Exact results for fixation probability of bithermal evolutionary graphs

TL;DR

This paper derives exact fixation probabilities for a broad class of structured populations called bithermal evolutionary graphs, advancing understanding of evolutionary dynamics in geographically structured communities.

Contribution

It introduces a novel analytical method using Probability Generating Functions to compute exact fixation probabilities for bithermal evolutionary graphs.

Findings

Exact fixation probabilities are derived for bithermal graphs.

The method simplifies analysis of complex structured populations.

Provides a new tool for evolutionary graph theory studies.

Abstract

One of the most fundamental concepts of evolutionary dynamics is the "fixation" probability, i.e. the probability that a mutant spreads through the whole population. Most natural communities are geographically structured into habitats exchanging individuals among each other and can be modeled by an evolutionary graph (EG), where directed links weight the probability for the offspring of one individual to replace another individual in the community. Very few exact analytical results are known for EGs. We show here how by using the techniques of the fixed point of Probability Generating Function, we can uncover a large class of of graphs, which we term bithermal, for which the exact fixation probability can be simply computed.