The effects of evolution on the stability of competing species
| Autor: | S. Elaydi, Y. Kang, R. Luís |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Journal of Biological Dynamics, Vol 16, Iss 1, Pp 816-839 (2022) |
| Druh dokumentu: | article |
| ISSN: | 17513758 1751-3766 1751-3758 |
| DOI: | 10.1080/17513758.2022.2154860 |
| Popis: | Based on evolutionary game theory and Darwinian evolution, we propose and study discrete-time competition models of two species where at least one species has an evolving trait that affects their intra-specific, but not their inter-specific competition coefficients. By using perturbation theory, and the theory of the limiting equations of non-autonomous discrete dynamical systems, we obtain global stability results. Our theoretical results indicate that evolution may promote and/or suppress the stability of the coexistence equilibrium depending on the environment. This relies crucially on the speed of evolution and on how the intra-specific competition coefficient depends on the evolving trait. In general, equilibrium destabilization occurs when [Formula: see text], when the speed of evolution is sufficiently slow. In this case, we conclude that evolution selects against complex dynamics. However, when evolution proceeds at a faster pace, destabilization can occur when [Formula: see text]. In this case, if the competition coefficient is highly sensitive to changes in the trait v, destabilization and complex dynamics occur. Moreover, destabilization may lead to either a period-doubling bifurcation, as in the non-evolutionary Ricker equation, or to a Neimark-Sacker bifurcation. |
| Databáze: | Directory of Open Access Journals |
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