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Full likelihood inference from the site frequency spectrum based on the optimal tree resolution

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  • Sainudiin, Raazesh
  • Véber, Amandine

Abstract

We develop a novel importance sampler to compute the full likelihood function of a demographic or structural scenario given the site frequency spectrum (SFS) at a locus free of intra-locus recombination. This sampler, instead of representing the hidden genealogy of a sample of individuals by a labelled binary tree, uses the minimal level of information about such a tree that is needed for the likelihood of the SFS and thus takes advantage of the huge reduction in the size of the state space that needs to be integrated. We assume that the population may have demographically changed and may be non-panmictically structured, as reflected by the branch lengths and the topology of the genealogical tree of the sample, respectively. We also assume that mutations conform to the infinitely-many-sites model. We achieve this by a controlled Markov process that generates ‘particles’ in the hidden space of SFS histories which are always compatible with the observed SFS.

Suggested Citation

  • Sainudiin, Raazesh & Véber, Amandine, 2018. "Full likelihood inference from the site frequency spectrum based on the optimal tree resolution," Theoretical Population Biology, Elsevier, vol. 124(C), pages 1-15.
    • Handle: RePEc:eee:thpobi:v:124:y:2018:i:c:p:1-15
    DOI: 10.1016/j.tpb.2018.07.002
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    References listed on IDEAS

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    1. Barton, N.H. & Etheridge, A.M. & Kelleher, J. & Véber, A., 2013. "Inference in two dimensions: Allele frequencies versus lengths of shared sequence blocks," Theoretical Population Biology, Elsevier, vol. 87(C), pages 105-119.
    2. Hobolth Asger & Uyenoyama Marcy K & Wiuf Carsten, 2008. "Importance Sampling for the Infinite Sites Model," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 7(1), pages 1-26, October.
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