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Time to the MRCA of a sample in a Wright–Fisher model with variable population size

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  • WojdyÅ‚a, Tomasz
  • Kimmel, Marek
  • Bobrowski, Adam

Abstract

Determining the expected distribution of the time to the most recent common ancestor of a sample of individuals may deliver important information about the genetic markers and evolution of the population. In this paper, we introduce a new recursive algorithm to calculate the distribution of the time to the most recent common ancestor of the sample from a population evolved by any conditional multinomial sampling model. The most important advantage of our method is that it can be applied to a sample of any size drawn from a population regardless of its size growth pattern. We also present a very efficient method to implement and store the genealogy tree of the population evolved by the Galton–Watson process. In the final section we present results applied to a simulated population with a single bottleneck event and to real populations of known size histories.

Suggested Citation

  • WojdyÅ‚a, Tomasz & Kimmel, Marek & Bobrowski, Adam, 2011. "Time to the MRCA of a sample in a Wright–Fisher model with variable population size," Theoretical Population Biology, Elsevier, vol. 80(4), pages 265-271.
    • Handle: RePEc:eee:thpobi:v:80:y:2011:i:4:p:265-271
    DOI: 10.1016/j.tpb.2011.09.003
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    References listed on IDEAS

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    3. Pfaffelhuber, P. & Wakolbinger, A., 2006. "The process of most recent common ancestors in an evolving coalescent," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1836-1859, December.
    4. Michael Kremer, 1993. "Population Growth and Technological Change: One Million B.C. to 1990," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(3), pages 681-716.
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