The excess of rare variation across the exome is consistent with explosive human population growth (22). To investigate this further, we used an out-of-Africa (OOA) demographic model (23) to predict the expected joint distribution of allele frequencies between EA and AA samples via a diffusion approximation (18). The OOA model, modified to account for admixture, captures prominent features of the joint frequency distribution. However, both populations contain more rare variants than predicted by this model (18) (Fig. 2), most likely because of rapid population growth in the past few thousand years that is undetectable with smaller sample sizes (fig. S9E). We revisited the demographic model from Gravel et al. (23), allowing for a reduced initial European expansion that is compensated for by accelerated growth starting after the split of European and Asian populations. Similarly, we introduced a phase of exponential growth in the African population starting at the same time. The resulting demographic model is an improved fit to the synonymous site-frequency spectrum (18) (Fig. 2B) and strongly supports a recent, dramatic acceleration of population growth. The maximum-likelihood time for accelerated growth was 5115 years ago (Fig. 2B).
