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The existence and abundance of ghost ancestors in biparental populations

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  • Gravel, Simon
  • Steel, Mike

Abstract

In a randomly-mating biparental population of size N there are, with high probability, individuals who are genealogical ancestors of every extant individual within approximately log2(N) generations into the past. We use this result of J. Chang to prove a curious corollary under standard models of recombination: there exist, with high probability, individuals within a constant multiple of log2(N) generations into the past who are simultaneously (i) genealogical ancestors of each of the individuals at the present, and (ii) genetic ancestors to none of the individuals at the present. Such ancestral individuals–ancestors of everyone today that left no genetic trace–represent ‘ghost’ ancestors in a strong sense. In this short note, we use simple analytical argument and simulations to estimate how many such individuals exist in finite Wright–Fisher populations.

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  • 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.
    • Handle: RePEc:eee:thpobi:v:101:y:2015:i:c:p:47-53
    DOI: 10.1016/j.tpb.2015.02.002
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    1. Derrida, Bernard & Manrubia, Susanna C. & Zanette, Damián H., 2000. "Distribution of repetitions of ancestors in genealogical trees," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 281(1), pages 1-16.
    2. 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.
    3. 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. 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.
    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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