How Population Growth Affects Linkage Disequilibrium

Linkage disequilibrium (LD) is often summarized using the "LD curve," which relates the LD between pairs of sites to the distance that separates them along the chromosome. This paper shows how the LD curve responds to changes in population size. An expansion of population size generates an LD curve that declines steeply, especially if that expansion has followed a bottleneck. A reduction in size generates an LD curve that is high but relatively flat. In European data, the curve is steep, suggesting a history of population expansion. These conclusions emerge from the study of $σ_d^2$, a measure of LD that has never played a central role. It has been seen merely as an approximation to another measure, $r^2$. Yet $σ_d^2$ has different dynamical behavior and provides deeper time depth. Furthermore, it is easily estimated from data and can be predicted from population history using a fast, deterministic algorithm.