How Population Growth Affects Linkage Disequilibrium

TL;DR

This paper investigates how population size changes influence linkage disequilibrium (LD) patterns, revealing that population expansions and contractions produce distinct LD curve shapes, with implications for understanding population history.

Contribution

It introduces the use of the measure $\sigma_d^2$ for analyzing LD dynamics, offering a new, computationally efficient method to infer population history from LD data.

Findings

Population expansion causes steeply declining LD curves.

Population reduction results in high, flat LD curves.

European data suggests a history of population expansion.

Abstract

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 $\sigma_d^2$, 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 $\sigma_d^2$ 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.