The optimal measure of allelic association

Allelic association between pairs of loci is derived in terms of the association probability rho as a function of recombination theta, effective population size N, linear systematic pressure v, and time t, predicting both rho(rt), the decrease of association from founders and rho(ct), the increase by genetic drift, with rho(t) = rho(rt) + rho(ct). These results conform to the Malecot equation, with time replaced by distance on the genetic map, or on the physical map if recombination in the region is uniform. Earlier evidence suggested that rho is less sensitive to variations in marker allele frequencies than alternative metrics for which there is no probability theory. This robustness is confirmed for six alternatives in eight samples. In none of these 48 tests was the residual variance as small as for rho. Overall, efficiency was less than 80% for all alternatives, and less than 30% for two of them. Efficiency of alternatives did not increase when information was estimated simultaneously. The swept radius within which substantial values of rho are conserved lies between 385 and 893 kb, but deviation of parameters between measures is enormously significant. The large effort now being devoted to allelic association has little value unless the rho metric with the strongest theoretical basis and least sensitivity to marker allele frequencies is used for mapping of marker association and localization of disease loci.