The Moran process on 2-chromatic graphs.

Autor: Kamran Kaveh, Alex McAvoy, Krishnendu Chatterjee, Martin A Nowak
Jazyk: angličtina
Rok vydání: 2020
Předmět:
Zdroj: PLoS Computational Biology, Vol 16, Iss 11, p e1008402 (2020)
Druh dokumentu: article
ISSN: 1553-734X
1553-7358
DOI: 10.1371/journal.pcbi.1008402
Popis: Resources are rarely distributed uniformly within a population. Heterogeneity in the concentration of a drug, the quality of breeding sites, or wealth can all affect evolutionary dynamics. In this study, we represent a collection of properties affecting the fitness at a given location using a color. A green node is rich in resources while a red node is poorer. More colors can represent a broader spectrum of resource qualities. For a population evolving according to the birth-death Moran model, the first question we address is which structures, identified by graph connectivity and graph coloring, are evolutionarily equivalent. We prove that all properly two-colored, undirected, regular graphs are evolutionarily equivalent (where "properly colored" means that no two neighbors have the same color). We then compare the effects of background heterogeneity on properly two-colored graphs to those with alternative schemes in which the colors are permuted. Finally, we discuss dynamic coloring as a model for spatiotemporal resource fluctuations, and we illustrate that random dynamic colorings often diminish the effects of background heterogeneity relative to a proper two-coloring.
Databáze: Directory of Open Access Journals
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