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Bayesian pedigree inference with small numbers of single nucleotide polymorphisms via a factor-graph representation

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  • Anderson, Eric C.
  • Ng, Thomas C.

Abstract

We develop a computational framework for addressing pedigree inference problems using small numbers (80–400) of single nucleotide polymorphisms (SNPs). Our approach relaxes the assumptions, which are commonly made, that sampling is complete with respect to the pedigree and that there is no genotyping error. It relies on representing the inferred pedigree as a factor graph and invoking the Sum-Product algorithm to compute and store quantities that allow the joint probability of the data to be rapidly computed under a large class of rearrangements of the pedigree structure. This allows efficient MCMC sampling over the space of pedigrees, and, hence, Bayesian inference of pedigree structure. In this paper we restrict ourselves to inference of pedigrees without loops using SNPs assumed to be unlinked. We present the methodology in general for multigenerational inference, and we illustrate the method by applying it to the inference of full sibling groups in a large sample (n=1157) of Chinook salmon typed at 95 SNPs. The results show that our method provides a better point estimate and estimate of uncertainty than the currently best-available maximum-likelihood sibling reconstruction method. Extensions of this work to more complex scenarios are briefly discussed.

Suggested Citation

  • Anderson, Eric C. & Ng, Thomas C., 2016. "Bayesian pedigree inference with small numbers of single nucleotide polymorphisms via a factor-graph representation," Theoretical Population Biology, Elsevier, vol. 107(C), pages 39-51.
    • Handle: RePEc:eee:thpobi:v:107:y:2016:i:c:p:39-51
    DOI: 10.1016/j.tpb.2015.09.005
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    References listed on IDEAS

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    1. Cowell, Robert G., 2009. "Efficient maximum likelihood pedigree reconstruction," Theoretical Population Biology, Elsevier, vol. 76(4), pages 285-291.
    2. Eddelbuettel, Dirk & Francois, Romain, 2011. "Rcpp: Seamless R and C++ Integration," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 40(i08).
    3. Almudevar, Anthony & LaCombe, Jason, 2012. "On the choice of prior density for the Bayesian analysis of pedigree structure," Theoretical Population Biology, Elsevier, vol. 81(2), pages 131-143.
    4. Sheehan, Nuala A. & Bartlett, Mark & Cussens, James, 2014. "Improved maximum likelihood reconstruction of complex multi-generational pedigrees," Theoretical Population Biology, Elsevier, vol. 97(C), pages 11-19.
    5. N. A. Sheehan, 2000. "On the Application of Markov Chain Monte Carlo Methods to Genetic Analyses on Complex Pedigrees," International Statistical Review, International Statistical Institute, vol. 68(1), pages 83-110, April.
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