Fixation dynamics on hypergraphs

Ruodan Liu and Naoki Masuda

PLOS Computational Biology, 2023, vol. 19, issue 9, 1-24

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.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pcbi00:1011494

DOI: 10.1371/journal.pcbi.1011494

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