How much do genetic covariances alter the rate of adaptation?

Abstract

Genetically correlated traits do not evolve independently, and the covariances between traits affect the rate at which a population adapts to a specified selection regime. To measure the impact of genetic covariances on the rate of adaptation, we compare the rate fitness increases given the observed G matrix to the expected rate if all the covariances in the G matrix are set to zero. Using data from the literature, we estimate the effect of genetic covariances in real populations. We find no net tendency for covariances to constrain the rate of adaptation, though the quality and heterogeneity of the data limit the certainty of this result. There are some examples in which covariances strongly constrain the rate of adaptation but these are balanced by counter examples in which covariances facilitate the rate of adaptation; in many cases, covariances have little or no effect. We also discuss how our metric can be used to identify traits or suites of traits whose genetic covariances to other traits have a particularly large impact on the rate of adaptation.

Figure 1

Frequency histogram of L-values for surveyed studies where L=log(R). R measures the rate of adaptation relative to the rate expected if all traits were genetically independent. Negative and positive values for log(R) indicate cases where genetic covariances constrain and facilitate the rate of adaptation, respectively. (a) Distribution based on best available data (n=45). The mean of this distribution is $\overline{L}=-0.05$ (i.e. $\overline{R}=0.89$) but this is not significantly different from $\overline{L}=0$. (b) Distribution based on data using the lowest common denominator (LCD) (see text for details; n=34). For this, distribution is $\overline{L}=-0.04$ (i.e. $\overline{R}=0.91$). See the electronic supplementary material for a list of surveyed studies.

Figure 2

Assessing the potential for covariances to affect the rate of adaptation. (a) The evenness of selection, E_β, is plotted against A=|log(R)|. The correlation between E_β and A is positive (ρ=0.24), indicating that when selection is more evenly distributed across traits, covariances are more likely to affect the rate of adaptation. (b) The evenness of the eigenvalues of the G matrix, E_λ, is plotted A. The negative correlation (ρ=−0.71) confirms that the rate of adaptation is more likely to be altered in cases where correlations cause genetic variation to be more abundant in some directions than others (E_λ≪1). See text for details.