S.D. Mylius, M. Doebeli & O. Diekmann, 1999. To appear in: U. Dieckmann & J.A.J. Metz (eds.), Elements of Adaptive Dynamics. Cambridge University Press, Cambridge, U.K.
In this chapter, we study invasibility and evolutionary stability under the condition that population dynamics do not lead to a steady state. We analyze two example models to do this. The first example deals with a temporally structured population, and studies the timing of reproduction of semelparous individuals. The second one considers a spatially structured population, and studies the rate of dispersal in a metapopulation. In both systems several population dynamic attractors can coexist. These attractors, which can be periodic and/or chaotic, can have different invasion properties. Moreover, successful invasion by a mutant strategy from one attractor can be followed by extinction of the former invader, caused by a switch of the resident system to another attractor. In other words, the resident strategy is ``invasible, yet unbeatable''. We discuss how this phenomenon of resilience relates to the theory of Adaptive Dynamics developed so far.
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