The stability of genetic variance-covariance matrix in the presence of selection.

Quantitative genetics provides one of the most important frameworks in which evolutionary biology and evolution can be studied. The primary goals of this field of study include the attempts to understand the history of selection that has resulted in the multiple phenotypic traits we observe today, and to predict the future trajectory of the multiple traits. Within quantitative genetics it is the genetic variance–covariance matrix G which summarizes the additive genetic variation of multiple traits and the genetic covariances between the traits, together with selection that control the direction and rate of evolution. The product of these two elements determine the response to selection from one generation to another (Lande, 1979). Mark Blows (Blows, 2007) discusses both of these elements and advocates their analysis in a truly multivariate fashion. Blows succeeds in providing a convincing overview of the benefits of analysing selection and genetic basis of traits in this fashion. In fact, it seems that regressing back to inspecting the selection coefficients and genetic variances in isolation from other correlated traits may largely be effort wasted. With an example from his own work Blows (2007) makes the point clear that with traditional methods one can observe selection and ample genetic variance for a trait, when in fact it may be that the genetic variance in the trait lies in a direction away from the direction of selection prohibiting any response to selection to take place. Therefore, with the traditional methods we may not be getting the correct picture of the evolution of the phenotypic traits. Nevertheless, if we aim at predicting further than a single generation changes in traits there is a point that should be considered: predicting the future or reconstructing the past evolution is dependent on the stability of the G-matrix. Is the G-matrix stable or does it evolve? Despite the methodological problems in comparing the G-matrices (Houle et al., 2002; Steppan et al., 2002; Mezey & Houle, 2003), the available evidence points to the direction that yes it does evolve, and the question now is how fast and in what manner (Steppan et al., 2002). One of the unresolved issues is how will selection affect the G-matrix. Perhaps the fact that under some circumstances directional selection may even promote the stability of the G-matrix (Jones et al., 2003, 2004), illustrates that our understanding of the evolution of the G-matrix is still far from perfect. Provided the G-matrix is stable, we may be able to predict evolution of multiple traits, but if the G-matrix is very unstable, understanding the evolution of traits over an evolutionary time may be unachievable. Regardless of the issue about the stability of the G-matrix, the application of the multivariate approaches discussed by Blows (this issue) can reveal intriguing insights, in particular, for students of sexual selection and those interested in the problem of lek paradox (Rowe & Houle, 1996; Kotiaho et al., 2001; Tomkins et al., 2004). As his own work shows (Blows et al., 2004; Hine et al., 2004), it may be that one can observe ample genetic variance for a trait, but that the variation may be nonexistent in the direction of the selection. This means that the proposed resolution to the lek paradox in terms of persistence of additive genetic variance and heritability in sexually selected traits (Pomiankowski & Møller, 1995) may not in reality be the resolution. Indeed, if the discrepancy between the orientation of the additive genetic variance and direction of selection turns out to be general for sexually selected traits, we seem to be back to square one in explaining female choice without direct benefits and resolving the lek paradox.