The Moran process on 2-chromatic graphs
Abstract
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Nov 05, 2020
- Source ID
- 10.1371/journal.pcbi.1008402
Entities
People
- Alex McAvoy
- Kamran Kaveh
- Krishnendu Chatterjee
- Martin A. Nowak
Organizations
- Gates Foundation
- Nvidia
- United States Army Research Laboratory