It has been proposed that modern humans evolved from a small ancestral population, which appeared several hundred thousand years ago in Africa. Descendants of the founder group migrated to Europe and ...then to Asia, not mixing with the pre-existing local populations but replacing them. Two demographic elements are present in this “out of Africa” hypothesis: numerical growth of the modern humans and their migration into Eurasia. Did these processes leave an imprint in our DNA? To address this question, we use the classical Fisher–Wright–Moran model of population genetics, assuming variable population size and two models of mutation: the infinite-sites model and the stepwise-mutation model. We use the coalescence theory, which amounts to tracing the common ancestors of contemporary genes. We obtain mathematical formulae expressing the distribution of alleles given the time changes of population size . In the framework of the infinite-sites model, simulations indicate that the pattern of past population size change leaves its signature on the pattern of DNA polymorphism. Application of the theory to the published mitochondrial DNA sequences indicates that the current mitochondrial DNA sequence variation is not inconsistent with the logistic growth of the modern human population. In the framework of the stepwise-mutation model, we demonstrate that population bottleneck followed by growth in size causes an imbalance between allele-size variance and heterozygosity. We analyze a set of data on tetranucleotide repeats which reveals the existence of this imbalance. The pattern of imbalance is consistent with the bottleneck being most ancient in Africans, most recent in Asians and intermediate in Europeans. These findings are consistent with the “out of Africa” hypothesis, although by no means do they constitute its proof.
