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Spread of pedigree versus genetic ancestry in spatially distributed populations

Author

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  • Kelleher, J.
  • Etheridge, A.M.
  • Véber, A.
  • Barton, N.H.

Abstract

Ancestral processes are fundamental to modern population genetics and spatial structure has been the subject of intense interest for many years. Despite this interest, almost nothing is known about the distribution of the locations of pedigree or genetic ancestors. Using both spatially continuous and stepping-stone models, we show that the distribution of pedigree ancestors approaches a travelling wave, for which we develop two alternative approximations. The speed and width of the wave are sensitive to the local details of the model. After a short time, genetic ancestors spread far more slowly than pedigree ancestors, ultimately diffusing out with radius ∼t rather than spreading at constant speed. In contrast to the wave of pedigree ancestors, the spread of genetic ancestry is insensitive to the local details of the models.

Suggested Citation

  • Kelleher, J. & Etheridge, A.M. & Véber, A. & Barton, N.H., 2016. "Spread of pedigree versus genetic ancestry in spatially distributed populations," Theoretical Population Biology, Elsevier, vol. 108(C), pages 1-12.
    • Handle: RePEc:eee:thpobi:v:108:y:2016:i:c:p:1-12
    DOI: 10.1016/j.tpb.2015.10.008
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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. 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.
    3. Kelleher, J. & Etheridge, A.M. & Barton, N.H., 2014. "Coalescent simulation in continuous space: Algorithms for large neighbourhood size," Theoretical Population Biology, Elsevier, vol. 95(C), pages 13-23.
    4. Douglas L. T. Rohde & Steve Olson & Joseph T. Chang, 2004. "Modelling the recent common ancestry of all living humans," Nature, Nature, vol. 431(7008), pages 562-566, September.
    5. Matsen, Frederick A. & Evans, Steven N., 2008. "To what extent does genealogical ancestry imply genetic ancestry?," Theoretical Population Biology, Elsevier, vol. 74(2), pages 182-190.
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    Cited by:

    1. Wilton, Peter R. & Baduel, Pierre & Landon, Matthieu M. & Wakeley, John, 2017. "Population structure and coalescence in pedigrees: Comparisons to the structured coalescent and a framework for inference," Theoretical Population Biology, Elsevier, vol. 115(C), pages 1-12.
    2. 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.

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