Reproductive value in graph-structured populations

Publication Date

1-7-2014

Document Type

Article

Publication Title

Journal of Theoretical Biology

Volume

340

DOI

10.1016/j.jtbi.2013.09.032

First Page

285

Last Page

293

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 translate 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.

Keywords

Fixation probability, Evolutionary graph theory, Evolutionary game theory, Reproductive value

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Department

Mathematics and Statistics

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