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Modelling Functional Shifts in Two-Species Hypercycles

Author

Listed:
  • Bernat Bassols

    (Department of Mathematics, Imperial College London, London SW7 2AZ, UK)

  • Ernest Fontich

    (Departament de Matemàtiques i Informàtica, Universitat de Barcelona (UB), Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain)

  • Daniel Oro

    (Theoretical and Computational Ecology Laboratory, Center for Advanced Studies of Blanes (CEAB-CSIC), Accés Cala Sant Francesc 14, 17300 Blanes, Spain)

  • David Alonso

    (Theoretical and Computational Ecology Laboratory, Center for Advanced Studies of Blanes (CEAB-CSIC), Accés Cala Sant Francesc 14, 17300 Blanes, Spain)

  • Josep Sardanyés

    (Centre de Recerca Matemàtica, Edicici C, Campus de Bellatera, 08193 Cerdanyola del Vallès, Spain)

Abstract

Research on hypercycles focuses on cooperative interactions among replicating species, including the emergence of catalytic parasites and catalytic shortcircuits. Further interactions may be expected to arise in cooperative systems. For instance, molecular replicators are subject to mutational processes and ecological species to behavioural shifts due to environmental and ecological changes. Such changes could involve switches from cooperative to antagonistic interactions, in what we call a functional shift . In this article, we investigate a model for a two-member hypercycle model, considering that one species performs a functional shift. First, we introduce the model dynamics without functional shifts to illustrate the dynamics only considering obligate and facultative cooperation. Then, two more cases maintaining cross-catalysis are considered: (i) a model describing the dynamics of ribozymes where a fraction of the population of one replicator degrades the other molecular species while the other fraction still receives catalytic aid; and (ii) a system in which a given fraction of the population predates on the cooperating species while the rest of the population still receives aid. We have characterised the key bifurcation parameters determining extinction, survival, and coexistence of species. We show that predation, regardless of the fraction that benefits from it, does not significantly change dynamics with respect to the degradative case (i), thus conserving dynamics and bifurcations. Their biological significance is interpreted, and their potential implications for the dynamics of early replicators and ecological species are outlined.

Suggested Citation

  • Bernat Bassols & Ernest Fontich & Daniel Oro & David Alonso & Josep Sardanyés, 2021. "Modelling Functional Shifts in Two-Species Hypercycles," Mathematics, MDPI, vol. 9(15), pages 1-22, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:15:p:1809-:d:605276
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    References listed on IDEAS

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    1. Jennifer A. Doudna & Thomas R. Cech, 2002. "The chemical repertoire of natural ribozymes," Nature, Nature, vol. 418(6894), pages 222-228, July.
    2. Stephen C. Votier & Robert W. Furness & Stuart Bearhop & Jonathan E. Crane & Richard W. G. Caldow & Paulo Catry & Kenny Ensor & Keith C. Hamer & Anne V. Hudson & Ellen Kalmbach & Nicholas I. Klomp & S, 2004. "Changes in fisheries discard rates and seabird communities," Nature, Nature, vol. 427(6976), pages 727-730, February.
    3. Bärbel M. R. Stadler & Peter F. Stadler, 2003. "Molecular Replicator Dynamics," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 47-77.
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