文章基本信息

标题：Evolutionary dynamics and strong Allee effects
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作者：J. M. Cushing ; Jarred T. Hudson
期刊名称：Journal of Biological Dynamics
印刷版ISSN：1751-3758
电子版ISSN：1751-3766
出版年度：2012
卷号：6
期号：2
页码：941-958
DOI：10.1080/17513758.2012.697196
出版社：Taylor & Francis
摘要：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.
关键词：population dynamics; Allee effects; evolution; evolutionary game theory; ESS