A multivariate comparison of phenotypic and genetic covariance matrices: when P can be used for making evolutionary...

Accurate predictions of evolutionary response are required to determine whether populations can adapt to rapidly changing environments, or whether they will go extinct. The multivariate breeder's equation enables us to make these predictions using information on the genetic variance and covariance between traits (G) and selection. However, estimating G is a challenge that requires known relatedness among individuals in a population, and large sample sizes. Phenotypic correlations are easier to estimate, and past studies have argued that they can be used as a proxy, known as Cheverud's conjecture. However, multivariate patterns of variation that are important for predicting the rate and direction of evolution are rarely captured in these studies. Here, we use simulated data in which we vary heritability, sample size, pleiotropy, and the alignment of genetic and environmental effects on phenotypes, and determine the similarity of G and P with multivariate matrix comparisons. We find that the extent of pleiotropy and the relationship between genetic and environmental effects are important determinants of the similarity between G and P. While we show that P can provide a better prediction of evolutionary response when sample sizes are small, or under the limited conditions of weak pleiotropy, congruent genetic and environmental effects, and access to accurate heritability estimates, quantitative genetic studies remain crucial for making good evolutionary predictions that cannot be bypassed by using P.