We propose a method that uses genetic data to test for the occurrence of a recent range expansion and to infer the location of the origin of the expansion. We introduce a statistic for pairs of populations $psi$ (the directionality index) that detect
s asymmetries in the two-dimensional allele frequency spectrum caused by the series of founder events that happen during an expansion. Such asymmetry arises because low frequency alleles tend to be lost during founder events, thus creating clines in the frequencies of surviving low-frequency alleles. Using simulations, we further show that $psi$ is more powerful for detecting range expansions than both $F_{ST}$ and clines in heterozygosity. We illustrate the utility of $psi$ by applying it to a data set from modern humans and show how we can include more complicated scenarios such as multiple expansion origins or barriers to migration in the model.
We examine the distribution of heterozygous sites in nine European and nine Yoruban individuals whose genomic sequences were made publicly available by Complete Genomics. We show that it is possible to obtain detailed information about inbreeding whe
n a relatively small set of whole-genome sequences is available. Rather than focus on testing for deviations from Hardy-Weinberg genotype frequencies at each site, we analyze the entire distribution of heterozygotes conditioned on the number of copies of the derived (non-chimpanzee) allele. Using Levenes exact test, we reject Hardy-Weinberg in both populations. We generalized Levenes distribution to obtain the exact distribution of the number of heterozygous individuals given that every individual has the same inbreeding coefficient, F. We estimated F to be 0.0026 in Europeans and 0.0005 in Yorubans, but we could also reject the hypothesis that F was the same in each individual. We used a composite likelihood method to estimate F in each individual and within each chromosome. Variation in F across chromosomes within individuals was too large to be consistent with sampling effects alone. Furthermore, estimates of F for each chromosome in different populations were not correlated. Our results show how detailed comparisons of population genomic data can be made to theoretical predictions. The application of methods to the Complete Genomics data set shows that the extent of apparent inbreeding varies across chromosomes and across individuals, and estimates of inbreeding coefficients are subject to unexpected levels of variation which might be partly accounted for by selection.
