Reproductive Value in Graph-structured Populations

TL;DR

This paper integrates Fisher's reproductive value into graph-structured population models, enabling precise calculation of mutant fixation probabilities in complex networks.

Contribution

It introduces reproductive value into evolutionary graph theory, linking individual connectivity to genetic contribution and fixation probabilities.

Findings

Reproductive value varies with individual connectivity in graphs.

Fixation probabilities can be calculated using reproductive value in Moran processes.

The approach bridges population genetics and network theory.

Abstract

Evolutionary graph theory has grown to be an area of intense study. Despite the amount of interest in the field, it seems to have grown separate from other subfields of population genetics and evolution. In the current work I introduce the concept of Fisher's (1930) reproductive value into the study of evolution on graphs. Reproductive value is a measure of the expected genetic contribution of an individual to a distant future generation. In a heterogeneous graph-structured population, differences in the number of connections among individuals translates into differences in the expected number of offspring, even if all individuals have the same fecundity. These differences are accounted for by reproductive value. The introduction of reproductive value permits the calculation of the fixation probability of a mutant in a neutral evolutionary process in any graph-structured population for either the moran birth-death or death-birth process.