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Invading the ideal free distribution

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  • 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.
    Mathematics Subject Classification: Primary: 35K57; Secondary: 92D25.

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