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Coalescent models derived from birth–death processes

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  • Crespo, Fausto F.
  • Posada, David
  • Wiuf, Carsten

Abstract

A coalescent model of a sample of size n is derived from a birth–death process that originates at a random time in the past from a single founder individual. Over time, the descendants of the founder evolve into a population of large (infinite) size from which a sample of size n is taken. The parameters and time of the birth–death process are scaled in N0, the size of the present-day population, while letting N0→∞, similarly to how the standard Kingman coalescent process arises from the Wright–Fisher model. The model is named the Limit Birth–Death (LBD) coalescent model. Simulations from the LBD coalescent model with sample size n are computationally slow compared to standard coalescent models. Therefore, we suggest different approximations to the LBD coalescent model assuming the population size is a deterministic function of time rather than a stochastic process. Furthermore, we introduce a hybrid LBD coalescent model, that combines the exactness of the LBD coalescent model model with the speed of the approximations.

Suggested Citation

  • Crespo, Fausto F. & Posada, David & Wiuf, Carsten, 2021. "Coalescent models derived from birth–death processes," Theoretical Population Biology, Elsevier, vol. 142(C), pages 1-11.
    • Handle: RePEc:eee:thpobi:v:142:y:2021:i:c:p:1-11
    DOI: 10.1016/j.tpb.2021.09.003
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    References listed on IDEAS

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    1. Ignatieva, Anastasia & Hein, Jotun & Jenkins, Paul A., 2020. "A characterisation of the reconstructed birth–death process through time rescaling," Theoretical Population Biology, Elsevier, vol. 134(C), pages 61-76.
    2. Wiuf, Carsten, 2018. "Some properties of the conditioned reconstructed process with Bernoulli sampling," Theoretical Population Biology, Elsevier, vol. 122(C), pages 36-45.
    3. Lambert, Amaury & Stadler, Tanja, 2013. "Birth–death models and coalescent point processes: The shape and probability of reconstructed phylogenies," Theoretical Population Biology, Elsevier, vol. 90(C), pages 113-128.
    4. Burden, Conrad J. & Soewongsono, Albert C., 2019. "Coalescence in the diffusion limit of a Bienaymé–Galton–Watson branching process," Theoretical Population Biology, Elsevier, vol. 130(C), pages 50-59.
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