Abstract
Demographic inference methods in population genetics typically assume that the ancestry of a sample can be modeled by the Kingman coalescent. A defining feature of this stochastic process is that it generates genealogies that are binary trees: no more than two ancestral lineages may coalesce at the same time. However, this assumption breaks down under several scenarios. For example, pervasive natural selection and extreme variation in offspring number can both generate genealogies with “multiple-merger” events in which more than two lineages coalesce instantaneously. Therefore, detecting multiple mergers is important both for understanding which forces have shaped the diversity of a population and for avoiding fitting misspecified models to data. Current methods to detect multiple mergers in genomic data rely on the site frequency spectrum (SFS). However, the signatures of multiple mergers in the SFS are also consistent with a Kingman coalescent with a time-varying population size. Here, we present a new method for detecting multiple mergers based on the pointwise mutual information of the two-site frequency spectrum for pairs of linked sites. Unlike the SFS, the pointwise mutual information depends mostly on the topologies of genealogies rather than on their branch lengths and is therefore largely insensitive to population size change. This statistic is global in the sense that it can detect when the genome-wide genetic diversity is inconsistent with the Kingman coalescent, rather than detecting outlier regions, as in selection scan methods. Finally, we demonstrate a graphical model-checking procedure based on the point-wise mutual information using genomic diversity data from Drosophila melanogaster.