A Test of the Conjecture That G-Matrices Are More Stable Than B-Matrices

Abstract

The G-matrix occupies an important position in evolutionary biology both as a summary of the inheritance of quantitative traits and as an ingredient in predicting how those traits will respond to selection and drift. Consequently, the stability of G has an important bearing on the accuracy of predicted evolutionary trajectories. Furthermore, G should evolve in response to stable features of the adaptive landscape and their trajectories through time. Although the stability and evolution of G might be predicted from knowledge of selection in natural populations, most empirical comparisons of G-matrices have been made in the absence of such a priori predictions. We present a theoretical argument that within-sex G-matrices should be more stable than between-sex B-matrices because they are more powerfully exposed to multivariate stabilizing selection. We tested this conjecture by comparing estimates of B-and within-sex G-matrices among three populations of the garter snake Thamnophis elegans. Matrix comparisons using Flury's hierarchical approach revealed that within-sex G-matrices had four principal components in common (full CPC), whereas B-matrices had only a single principal component in common and eigenvalues that were more variable among populations. These results suggest that within-sex G is more stable than B, as predicted by our theoretical argument. K E Y W O R D S : Flury hierarchy, genetic covariance matrix, sexual dimorphism, Thamnophis elegans.The additive genetic variance-covariance matrix, or G-matrix, plays a central role in evolutionary theory in predicting deterministic responses to selection as well as the stochastic consequences of finite population size (Lande 1979). In particular, the deterministic evolution of the phenotypic mean is affected both by selection and the G-matrix. Unfortunately, however, we lack an analytical framework for predicting how G itself will evolve in response to selection in populations of finite size. Likewise, no equations have been derived that specify the stability of G in evolving populations. In the absence of an analytical framework, our knowledge of how G responds to selection and finite population size is based on simulation and empirical studies .Correlational selection should have profound consequences for G-matrix evolution and stability. Indeed, simulations have shown that G stability depends on trait-specific issues of mutation and selection, as well as on population size. As expected from theoretical considerations (Lande 1980a), the stability of the principal components of G (i.e., the angle of its eigenvectors) is enhanced by strong correlational selection, as well as by large population size (Jones et al.

The Evolutionary Stability of Cross-Sex, Cross-Trait Genetic Covariances

“…We found evidence that this divergence is likely due to the higher relative instability of B when compared to the within‐sex G (Fig. ), in line with Barker et al's () theoretical prediction that within‐sex covariance matrices are more stable than cross‐sex covariance matrices. Furthermore, all populations exhibited asymmetry about the diagonal in B , and the level of asymmetry within a population closely matched the overall level of divergence in B lower and B upper (Fig.…”

“…There is also substantial evidence of genetic divergence in CHC trait means along this cline, likely due to both sexual and natural selection (Chenoweth and Blows ; Frentiu and Chenoweth ). Therefore, the natural divergence of male and female CHCs in D. serrata represents an ideal model system for examining the stability of B (Barker et al ).…”

Sex‐biased transcriptome divergence along a latitudinal gradient

“…However, there is some evidence that cross‐sex genetic covariances tend to vary across populations (Barker et al . ; Gosden & Chenoweth ), and therefore how such constraints manifest would be an interesting starting point for future studies.…”

A simple procedure for the comparison of covariance matrices

“…The more easily estimated matrix of phenotypic variances and covariances P can be used as a surrogate for G , especially in the case of high heritability morphological characters [1-4]. Comparisons between covariance matrices are carried out in the study of a wide array of evolutionary problems, such as the stability of G in the presence of selection and drift [5-7], the role of genetic constraints on determining evolutionary trajectories in adaptive radiations [8], the response of genetic architecture to environmental heterogeneity [9], the evolution of phenotypic integration [4,10], multi-character phenotypic plasticity [11] and sexual dimorphism [12,13]. …”