Abstract
As genetic sequencing costs have plummeted, datasets with sizes previously unthinkable have begun to appear. Such datasets present opportunities to learn about evolutionary history, particularly via rare alleles that record the very recent past. However, beyond the computational challenges inherent in the analysis of many large-scale datasets, large population-genetic datasets present theoretical problems. In particular, the majority of population-genetic tools require the assumption that each mutant allele in the sample is the result of a single mutation (the "infinite-sites" assumption), which is violated in large samples. Here, we present DR EVIL, a method for estimating mutation rates and recent demographic history from very large samples. DR EVIL avoids the infinite-sites assumption by using a diffusion approximation to a branching-process model with recurrent mutation. This approach results in tractable likelihoods that are accurate for rare alleles. We show that DR EVIL performs well in simulations and apply it to rare-variant data from one million haploid samples. We identify mutation-rate heterogeneity even after accounting for trinucleotide context and methylation status. We also predict that at modern sample sizes, the alleles at most polymorphic sites with high mutation rates represent the descendants of multiple mutation events.