Evolutionary Games on Isothermal Graphs

Abstract

Population structure affects the outcome of natural selection. Static population structures can be described by graphs, where individuals occupy the nodes, and interactions occur along the edges. General conditions for evolutionary success on any weighted graph were recently derived, for weak selection, in terms of coalescence times of random walks. Here we show that for a special class of graphs, the conditions for success take a particularly simple form, in which all effects of graph structure are described by the graph's "effective degree"---a measure of the effective number of neighbors per individual. This result holds for all weighted graphs that are isothermal, meaning that the sum of edge weights is the same at each node. Isothermal graphs encompass a wide variety of underlying topologies, and arise naturally from supposing that each individual devotes the same amount of time to interaction. Cooperative behavior is favored on a large isothermal graph if the benefit-to-cost ratio exceeds the effective degree. We relate the effective degree of a graph to its spectral gap, thereby providing a link between evolutionary dynamics and the theory of expander graphs. As a surprising example, we report graphs of infinite average degree that are nonetheless highly conducive for promoting cooperation.

40 pages, 6 figures

References in corpus (13)

• Emergence of scaling in random networks
• Evolutionary games on graphs
• Structure of Growing Networks: Exact Solution of the Barabasi--Albert's Model
• Organization of Growing Random Networks
• Evolutionary dynamics on any population structure
• Voter Models on Heterogeneous Networks
• Evolutionary dynamics on degree-heterogeneous graphs
• Strategy abundance in 2x2 games for arbitrary mutation rates
• Conjoining uncooperative societies facilitates evolution of cooperation
• The molecular clock of neutral evolution can be accelerated or slowed by asymmetric spatial structure
• Reproductive Value in Graph-structured Populations
• Sharp benefit-to-cost rules for the evolution of cooperation on regular graphs
• A mathematical formalism for natural selection with arbitrary spatial and genetic structure

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• The conflict between self-interaction and updating passivity in the evolution of cooperation
• Uncovering hidden dependency in weighted networks via information entropy
• Fixation probability in evolutionary dynamics on switching temporal networks
• The dual problems of coordination and anti-coordination on random bipartite graphs
• Nash Equilibria in certain two-choice multi-player games played on the ladder graph