Linkage disequilibrium under recurrent bottlenecks

TL;DR

This paper investigates how recurrent population bottlenecks influence linkage disequilibrium patterns across multiple loci, revealing conditions under which long-range linkage disequilibrium occurs and its limitations in current measures.

Contribution

It introduces coalescent approximations for two-locus genealogies under recurrent bottlenecks and identifies scenarios where long-range linkage disequilibrium arises, extending understanding beyond constant population models.

Findings

Effective population-size approximation works under certain recombination regimes.

Long-range linkage disequilibrium occurs when recombination is frequent between bottlenecks.

Standard measures like sigma_d^2 may fail to detect long-range linkage disequilibrium.

Abstract

Understanding patterns of selectively neutral genetic variation is essential in order to model deviations from neutrality, caused for example by different forms of selection. Best understood is neutral genetic variation at a single locus, but additional insights can be gained by investigating genetic variation at multiple loci. The corresponding patterns of variation reflect linkage disequilibrium and provide information about the underlying multi-locus gene genealogies. The statistical properties of two-locus genealogies have been intensively studied for populations of constant census size, as well as for simple demographic histories such as exponential population growth, and single bottlenecks. By contrast, the combined effect of recombination and sustained demographic fluctuations is poorly understood. Addressing this issue, we study a two-locus Wright-Fisher model of a population subject to recurrent bottlenecks. We derive coalescent approximations for the covariance of the times to the most recent common ancestor at two loci. We find, first, that an effective population-size approximation describes the numerically observed linkage disequilibrium provided that recombination occurs either much faster or much more slowly than the population size changes. Second, when recombination occurs frequently between bottlenecks but rarely within bottlenecks, we observe long-range linkage disequilibrium. Third, we show that in the latter case, a commonly used measure of linkage disequilibrium, sigma_d^2 (closely related to r^2), fails to capture long-range linkage disequilibrium because constituent terms, each reflecting long-range linkage disequilibrium, cancel. Fourth, we analyse a limiting case in which long-range linkage disequilibrium can be described in terms of a Xi-coalescent process allowing for simultaneous multiple mergers of ancestral lines.