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Fixation dynamics on hypergraphs

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  • Ruodan Liu
  • Naoki Masuda

Abstract

Hypergraphs have been a useful tool for analyzing population dynamics such as opinion formation and the public goods game occurring in overlapping groups of individuals. In the present study, we propose and analyze evolutionary dynamics on hypergraphs, in which each node takes one of the two types of different but constant fitness values. For the corresponding dynamics on conventional networks, under the birth-death process and uniform initial conditions, most networks are known to be amplifiers of natural selection; amplifiers by definition enhance the difference in the strength of the two competing types in terms of the probability that the mutant type fixates in the population. In contrast, we provide strong computational evidence that a majority of hypergraphs are suppressors of selection under the same conditions by combining theoretical and numerical analyses. We also show that this suppressing effect is not explained by one-mode projection, which is a standard method for expressing hypergraph data as a conventional network. Our results suggest that the modeling framework for structured populations in addition to the specific network structure is an important determinant of evolutionary dynamics, paving a way to studying fixation dynamics on higher-order networks including hypergraphs.Author summary: Evolutionary dynamics describes spreading and competition of different types of individuals in a population. Prior research has revealed that the population structure, which is typically modeled by networks, is a key factor that affects evolutionary dynamics. Hypergraphs are a generalization of networks and model a set of groups in a population in which a group can involve more than two individuals who simultaneously interact, differently from conventional networks. In the present study, we ask a key question: do hypergraphs yield evolutionary dynamics that are drastically different from those on conventional networks? We have found that the hypergraphs that we have examined are suppressors of natural selection, which discounts the strength of the stronger type towards neutrality. This result is surprising because most conventional networks are amplifiers of natural selection, which magnifies the strength of the stronger type, under the same conditions. Our results suggest that how we model population structure in addition to the specific network structure is an important determinant of evolutionary dynamics.

Suggested Citation

  • Ruodan Liu & Naoki Masuda, 2023. "Fixation dynamics on hypergraphs," PLOS Computational Biology, Public Library of Science, vol. 19(9), pages 1-24, September.
    • Handle: RePEc:plo:pcbi00:1011494
    DOI: 10.1371/journal.pcbi.1011494
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    References listed on IDEAS

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    1. 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.
    2. Francisco C. Santos & Marta D. Santos & Jorge M. Pacheco, 2008. "Social diversity promotes the emergence of cooperation in public goods games," Nature, Nature, vol. 454(7201), pages 213-216, July.
    3. repec:plo:pone00:0136497 is not listed on IDEAS
    4. Hisashi Ohtsuki & Christoph Hauert & Erez Lieberman & Martin A. Nowak, 2006. "A simple rule for the evolution of cooperation on graphs and social networks," Nature, Nature, vol. 441(7092), pages 502-505, May.
    5. Yunming Xiao & Bin Wu, 2019. "Close spatial arrangement of mutants favors and disfavors fixation," PLOS Computational Biology, Public Library of Science, vol. 15(9), pages 1-20, September.
    6. Benjamin Allen & Christine Sample & Patricia Steinhagen & Julia Shapiro & Matthew King & Timothy Hedspeth & Megan Goncalves, 2021. "Fixation probabilities in graph-structured populations under weak selection," PLOS Computational Biology, Public Library of Science, vol. 17(2), pages 1-25, February.
    7. Erez Lieberman & Christoph Hauert & Martin A. Nowak, 2005. "Evolutionary dynamics on graphs," Nature, Nature, vol. 433(7023), pages 312-316, January.
    8. S. S. Askar & A. A. Karawia, 2015. "On Solving Pentadiagonal Linear Systems via Transformations," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-9, March.
    9. Laura Hindersin & Arne Traulsen, 2015. "Most Undirected Random Graphs Are Amplifiers of Selection for Birth-Death Dynamics, but Suppressors of Selection for Death-Birth Dynamics," PLOS Computational Biology, Public Library of Science, vol. 11(11), pages 1-14, November.
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