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The effects of evolution on the stability of competing species
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Authors
Advisor(s)
Abstract(s)
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 destabiliza tion occurs when α > 2, when the speed of evolution is sufficiently
slow. In this case, we conclude that evolution selects against com plex dynamics. However, when evolution proceeds at a faster pace,
destabilization can occur when α < 2. 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.
Description
Keywords
Competition models Evolutionary dynamics Traits Local stability Asymptotically autonomous Global stability . Faculdade de Ciências Exatas e da Engenharia
Pedagogical Context
Citation
S. Elaydi, Y. Kang & R. Luís (2022) The effects of evolution on the stability of competing species, Journal of Biological Dynamics, 16:1, 816-839, DOI: 10.1080/17513758.2022.2154860
Publisher
Taylor and Francis