# An evolutionary model that satisfies detailed balance

## TL;DR

This paper introduces a class of evolutionary models with exchangeable breeding and fitness-based selection, enabling explicit analysis of mutation-selection equilibrium and phase transitions as population size grows.

## Contribution

It presents a novel evolutionary model framework where the stationary distribution can be explicitly derived and studied, including phase transition phenomena.

## Key findings

- Explicit stationary distribution derived
- Phase transition theorems proved
- Behavior analyzed as population size increases

## 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.