Limits on amplifiers of natural selection under death-Birth updating

Abstract

The fixation probability of a single mutant invading a population of residents is among the most widely-studied quantities in evolutionary dynamics. Amplifiers of natural selection are population structures that increase the fixation probability of advantageous mutants, compared to well-mixed populations. Extensive studies have shown that many amplifiers exist for the Birth-death Moran process, some of them substantially increasing the fixation probability or even guaranteeing fixation in the limit of large population size. On the other hand, no amplifiers are known for the death-Birth Moran process, and computer-assisted exhaustive searches have failed to discover amplification. In this work we resolve this disparity, by showing that any amplification under death-Birth updating is necessarily \emph{bounded} and \emph{transient}. Our boundedness result states that even if a population structure does amplify selection, the resulting fixation probability is close to that of the well-mixed population. Our transience result states that for any population structure there exists a threshold $r^{\ast }$ such that the population structure ceases to amplify selection if the mutant fitness advantage $r$ is larger than $r^{\star }$. Finally, we also extend the above results to $\delta$-death-Birth updating, which is a combination of Birth-death and death-Birth updating. On the positive side, we identify population structures that maintain amplification for a wide range of values $r$ and $\delta$. These results demonstrate that amplification of natural selection depends on the specific mechanisms of the evolutionary process.

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Cited by in corpus (17)

• Evolution of cooperation with asymmetric social interactions
• Fixation probabilities in evolutionary dynamics under weak selection
• Toward a universal model for spatially structured populations
• Transient amplifiers of selection and reducers of fixation for death-Birth updating on graphs
• Evolution of cooperation under a generalized death-birth process
• Frequent asymmetric migrations suppress natural selection in spatially structured populations
• Mutant fate in spatially structured populations on graphs: connecting models to experiments
• Evolution of cooperation in deme-structured populations on graphs
• The Moran process on 2-chromatic graphs
• Fixation dynamics on hypergraphs
• Fixation probability in evolutionary dynamics on switching temporal networks
• Evolutionary graph theory derived from eco-evolutionary dynamics
• Effect of the degree of an initial mutant in Moran processes in structured populations
• Fixation times on directed graphs
• Maintaining diversity in structured populations
• Constant-selection evolutionary dynamics on weighted networks
• Constructing transient amplifiers for death-Birth updating: A case study of cubic and quartic regular graphs