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Some properties of the conditioned reconstructed process with Bernoulli sampling

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  • Wiuf, Carsten

Abstract

In many areas of genetics it is of relevance to consider a population of individuals that is founded by a single individual in the past. One model for such a scenario is the conditioned reconstructed process with Bernoulli sampling that describes the evolution of a population of individuals that originates from a single individual. Several aspects of this reconstructed process are studied, in particular the Markov structure of the process. It is shown that at any given time in the past, the conditioned reconstructed process behaves as the original conditioned reconstructed process after a suitable time-dependent change of the sampling probability. Additionally, it is discussed how mutations accumulate in a sample of particles. It is shown that random sampling of particles at the present time has the effect of making the mutation rate look time-dependent. Conditions are given under which this sampling effect is negligible. A possible extension of the reconstructed process that allows for multiple founding particles is discussed.

Suggested Citation

  • Wiuf, Carsten, 2018. "Some properties of the conditioned reconstructed process with Bernoulli sampling," Theoretical Population Biology, Elsevier, vol. 122(C), pages 36-45.
    • Handle: RePEc:eee:thpobi:v:122:y:2018:i:c:p:36-45
    DOI: 10.1016/j.tpb.2018.02.003
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    References listed on IDEAS

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    1. Champagnat, Nicolas & Lambert, Amaury, 2012. "Splitting trees with neutral Poissonian mutations I: Small families," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 1003-1033.
    2. 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.
    3. Nicolas Champagnat & Amaury Lambert & Mathieu Richard, 2012. "Birth and Death Processes with Neutral Mutations," International Journal of Stochastic Analysis, Hindawi, vol. 2012, pages 1-20, December.
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    Cited by:

    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. 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.

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