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Variance and limiting distribution of coalescence times in a diploid model of a consanguineous population

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  • Severson, Alissa L.
  • Carmi, Shai
  • Rosenberg, Noah A.

Abstract

Recent modeling studies interested in runs of homozygosity (ROH) and identity by descent (IBD) have sought to connect these properties of genomic sharing to pairwise coalescence times. Here, we examine a variety of features of pairwise coalescence times in models that consider consanguinity. In particular, we extend a recent diploid analysis of mean coalescence times for lineage pairs within and between individuals in a consanguineous population to derive the variance of coalescence times, studying its dependence on the frequency of consanguinity and the kinship coefficient of consanguineous relationships. We also introduce a separation-of-time-scales approach that treats consanguinity models analogously to mathematically similar phenomena such as partial selfing, using this approach to obtain coalescence-time distributions. This approach shows that the consanguinity model behaves similarly to a standard coalescent, scaling population size by a factor 1−3c, where c represents the kinship coefficient of a randomly chosen mating pair. It provides the explanation for an earlier result describing mean coalescence time in the consanguinity model in terms of c. The results extend the potential to make predictions about ROH and IBD in relation to demographic parameters of diploid populations.

Suggested Citation

  • Severson, Alissa L. & Carmi, Shai & Rosenberg, Noah A., 2021. "Variance and limiting distribution of coalescence times in a diploid model of a consanguineous population," Theoretical Population Biology, Elsevier, vol. 139(C), pages 50-65.
    • Handle: RePEc:eee:thpobi:v:139:y:2021:i:c:p:50-65
    DOI: 10.1016/j.tpb.2021.02.002
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    References listed on IDEAS

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    1. Gravel, Simon & Steel, Mike, 2015. "The existence and abundance of ghost ancestors in biparental populations," Theoretical Population Biology, Elsevier, vol. 101(C), pages 47-53.
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    Cited by:

    1. Cotter, Daniel J. & Severson, Alissa L. & Carmi, Shai & Rosenberg, Noah A., 2022. "Limiting distribution of X-chromosomal coalescence times under first-cousin consanguineous mating," Theoretical Population Biology, Elsevier, vol. 147(C), pages 1-15.
    2. Elena Arciero & Sufyan A. Dogra & Daniel S. Malawsky & Massimo Mezzavilla & Theofanis Tsismentzoglou & Qin Qin Huang & Karen A. Hunt & Dan Mason & Saghira Malik Sharif & David A. Heel & Eamonn Sherida, 2021. "Fine-scale population structure and demographic history of British Pakistanis," Nature Communications, Nature, vol. 12(1), pages 1-16, December.
    3. Cotter, Daniel J. & Severson, Alissa L. & Rosenberg, Noah A., 2021. "The effect of consanguinity on coalescence times on the X chromosome," Theoretical Population Biology, Elsevier, vol. 140(C), pages 32-43.
    4. Hobolth, Asger & Rivas-González, Iker & Bladt, Mogens & Futschik, Andreas, 2024. "Phase-type distributions in mathematical population genetics: An emerging framework," Theoretical Population Biology, Elsevier, vol. 157(C), pages 14-32.

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