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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Tractable diffusion and coalescent processes for weakly correlated loci
AU - A. Jenkins, Paul
AU - Fearnhead, Paul
AU - S. Song, Yun
N1 - Supersedes arXiv:1405.6863v2
PY - 2015/5/29
Y1 - 2015/5/29
N2 - 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 ancestralrecombination 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.
AB - 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 ancestralrecombination 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.
KW - math.PR
KW - q-bio.PE
KW - 92D15 (Primary) 65C50, 92D10 (Secondary)
U2 - 10.1214/EJP.v20-3564
DO - 10.1214/EJP.v20-3564
M3 - Journal article
VL - 20
JO - Electronic Journal of Probability
JF - Electronic Journal of Probability
SN - 1083-6489
M1 - 58
ER -