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Knowledge of genome-wide genealogies for thousands of individuals would simplify most evolutionary analyses for humans and other species, but has remained computationally infeasible. We developed a method, Relate, scaling to > 10,000 sequences while simultaneously estimating branch lengths, mutational ages, and variable historical population sizes, as well as allowing for data errors. Application to 1000 Genomes Project haplotypes produces joint genealogical histories for 26 human populations. Highly diverged lineages are present in all groups, but most frequent in Africa. Outside Africa, these mainly reflect ancient introgression from groups related to Neanderthals and Denisovans, while African signals instead reflect unknown events, unique to that continent. Our approach allows more powerful inferences of natural selection than previously possible. We identify multiple novel regions under strong positive selection, and multi-allelic traits including hair colour, BMI, and blood pressure, showing strong evidence of directional selection, varying among human groups.

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