Distinguishing multiple-merger from Kingman coalescence using two-site frequency spectra

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 (and other violations of the Kingman assumptions) 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 primarily 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 statistical test for determining whether the Kingman coalescent with any population size history is consistent with population data. Our approach is based on information contained in the two-site joint frequency spectrum (2-SFS) for pairs of linked sites, which has a different dependence on the topologies of genealogies than the SFS. Our statistical test is global in the sense that it can detect when the genome-wide genetic diversity is inconsistent with the Kingman model, rather than detecting outlier regions, as in selection scan methods. We validate this test using simulations, and then apply it to demonstrate that genomic diversity data from Drosophila melanogaster is inconsistent with the Kingman coalescent.