Evolutionary graph theory beyond pairwise interactions: higher-order network motifs shape times to fixation in structured populations

Carja, Oana; Yp, Kuo

doi:10.1101/2021.06.26.450017

Cited by 5 publications

(7 citation statements)

References 56 publications

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“…For conventional networks, the time to fixation has been shown to be in a tradeoff relationship with the fixation probability [53][54][55][56][57]. In other words, a strongly amplifying network tends to accompany a large mean fixation time.…”

Section: Discussionmentioning

confidence: 99%

Fixation dynamics on hypergraphs

Liu¹,

Masuda²

2023

Preprint

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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 same dynamics on conventional networks, under the birth-death process and uniform initial conditions, most networks are known to be amplifiers of natural selection, which by definition enhances the difference in the strength of the two completing types in terms of the probability that the mutant type fixates in the population. In contrast, we show that a vast 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.

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Section: Discussionmentioning

confidence: 99%

Fixation dynamics on hypergraphs

Liu¹,

Masuda²

2023

Preprint

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“…For conventional networks, the time to fixation has been shown to be in a tradeoff relationship with the fixation probability [ 61 – 65 ]. In other words, a strongly amplifying network tends to accompany a large mean fixation time.…”

Section: Discussionmentioning

confidence: 99%

Fixation dynamics on hypergraphs

Liu,

Masuda

2023

PLoS Comput Biol

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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.

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“…The prospects of engineering a population structure that can optimize the chances to evolve certain mutations or to observe evolved population structures that minimize the evolution of mutations seem exciting, but these applications call for an extension of the field of evolutionary graph theory: Most applications implicitly assume that each node is a small population, and not all results carry over from graphs of individuals to graphs of subpopulations ( 38 – 41 ). In addition, the field has focused so far on fixation probability and fixation time ( 42 – 49 ).…”

Section: Discussionmentioning

confidence: 99%

Suppressors of fixation can increase average fitness beyond amplifiers of selection

Sharma

Traulsen

2022

Proc. Natl. Acad. Sci. U.S.A.

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Evolutionary dynamics on graphs has remarkable features: For example, it has been shown that amplifiers of selection exist that—compared to an unstructured population—increase the fixation probability of advantageous mutations, while they decrease the fixation probability of disadvantageous mutations. So far, the theoretical literature has focused on the case of a single mutant entering a graph-structured population, asking how the graph affects the probability that a mutant takes over a population and the time until this typically happens. For continuously evolving systems, the more relevant case is that mutants constantly arise in an evolving population. Typically, such mutations occur with a small probability during reproduction events. We thus focus on the low mutation rate limit. The probability distribution for the fitness in this process converges to a steady state at long times. Intuitively, amplifiers of selection are expected to increase the population’s mean fitness in the steady state. Similarly, suppressors of selection are expected to decrease the population’s mean fitness in the steady state. However, we show that another set of graphs, called suppressors of fixation, can attain the highest population mean fitness. The key reason behind this is their ability to efficiently reject deleterious mutants. This illustrates the importance of the deleterious mutant regime for the long-term evolutionary dynamics, something that seems to have been overlooked in the literature so far.

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Evolutionary graph theory beyond pairwise interactions: higher-order network motifs shape times to fixation in structured populations

Cited by 5 publications

References 56 publications

Fixation dynamics on hypergraphs

Fixation dynamics on hypergraphs

Fixation dynamics on hypergraphs

Suppressors of fixation can increase average fitness beyond amplifiers of selection

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