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Tractable diffusion and coalescent processes for weakly correlated loci

A. Jenkins, Paul and Fearnhead, Paul and S. Song, Yun (2015) Tractable diffusion and coalescent processes for weakly correlated loci. Electronic Journal of Probability, 20. ISSN 1083-6489

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      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.

      Item Type: Article
      Journal or Publication Title: Electronic Journal of Probability
      Additional Information: Supersedes arXiv:1405.6863v2
      Uncontrolled Keywords: math.PR ; q-bio.PE ; 92D15 (Primary) 65C50, 92D10 (Secondary)
      Subjects:
      Departments: Faculty of Science and Technology > Mathematics and Statistics
      ID Code: 70540
      Deposited By: ep_importer_pure
      Deposited On: 22 Aug 2014 16:17
      Refereed?: Yes
      Published?: Published
      Last Modified: 21 Nov 2017 19:05
      Identification Number:
      URI: http://eprints.lancs.ac.uk/id/eprint/70540

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