Fixation and fluctuations in two-species cooperation

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• dc.contributor.author Piñero, Jordi
• dc.contributor.author Redner, Sidney
• dc.contributor.author Solé Vicente, Ricard, 1962-
• dc.date.accessioned 2022-06-14T06:01:00Z
• dc.date.available 2022-06-14T06:01:00Z
• dc.date.issued 2022
• dc.description.abstract Cooperative interactions pervade in a broad range of many-body populations, such as ecological communities, social organizations, and economic webs. We investigate the dynamics of a population of two equivalent species A and B that are driven by cooperative and symmetric interactions between these species. For an isolated population, we determine the probability to reach fixation, where only one species remains, as a function of the initial concentrations of the two species, as well as the time to reach fixation. The latter scales exponentially with the population size. When members of each species migrate into the population at rate λ and replace a randomly selected individual, surprisingly rich dynamics ensues. Ostensibly, the population reaches a steady state, but the steady-state population distribution undergoes a unimodal to trimodal transition as the migration rate decreases below a critical value λc. In the low-migration regime, λ < λc, the steady state is not truly steady, but instead strongly fluctuates between near-fixation states, where the population consists of mostly A's or of mostly B's. The characteristic time scale of these fluctuations diverges as λ−1. Thus in spite of the cooperative interaction, a typical snapshot of the population will contain almost all A's or almost all B's.
• dc.description.sponsorship The authors thank Deepak Bhat and Jacopo Grilli for fruitful discussions, and Eric A Blair for inspiring ideas. JP and RS were supported by the Botín Foundation and the Spanish Ministry of Economy and Competitiveness through Grant FIS2015-67616-P MINEICO/AEI/FEDER. JP is also supported by 'María de Maeztú' fellowship MDM-2014-0370-17-2. SRs research was supported in part by NSF Grant DMR-1910736. JP and RS thank the hospitality of the Santa Fe Institute, where this project began.
• dc.format.mimetype application/pdf
• dc.identifier.citation Piñero J, Redner S, Solé R. Fixation and fluctuations in two-species cooperation. J Phys Complex. 2022;3(1):015011. DOI: 10.1088/2632-072X/ac52e7
• dc.identifier.doi http://dx.doi.org/10.1088/2632-072X/ac52e7
• dc.identifier.issn 2632-072X
• dc.identifier.uri http://hdl.handle.net/10230/53480
• dc.language.iso eng
• dc.publisher IOP Publishing Ltd.
• dc.relation.ispartof J Phys Complex. 2022;3(1):015011
• dc.relation.projectID info:eu-repo/grantAgreement/ES/1PE/FIS2015-67616-P
• dc.rights © 2022 The Author(s). Published by IOP Publishing Ltd. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri https://creativecommons.org/licenses/by/4.0/
• dc.subject.keyword Fixation
• dc.subject.keyword Extinction
• dc.subject.keyword First passage
• dc.subject.keyword Stochastic processes
• dc.subject.keyword Cooperation
• dc.title Fixation and fluctuations in two-species cooperation
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion