Learning the properties of adaptive regions with functional data analysis

Identifying regions of positive selection in genomic data remains a challenge in population genetics. Most current approaches rely on comparing values of summary statistics calculated in windows. We present an approach termed SURFDAWave, which translates measures of genetic diversity calculated in genomic windows to functional data. By transforming our discrete data points to be outputs of continuous functions defined over genomic space, we are able to learn the features of these functions that signify selection. This enables us to confidently identify complex modes of natural selection, including adaptive introgression. We are also able to predict important selection parameters that are responsible for shaping the inferred selection events. By applying our model to human population-genomic data, we recapitulate previously identified regions of selective sweeps, such as OCA2 in Europeans, and predict that its beneficial mutation reached a frequency of 0.02 before it swept 1,802 generations ago, a time when humans were relatively new to Europe. In addition, we identify BNC2 in Europeans as a target of adaptive introgression, and predict that it harbors a beneficial mutation that arose in an archaic human population that split from modern humans within the hypothesized modern human-Neanderthal divergence range.Author summary: As populations adapt to their environments, specific patterns indicating selection remain in the distribution of genetic diversity across their genomes. A hallmark of positive natural selection is the reduction of genetic diversity surrounding beneficial mutations. The origin of the beneficial mutation, or whether it originated in a population being examined or within another, can be uncovered through the spatial distribution of the reduction of genetic diversity. In addition, other information about the strength, timing, and initial frequency of beneficial mutations can be learned by examining patterns of diversity across genomic regions. We use functional data analysis to capture differences among the spatial distributions of genetic variation expected by diverse evolutionary processes, and further apply it to dissect how selection parameters affect such patterns. Using this method, we learn the underlying origins, timings, and strengths of beneficial mutations that have impacted modern human genomic diversity.