Quantitative Trait Evolution with Arbitrary Mutational Models

When models of quantitative genetic variation are built from population genetic first principles, several assumptions are often made. One of the most important assumptions is that traits are controlled by many genes of small effect. This leads to a prediction of a Gaussian trait distribution in the population, via the Central Limit Theorem. Since these biological assumptions are often unknown or untrue, we characterized how finite numbers of loci or large mutational effects can impact the sampling distribution of a quantitative trait. To do so, we developed a neutral coalescent-based framework, allowing us to experiment freely with the number of loci and the underlying mutational model. Through both analytical theory and simulation we found the normality assumption was highly sensitive to the details of the mutational process, with the greatest discrepancies arising when the number of loci was small or the mutational kernel was heavy-tailed. In particular, fat-tailed mutational kernels result in multimodal sampling distributions for any number of loci. Since selection models and robust neutral models may produce qualitatively similar sampling distributions, we advise extra caution should be taken when interpreting model-based results for poorly understood systems of quantitative traits.