Tractable diffusion and coalescent processes for weakly correlated loci

Abstract

Widely used models in genetics include the Wright-Fisher diffusion and its moment dual, Kingman's coalescent. Each has a multilocus extension but under neither extension is the sampling distribution available in closed-form, and their computation is extremely difficult. In this paper we derive two new multilocus population genetic models, one a diffusion and the other a coalescent process, which are much simpler than the standard models, but which capture their key properties for large recombination rates. The diffusion model is based on a central limit theorem for density dependent population processes, and we show that the sampling distribution is a linear combination of moments of Gaussian distributions and hence available in closed-form. The coalescent process is based on a probabilistic coupling of the ancestral recombination graph to a simpler genealogical process which exposes the leading dynamics of the former. We further demonstrate that when we consider the sampling distribution as an asymptotic expansion in inverse powers of the recombination parameter, the sampling distributions of the new models agree with the standard ones up to the first two orders.

34 pages, 1 figure

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• Identifying Signatures of Selection in Genetic Time Series
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• Padé approximants and exact two-locus sampling distributions
• An asymptotic sampling formula for the coalescent with Recombination
• Closed-form asymptotic sampling distributions under the coalescent with recombination for an arbitrary number of loci
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Cited by in corpus (4)

• Quantifying model uncertainty for the observed non-Gaussian data by the Hellinger distance
• Chromosome Painting: how recombination mixes ancestral colors
• Sampling probabilities, diffusions, ancestral graphs, and duality under strong selection
• Solving the selection-recombination equation: Ancestral lines under selection and recombination