Using environmental correlations to identify loci underlying local adaptation.

Loci involved in local adaptation can potentially be identified by an unusual correlation between allele frequencies and important ecological variables or by extreme allele frequency differences between geographic regions. However, such comparisons are complicated by differences in sample sizes and the neutral correlation of allele frequencies across populations due to shared history and gene flow. To overcome these difficulties, we have developed a Bayesian method that estimates the empirical pattern of covariance in allele frequencies between populations from a set of markers and then uses this as a null model for a test at individual SNPs. In our model the sample frequencies of an allele across populations are drawn from a set of underlying population frequencies; a transform of these population frequencies is assumed to follow a multivariate normal distribution. We first estimate the covariance matrix of this multivariate normal across loci using a Monte Carlo Markov chain. At each SNP, we then provide a measure of the support, a Bayes factor, for a model where an environmental variable has a linear effect on the transformed allele frequencies compared to a model given by the covariance matrix alone. This test is shown through power simulations to outperform existing correlation tests. We also demonstrate that our method can be used to identify SNPs with unusually large allele frequency differentiation and offers a powerful alternative to tests based on pairwise or global F(ST). Software is available at http://www.eve.ucdavis.edu/gmcoop/.