternative explanation that G can evolve due to gene flow to conform to the direction of divergence between incipient species. We use computer simulations in a mainland-island migration model with stabilizing selection on two quantitative traits. We show that a high level of gene flow from a mainland population is required to significantly affect the orientation of the G-matrix in an island population. The changes caused by the introgression of the mainland alleles into the island population affect all aspects of the shape of G (size, eccentricity, and orientation) and lead to the alignment of g(max) with the line of divergence between the two populations' phenotypic optima. Those changes decrease with increased correlation in mutational effects and with a correlated selection. Our results suggest that high migration rates, such as those often seen at the intraspecific level, will substantially affect the shape and orientation of G, whereas low migration (e.g., at the interspecific level) is unlikely to substantially affect the evolution of G.