The Effects of Demography and Genetics on the Neutral Distribution of Quantitative Traits

Neutral models for quantitative trait evolution are useful for identifying phenotypes under selection. These models often assume normally distributed phenotypes. This assumption may be violated when a trait is affected by relatively few variants or when the effects of those variants arise from skewed or heavy tailed distributions. Molecular phenotypes such as gene expression levels may have these properties. To accommodate deviations from normality, models making fewer assumptions about the underlying genetics and patterns of variation are needed. Here, we develop a general neutral model for quantitative trait variation using a coalescent approach. This model allows interpretation of trait distributions in terms of familiar population genetic parameters because it is based on the coalescent. We show how the normal distribution resulting from the infinitesimal limit, where the number of loci grows large as the effect size per mutation becomes small, depends only on expected pairwise coalescent times. We then demonstrate how deviations from normality depend on demography through the distribution of coalescence times as well as through genetic parameters. In particular, population growth events exacerbate deviations while bottlenecks reduce them. We demonstrate the practical applications of this model by showing how to sample from the neutral distribution of QST, the ratio of the variance between subpopulations to that in the overall population. We further show it is likely impossible to distinguish sparsity from skewed or heavy tailed mutational effects using only sampled trait values. The model analyzed here greatly expands the parameter space for neutral trait models.