Paper
S.D. Mylius & O. Diekmann, 2001. J. theor. Biol. 211 (4): 297-311
The aim of this paper is two-fold: (a) by way of example, we elucidate the phenomenon of invader-induced switches in a resident attractor; (b) we expose in detail how resonance and phase have a strong impact when semelparous organisms (as, e.g. Pacific salmon) with different life-cycle lengths compete in a self-induced periodically fluctuating environment. We analyse a simple model for the competition between annuals and biennials, focusing on the situation that the annual population in isolation converges to a two-cycle. Well-timed biennial mutants sample the periodically varying environment more efficiently than the annual resident. They can invade successfully even when they are inferior to the resident, in the sense that they have lower viability and/or fertility. Successful invasion can lead to resonance-mediated coexistence if the invader is rather inferior to the resident. Remarkably, for mutants that are less inferior to the resident, successful invasion by a mutant strategy will inevitably be followed by extinction of the former invader and concurrent re-establishment of the resident. The expulsion of the invader is brought about by an invasion-induced phase shift or attractor switch. We call this phenomenon ``the resident strikes back'' and say that the resident strategy is invasible, yet invincible. After the resident has struck back, other mutants can successfully invade again. On a longer time-scale, this might lead to an intermittent occurrence of ultimately inferior strategies. The results show that even in a deterministic setting, successful invasion does not necessarily lead to establishment and that mutual invasibility is not always sufficient for coexistence.
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