An evolutionary model that satisfies detailed balance

Jüri Lember; Chris Watkins

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arXiv · 1902.10834

An evolutionary model that satisfies detailed balance

Jüri Lember·Chris Watkins

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Abstract

We propose a class of evolutionary 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 then 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 be easily found and studied. The behaviour of the stationary distribution when the population size increases is our main object of interest. Several phase-transition theorems are proved.

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Jüri Lember, Chris Watkins. 2019-02-27. An evolutionary model that satisfies detailed balance. https://arxiv.org/abs/1902.10834

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