Correlation measures for linkage disequilibrium within and between populations

Abstract

SummaryCorrelation statistics can be used to measure the amount of linkage disequilibrium (LD) between two loci in subdivided populations. Within populations, the square of the correlation of gene frequencies,r2, is a convenient measure of LD. Between populations, the statisticrirj, for populationsiandj, measures the relatedness of LD. Recurrence relationships for these two parameters are derived for the island model of population subdivision, under the assumptions of the linked identity-by-descent (LIBD) model in which correlation measures are equated to probability measures. The recurrence relationships closely predict the build-up ofr2andrirjfollowing population subdivision in computer simulations. The LIBD model predicts that a steady state will be reached withr2equal to 1/[1+4Nec(1+(k−1)ρ)], wherekis the number of island populations,Neis the effective local population (island) size, and ρ measures the ratio of migration (m) to recombination (c) and is equal tom/[c(k−1)+m]. For low values ofm/c, ρ=0, andE(r2) is equal to 1/(1+4Nec). For high values ofm/c, ρ=1, andE(r2) is equal to 1/(1+4kNec). The value ofrirjfollowing separation eventually settles down to a steady state whose expectation,E(rirj), is equal toE(r2) multiplied by ρ. Equations predicting the change inrirjvalues are applied to the separation of African (Yoruba – YRI) and non-African (European – CEU) populations, using data from Hapmap. The primary data lead to an estimate of separation time of less than 1000 generations if there has been no migration, which is around one-third of minimum current estimates. Ancient rather than recent migration can explain the form of the data.