# Wright-fisher-like models with constant population size on average

## TL;DR

This paper introduces a new class of population genetics models where the total population size fluctuates but remains constant on average, analyzing their extinction, fixation, and survival probabilities.

## Contribution

It extends Wright-Fisher models by incorporating average population size conservation through a Galton-Watson process framework, providing new insights into population dynamics.

## Key findings

- Analysis of extinction probabilities
- Results on fixation times and probabilities
- Impact of environmental bottlenecks

## Abstract

We first recall some basic facts from the theory of discrete-time Markov chains arising from two types neutral and non-neutral evolution models of population genetics with constant size. We then define and analyse a version of such models whose fluctuating total population size is conserved on average only. In our model, the population of interest is seen as being embedded in a frame process which is a critical Galton-Watson process. In this context, we address problems such as extinction, fixation, size of the population at fixation and survival probability to a bottleneck effect of the environment. Running title: constant population size on average