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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 2 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 2 lineages coalesce instantaneously. Therefore, detecting violations of the Kingman assumptions (e.g. due to 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 deviations from Kingman coalescence in genomic data rely primarily on the site frequency spectrum (SFS). However, the signatures of some non-Kingman processes (e.g. 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 2-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.
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Bursts of coalescence within population pedigrees whenever big families occur
Abstract We consider a simple diploid population-genetic model with potentially high variability of offspring numbers among individuals. Specifically, against a backdrop of Wright–Fisher reproduction and no selection, there is an additional probability that a big family occurs, meaning that a pair of individuals has a number of offspring on the order of the population size. We study how the pedigree of the population generated under this model affects the ancestral genetic process of a sample of size two at a single autosomal locus without recombination. Our population model is of the type for which multiple-merger coalescent processes have been described. We prove that the conditional distribution of the pairwise coalescence time given the random pedigree converges to a limit law as the population size tends to infinity. This limit law may or may not be the usual exponential distribution of the Kingman coalescent, depending on the frequency of big families. But because it includes the number and times of big families, it differs from the usual multiple-merger coalescent models. The usual multiple-merger coalescent models are seen as describing the ancestral process marginal to, or averaging over, the pedigree. In the limiting ancestral process conditional on the pedigree, the intervals between big families can be modeled using the Kingman coalescent but each big family causes a discrete jump in the probability of coalescence. Analogous results should hold for larger samples and other population models. We illustrate these results with simulations and additional analysis, highlighting their implications for inference and understanding of multilocus data.
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- PAR ID:
- 10505486
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- GENETICS
- Volume:
- 227
- Issue:
- 1
- ISSN:
- 1943-2631
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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