Modelling functional shifts in two-species hypercycles
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Author(s)
Bassols, Bernat
Fontich, Ernest
Oro, Daniel
Alonso, David
Sardanyés, Josep
Type
Journal Article
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.
Date Issued
2021-08
Date Acceptance
2021-07-23
Citation
Mathematics, 2021, 9 (15)
ISSN
2227-7390
Publisher
MDPI AG
Journal / Book Title
Mathematics
Volume
9
Issue
15
Copyright Statement
© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
License URL
Identifier
http://dx.doi.org/10.3390/math9151809
Publication Status
Published
Article Number
1809
Date Publish Online
2021-07-30