Moran-type bounds for the fixation probability in a frequency-dependent Wright-Fisher model

TL;DR

This paper derives bounds on the probability that an advantageous group will fixate in a finite population under frequency-dependent Wright-Fisher dynamics, providing insights into invasion and fixation times.

Contribution

It introduces Moran-type bounds for fixation probabilities in a frequency-dependent Wright-Fisher model, including exact results in the infinite population limit.

Findings

Lower and upper bounds for fixation probability under strong selection

Exact fixation probability for a single mutant in infinite populations

Asymptotically sharp bounds for fixation time distribution

Abstract

We study stochastic evolutionary game dynamics in a population of finite size. Individuals in the population are divided into two dynamically evolving groups. The structure of the population is formally described by a Wright-Fisher type Markov chain with a frequency dependent fitness. In a strong selection regime that favors one of the two groups, we obtain qualitatively matching lower and upper bounds for the fixation probability of the advantageous population. In the infinite population limit we obtain an exact result showing that a single advantageous mutant can invade an infinite population with a positive probability. We also give asymptotically sharp bounds for the fixation time distribution.