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

Evolution. 2004 Aug;58(8):1639-54. doi: 10.1111/j.0014-3820.2004.tb00450.x.


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.

Publication types

  • Comparative Study
  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.
  • Research Support, U.S. Gov't, P.H.S.

MeSH terms

  • Adaptation, Biological*
  • Analysis of Variance
  • Biological Evolution*
  • Computer Simulation
  • Genetics, Population*
  • Models, Genetic*
  • Mutation / genetics
  • Phylogeny
  • Population Density
  • Quantitative Trait, Heritable*
  • Selection, Genetic
  • Stochastic Processes