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Sequential Markov coalescent algorithms for population models with demographic structure

Author

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  • Eriksson, A.
  • Mahjani, B.
  • Mehlig, B.

Abstract

We analyse sequential Markov coalescent algorithms for populations with demographic structure: for a bottleneck model, a population-divergence model, and for a two-island model with migration. The sequential Markov coalescent method is an approximation to the coalescent suggested by McVean and Cardin, and by Marjoram and Wall. Within this algorithm we compute, for two individuals randomly sampled from the population, the correlation between times to the most recent common ancestor and the linkage probability corresponding to two different loci with recombination rate R between them. These quantities characterise the linkage between the two loci in question. We find that the sequential Markov coalescent method approximates the coalescent well in general in models with demographic structure. An exception is the case where individuals are sampled from populations separated by reduced gene flow. In this situation, the correlations may be significantly underestimated. We explain why this is the case.

Suggested Citation

  • Eriksson, A. & Mahjani, B. & Mehlig, B., 2009. "Sequential Markov coalescent algorithms for population models with demographic structure," Theoretical Population Biology, Elsevier, vol. 76(2), pages 84-91.
    • Handle: RePEc:eee:thpobi:v:76:y:2009:i:2:p:84-91
    DOI: 10.1016/j.tpb.2009.05.002
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    1. Magnus Nordborg & Tina T Hu & Yoko Ishino & Jinal Jhaveri & Christopher Toomajian & Honggang Zheng & Erica Bakker & Peter Calabrese & Jean Gladstone & Rana Goyal & Mattias Jakobsson & Sung Kim & Yuri , 2005. "The Pattern of Polymorphism in Arabidopsis thaliana," PLOS Biology, Public Library of Science, vol. 3(7), pages 1-1, May.
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    Cited by:

    1. Miroshnikov, Alexey & Steinrücken, Matthias, 2017. "Computing the joint distribution of the total tree length across loci in populations with variable size," Theoretical Population Biology, Elsevier, vol. 118(C), pages 1-19.
    2. Haipeng Li & Thomas Wiehe, 2013. "Coalescent Tree Imbalance and a Simple Test for Selective Sweeps Based on Microsatellite Variation," PLOS Computational Biology, Public Library of Science, vol. 9(5), pages 1-14, May.
    3. King, Léandra & Wakeley, John & Carmi, Shai, 2018. "A non-zero variance of Tajima’s estimator for two sequences even for infinitely many unlinked loci," Theoretical Population Biology, Elsevier, vol. 122(C), pages 22-29.
    4. Jerome Kelleher & Alison M Etheridge & Gilean McVean, 2016. "Efficient Coalescent Simulation and Genealogical Analysis for Large Sample Sizes," PLOS Computational Biology, Public Library of Science, vol. 12(5), pages 1-22, May.

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