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 the differentiated local populations in terms of population splits and migrations between populations. The history and the associated levels of genetic drift and admixture can be estimated based on the genome-wide SNP 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. A Brownian motion model with admixture reconstructs the ancestral states of the allele frequencies. 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 drift parameter values. Mapping the history of adaptations onto a world map enables us to identify the factors responsible for the current regional population heterogeneity.