An evolutionary model that satisfies detailed balance
This work provides a theoretical framework for evolutionary biology, offering incremental improvements by enabling easier study of stationary distributions compared to existing models.
The authors tackled the problem of modeling evolutionary dynamics with constant population size, proposing a class of models that maintain detailed balance and allow easy analysis of mutation-selection equilibrium, proving several phase-transition theorems as population size increases.
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.