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Limiting distribution of X-chromosomal coalescence times under first-cousin consanguineous mating

Author

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  • Cotter, Daniel J.
  • Severson, Alissa L.
  • Carmi, Shai
  • Rosenberg, Noah A.

Abstract

By providing additional opportunities for coalescence within families, the presence of consanguineous unions in a population reduces coalescence times relative to non-consanguineous populations. First-cousin consanguinity can take one of six forms differing in the configuration of sexes in the pedigree of the male and female cousins who join in a consanguineous union: patrilateral parallel, patrilateral cross, matrilateral parallel, matrilateral cross, bilateral parallel, and bilateral cross. Considering populations with each of the six types of first-cousin consanguinity individually and a population with a mixture of the four unilateral types, we examine coalescent models of consanguinity. We previously computed, for first-cousin consanguinity models, the mean coalescence time for X-chromosomal loci and the limiting distribution of coalescence times for autosomal loci. Here, we use the separation-of-time-scales approach to obtain the limiting distribution of coalescence times for X-chromosomal loci. This limiting distribution has an instantaneous coalescence probability that depends on the probability that a union is consanguineous; lineages that do not coalesce instantaneously coalesce according to an exponential distribution. We study the effects on the coalescence time distribution of the type of first-cousin consanguinity, showing that patrilateral-parallel and patrilateral-cross consanguinity have no effect on X-chromosomal coalescence time distributions and that matrilateral-parallel consanguinity decreases coalescence times to a greater extent than does matrilateral-cross consanguinity.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:thpobi:v:147:y:2022:i:c:p:1-15
    DOI: 10.1016/j.tpb.2022.07.002
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    References listed on IDEAS

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    1. 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.
    2. Ramachandran, Sohini & Rosenberg, Noah A. & Feldman, Marcus W. & Wakeley, John, 2008. "Population differentiation and migration: Coalescence times in a two-sex island model for autosomal and X-linked loci," Theoretical Population Biology, Elsevier, vol. 74(4), pages 291-301.
    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. Carmi, Shai & Wilton, Peter R. & Wakeley, John & Pe’er, Itsik, 2014. "A renewal theory approach to IBD sharing," Theoretical Population Biology, Elsevier, vol. 97(C), pages 35-48.
    5. David W Clark & Yukinori Okada & Kristjan H S Moore & Dan Mason & Nicola Pirastu & Ilaria Gandin & Hannele Mattsson & Catriona L K Barnes & Kuang Lin & Jing Hua Zhao & Patrick Deelen & Rebecca Rohde &, 2019. "Associations of autozygosity with a broad range of human phenotypes," Nature Communications, Nature, vol. 10(1), pages 1-17, December.
    6. 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.
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