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An Evolutionary Model that Satisfies Detailed Balance

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  • Jüri Lember

    (University of Tartu)

  • Chris Watkins

    (Royal Holloway, University of London)

Abstract

We propose a class of evolution models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and after that a genome is removed according to the selection scheme that involves fitness. Thus, the population size remains constant. The process evolves according to a Markov chain, and, unlike in many other existing models, the stationary distribution – so called mutation-selection equilibrium – can easily found and studied. As a special case our model contains a (sub) class of Moran models. The behaviour of the stationary distribution when the population size increases is our main object of interest. Several phase-transition theorems are proved.

Suggested Citation

  • Jüri Lember & Chris Watkins, 2022. "An Evolutionary Model that Satisfies Detailed Balance," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 1-37, March.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:1:d:10.1007_s11009-020-09835-5
    DOI: 10.1007/s11009-020-09835-5
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    References listed on IDEAS

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    1. Vogl, Claus & Clemente, Florian, 2012. "The allele-frequency spectrum in a decoupled Moran model with mutation, drift, and directional selection, assuming small mutation rates," Theoretical Population Biology, Elsevier, vol. 81(3), pages 197-209.
    2. Etheridge, A.M. & Griffiths, R.C., 2009. "A coalescent dual process in a Moran model with genic selection," Theoretical Population Biology, Elsevier, vol. 75(4), pages 320-330.
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