Evolution and stability of the G-matrix on a landscape with a moving optimum

In quantitative genetics, the genetic architecture of traits, described in terms of variances and covariances, plays a major role in determining the trajectory of evolutionary change. Hence, the genetic variance-covariance matrix (G-matrix) is a critical component of modern quantitative genetics theory. Considerable debate has surrounded the issue of G-matrix constancy because unstable G-matrices provide major difficulties for evolutionary inference. Empirical studies and analytical theory have not resolved the debate. Here we present the results of stochastic models of G-matrix evolution in a population responding to an adaptive landscape with an optimum that moves at a constant rate. This study builds on the previous results of stochastic simulations of G-matrix stability under stabilizing selection arising from a stationary optimum. The addition of a moving optimum leads to several important new insights. First, evolution along genetic lines of least resistance increases stability of the orientation of the G-matrix relative to stabilizing selection alone. Evolution across genetic lines of least resistance decreases G-matrix stability. Second, evolution in response to a continuously changing optimum can produce persistent maladaptation for a correlated trait, even if its optimum does not change. Third, the retrospective analysis of selection performs very well when the mean G-matrix (G) is known with certainty, indicating that covariance between G and the directional selection gradient beta is usually small enough in magnitude that it introduces only a small bias in estimates of the net selection gradient. Our results also show, however, that the contemporary G-matrix only serves as a rough guide to G. The most promising approach for the estimation of G is probably through comparative phylogenetic analysis. Overall, our results show that directional selection actually can increase stability of the G-matrix and that retrospective analysis of selection is inherently feasible. One major remaining challenge is to gain a sufficient understanding of the G-matrix to allow the confident estimation of G.