Fixation dynamics on hypergraphs

TL;DR

This paper investigates how hypergraph structures influence evolutionary fixation dynamics, revealing that most hypergraphs suppress natural selection, contrasting with traditional networks which typically amplify it.

Contribution

The study introduces a novel analysis of evolutionary dynamics on hypergraphs, demonstrating their tendency to suppress selection and showing this effect is not due to one-mode projection.

Findings

Most hypergraphs are suppressors of selection.

Suppression effect is not explained by one-mode projection.

Hypergraph structure significantly influences fixation probabilities.

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.