Perspective: Genomic inference using diffusion models and the allele frequency spectrum

Evolutionary, biological, and demographic processes combine to shape the variation observed in populations. Understanding how these processes are expected to influence variation allows us to infer past demographic events and the nature of selection in human populations. Forward models such as the diffusion approximation provide a powerful tool for analyzing the distribution of allele frequencies in contemporary populations due to their computational tractability and model flexibility. Here, we discuss recent computational developments and their application to reconstructing human demographic history and patterns of selection at new mutations. We also reexamine how some classical assumptions that are still commonly used in inference studies fare when applied to modern data. We use whole-genome sequence data for 797 French Canadian individuals to examine the neutrality of synonymous sites. We find that selection can lead to strong biases in the inferred demography, mutation rate, and distributions of fitness effects. We use these distributions of fitness effects together with demographic and phenotype-fitness models to predict the relationship between effect size and allele frequency, and contrast those predictions to commonly used models in statistical genetics. Thus the simple evolutionary models investigated by Kimura and Ohta still provide important insight into modern genetic research.