Using drift coefficients as a basis for inferring times, effective population sizes, and genetic adaptations.

Genetic drift and gene flow can give rise to a complex population genetic structure. The inverse problem of estimating the genetic drift and gene flow in the past, based on the present-day genomic population structure, can be solved using an admixture graph. This describes differentiated local populations in terms of population splits and migrations between populations. The history and associated levels of genetic drift and admixture can be estimated based on the genome-wide single nucleotide polymorphism allele frequency data. Here, we present a set of statistical methods based on the admixture graph. Applying a prior on the stochastic variation of the effective population size decomposes the genetic drift values that are associated with the non-migration edges into the timings of the population splits and the effective population sizes at those times. This decomposition facilitates downstream analyses such as reconstruction of ancestral allele frequencies via a Brownian motion model with admixture. To trace changes in allele frequencies on a world map, we estimated the geographic locations of the ancestral populations using Brownian motion, the rate of which depends on the genetic drift values. Mapping the history of putative adaptations onto a world map can illuminate factors responsible for regional population heterogeneity. We investigated the effectiveness of detecting adaptations with a numerical simulation that mimics human population history, and by analyzing the expression quantitative trait loci of the melanocortin 1 receptor gene, which is involved in regulation of skin and hair pigmentation.