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Amplifiers of selection for the Moran process with both Birth-death and death-Birth updating

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  • Jakub Svoboda
  • Soham Joshi
  • Josef Tkadlec
  • Krishnendu Chatterjee

Abstract

Populations evolve by accumulating advantageous mutations. Every population has some spatial structure that can be modeled by an underlying network. The network then influences the probability that new advantageous mutations fixate. Amplifiers of selection are networks that increase the fixation probability of advantageous mutants, as compared to the unstructured fully-connected network. Whether or not a network is an amplifier depends on the choice of the random process that governs the evolutionary dynamics. Two popular choices are Moran process with Birth-death updating and Moran process with death-Birth updating. Interestingly, while some networks are amplifiers under Birth-death updating and other networks are amplifiers under death-Birth updating, so far no spatial structures have been found that function as an amplifier under both types of updating simultaneously. In this work, we identify networks that act as amplifiers of selection under both versions of the Moran process. The amplifiers are robust, modular, and increase fixation probability for any mutant fitness advantage in a range r ∈ (1, 1.2). To complement this positive result, we also prove that for certain quantities closely related to fixation probability, it is impossible to improve them simultaneously for both versions of the Moran process. Together, our results highlight how the two versions of the Moran process differ and what they have in common.Author summary: The long-term fate of an evolving population depends on its spatial structure. Amplifiers of selection are spatial structures that enhance the probability that a new advantageous mutation propagates through the whole population, as opposed to going extinct. Many amplifiers of selection are known when the population evolves according to the Moran Birth-death updating, and several amplifiers are known for the Moran death-Birth updating. Interestingly, none of the spatial structures that work for one updating seem to work for the other one. Nevertheless, in this work we identify spatial structures that function as amplifiers of selection for both types of updating. We also prove two negative results that suggest that stumbling upon such spatial structures by pure chance is unlikely.

Suggested Citation

  • Jakub Svoboda & Soham Joshi & Josef Tkadlec & Krishnendu Chatterjee, 2024. "Amplifiers of selection for the Moran process with both Birth-death and death-Birth updating," PLOS Computational Biology, Public Library of Science, vol. 20(3), pages 1-12, March.
    • Handle: RePEc:plo:pcbi00:1012008
    DOI: 10.1371/journal.pcbi.1012008
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    References listed on IDEAS

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    1. Erez Lieberman & Christoph Hauert & Martin A. Nowak, 2005. "Evolutionary dynamics on graphs," Nature, Nature, vol. 433(7023), pages 312-316, January.
    2. C. Hadjichrysanthou & M. Broom & J. Rychtář, 2011. "Evolutionary Games on Star Graphs Under Various Updating Rules," Dynamic Games and Applications, Springer, vol. 1(3), pages 386-407, September.
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