Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Invading the ideal free distribution

Pages: 3219 - 3244, Volume 19, Issue 10, December 2014      doi:10.3934/dcdsb.2014.19.3219

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King-Yeung Lam - Department of Mathematics, Ohio State University, Columbus, OH 43210, United States (email)
Daniel Munther - Department of Mathematics, Cleveland State University, Cleveland, OH 44115, United States (email)

Abstract: Recently, the ideal free dispersal strategy has been proven to be evolutionarily stable in the spatially discrete as well as continuous setting. That is, at equilibrium a species adopting the strategy is immune against invasion by any species carrying a different dispersal strategy, other conditions being held equal. In this paper, we consider a two-species competition model where one of the species adopts an ideal free dispersal strategy, but is penalized by a weak Allee effect. We will show rigorously in this case that the ideal free disperser is invasible by a range of non-ideal free strategies, illustrating the trade-off between the advantage of being an ideal free disperser and the setback caused by the weak Allee effect. Moreover, an integral criterion is given to determine the stability/instability of one of the semi-trivial steady states, which is always linearly neutrally stable due to the degeneracy caused by the weak Allee effect.

Keywords:  Dispersal, competition exclusion, weak Allee effect, reaction-diffusion-advection, ideal free distribution.
Mathematics Subject Classification:  Primary: 35K57; Secondary: 92D25.

Received: August 2013;      Revised: September 2013;      Available Online: October 2014.