An Evolutionary Model that Satisfies Detailed Balance

Jüri Lember () and Chris Watkins
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Jüri Lember: University of Tartu
Chris Watkins: Royal Holloway, University of London

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 1, 1-37

Abstract: 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.

Keywords: Markov chain Monte Carlo; Dirichlet distribution; De Finetti theorem; Weak convergence of probability measures; Moran model; 60J10; 60B10 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11009-020-09835-5

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