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Most Undirected Random Graphs Are Amplifiers of Selection for Birth-Death Dynamics, but Suppressors of Selection for Death-Birth Dynamics

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  • Laura Hindersin
  • Arne Traulsen

Abstract

We analyze evolutionary dynamics on graphs, where the nodes represent individuals of a population. The links of a node describe which other individuals can be displaced by the offspring of the individual on that node. Amplifiers of selection are graphs for which the fixation probability is increased for advantageous mutants and decreased for disadvantageous mutants. A few examples of such amplifiers have been developed, but so far it is unclear how many such structures exist and how to construct them. Here, we show that almost any undirected random graph is an amplifier of selection for Birth-death updating, where an individual is selected to reproduce with probability proportional to its fitness and one of its neighbors is replaced by that offspring at random. If we instead focus on death-Birth updating, in which a random individual is removed and its neighbors compete for the empty spot, then the same ensemble of graphs consists of almost only suppressors of selection for which the fixation probability is decreased for advantageous mutants and increased for disadvantageous mutants. Thus, the impact of population structure on evolutionary dynamics is a subtle issue that will depend on seemingly minor details of the underlying evolutionary process.Author Summary: Evolutionary dynamics describes the spread of individuals with different features within a population. This spreading process can be strongly influenced by the population structure—if a highly successful individual can only displace a few neighbors, it may take more time to spread than an individual that can displace all other individuals from the population. In particular, a population structure can also amplify the evolutionary success of a type. We show that almost all random population structures lead to such an amplification. However, if we change a presumably minor detail of the evolutionary model, almost all random population structures have the opposite effect and suppress the evolutionary success of a type. Thus, it is crucial to consider the underlying assumptions of such models when discussing their possible implications for real biological systems.

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  • 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.
    • Handle: RePEc:plo:pcbi00:1004437
    DOI: 10.1371/journal.pcbi.1004437
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    2. Szolnoki, Attila & Danku, Zsuzsa, 2018. "Dynamic-sensitive cooperation in the presence of multiple strategy updating rules," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 371-377.
    3. 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.
    4. Fernando Alcalde Cuesta & Pablo González Sequeiros & Álvaro Lozano Rojo, 2018. "Evolutionary regime transitions in structured populations," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-18, November.
    5. Li, Xiaopeng & Han, Weiwei & Yang, Wenjun & Wang, Juan & Xia, Chengyi & Li, Hui-jia & Shi, Yong, 2022. "Impact of resource-based conditional interaction on cooperation in spatial social dilemmas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 594(C).
    6. Takesue, Hirofumi, 2019. "Effects of updating rules on the coevolving prisoner’s dilemma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 399-408.
    7. 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.
    8. 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.
    9. Sanz Nogales, Jose M. & Zazo, S., 2020. "Replicator based on imitation for finite and arbitrary networked communities," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    10. Kamran Kaveh & Alex McAvoy & Krishnendu Chatterjee & Martin A Nowak, 2020. "The Moran process on 2-chromatic graphs," PLOS Computational Biology, Public Library of Science, vol. 16(11), pages 1-18, November.
    11. Mahdi Hajihashemi & Keivan Aghababaei Samani, 2022. "Multi-strategy evolutionary games: A Markov chain approach," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-17, February.
    12. Jorge Peña & Bin Wu & Jordi Arranz & Arne Traulsen, 2016. "Evolutionary Games of Multiplayer Cooperation on Graphs," PLOS Computational Biology, Public Library of Science, vol. 12(8), pages 1-15, August.

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