The genetic diversity of humans, like many species, has been shaped by a complex pattern of population separations followed by isolation and subsequent admixture. This pattern, reaching at least as far back as the appearance of our species in the paleontological record, has left its traces in our genomes. Reconstructing a population's history from these traces is a challenging problem. Here we present a novel approach based on the Multiple Sequentially Markovian Coalescent (MSMC) to analyse the population separation history. Our approach, called MSMC-IM, uses an improved implementation of the MSMC (MSMC2) to estimate coalescence rates within and across pairs of populations, and then fits a continuous Isolation-Migration model to these rates to obtain a time-dependent estimate of gene flow. We show, using simulations, that our method can identify complex demographic scenarios involving post-split admixture or archaic introgression. We apply MSMC-IM to whole genome sequences from 15 worldwide populations, tracking the process of human genetic diversification. We detect traces of extremely deep ancestry between some African populations, with around 1% of ancestry dating to divergences older than a million years ago.

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