期刊
JOURNAL OF BIOLOGICAL DYNAMICS
卷 6, 期 2, 页码 941-958出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/17513758.2012.697196
关键词
population dynamics; Allee effects; evolution; evolutionary game theory; ESS
资金
- NSF [DMS 0917435]
- REU programme by NSF [DMS 0917435]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [917435] Funding Source: National Science Foundation
We describe the dynamics of an evolutionary model for a population subject to a strong Allee effect. The model assumes that the carrying capacity k(u), inherent growth rate r(u), and Allee threshold a(u) are functions of a mean phenotypic trait u subject to evolution. The model is a plane autonomous system that describes the coupled population and mean trait dynamics. We show bounded orbits equilibrate and that the Allee basin shrinks (and can even disappear) as a result of evolution. We also show that stable non-extinction equilibria occur at the local maxima of k(u) and that stable extinction equilibria occur at local minima of r(u). We give examples that illustrate these results and demonstrate other consequences of an Allee threshold in an evolutionary setting. These include the existence of multiple evolutionarily stable, non-extinction equilibria, and the possibility of evolving to a non-evolutionary stable strategy (ESS) trait from an initial trait near an ESS.
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