Methods for Estimating Demography and Detecting Between-Locus Differences in the Effective Population Size and Mutation Rate

Abstract

It is known that the effective population size (Ne) and the mutation rate (u) vary across the genome. Here, we show that ignoring this heterogeneity may lead to biased estimates of past demography. To solve the problem, we develop new methods for jointly inferring past changes in population size and detecting variation in Ne and u between loci. These methods rely on either polymorphism data alone or both polymorphism and divergence data. In addition to inferring demography, we can use the methods to study a variety of questions: 1) comparing sex chromosomes with autosomes (for finding evidence for male-driven evolution, an unequal sex ratio, or sex-biased demographic changes) and 2) analyzing multilocus data from within autosomes or sex chromosomes (for studying determinants of variability in Ne and u). Simulations suggest that the methods can provide accurate parameter estimates and have substantial statistical power for detecting difference in Ne and u. As an example, we use the methods to analyze a polymorphism data set from Drosophila simulans. We find clear evidence for rapid population expansion. The results also indicate that the autosomes have a higher mutation rate than the X chromosome and that the sex ratio is probably female-biased. The new methods have been implemented in a user-friendly package.

Fig. 1.

MLEs obtained by fitting the simplified model to simulated data from 20 loci. Each locus is 5 kb long. The solid blue line in each plot shows the true parameter values across loci. The population size expanded recently with parameters $g_1=10$ and ${\tau }_1=0.5$. The results are based on 100 replicates. The sample size is 100.