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Limits on amplifiers of natural selection under death-Birth updating

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  • Josef Tkadlec
  • Andreas Pavlogiannis
  • Krishnendu Chatterjee
  • Martin A Nowak

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 bounded and 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⋆ such that the population structure ceases to amplify selection if the mutant fitness advantage r is larger than r⋆. Finally, we also extend the above results to δ-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 δ. These results demonstrate that amplification of natural selection depends on the specific mechanisms of the evolutionary process.Author summary: Extensive literature exists on amplifiers of natural selection for the Birth-death Moran process, but no amplifiers are known for the death-Birth Moran process. Here we show that if amplifiers exist under death-Birth updating, they must be bounded and transient. Boundedness implies weak amplification, and transience implies amplification for only a limited range of the mutant fitness advantage. These results demonstrate that amplification depends on the specific mechanisms of the evolutionary process.

Suggested Citation

  • Josef Tkadlec & Andreas Pavlogiannis & Krishnendu Chatterjee & Martin A Nowak, 2020. "Limits on amplifiers of natural selection under death-Birth updating," PLOS Computational Biology, Public Library of Science, vol. 16(1), pages 1-13, January.
    • Handle: RePEc:plo:pcbi00:1007494
    DOI: 10.1371/journal.pcbi.1007494
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    References listed on IDEAS

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    Cited by:

    1. Mark Broom & Igor V. Erovenko & Jan Rychtář, 2021. "Modelling Evolution in Structured Populations Involving Multiplayer Interactions," Dynamic Games and Applications, Springer, vol. 11(2), pages 270-293, June.
    2. Benjamin Allen & Christine Sample & Robert Jencks & James Withers & Patricia Steinhagen & Lori Brizuela & Joshua Kolodny & Darren Parke & Gabor Lippner & Yulia A Dementieva, 2020. "Transient amplifiers of selection and reducers of fixation for death-Birth updating on graphs," PLOS Computational Biology, Public Library of Science, vol. 16(1), pages 1-20, January.
    3. Kamran Kaveh & Alex McAvoy & Krishnendu Chatterjee & Martin A Nowak, 2020. "The Moran process on 2-chromatic graphs," PLOS Computational Biology, Public Library of Science, vol. 16(11), pages 1-18, November.

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