In chapters 3 and 4, I present the analysis of a simple model for the competition between different ages at reproduction of Pacific salmon, focusing on the situation that the resident population numbers have converged to one of several low-periodic attractors. These different local attractors of the resident population dynamics can have different invasion properties.
Well-timed mutant strategies are able to sample the periodically varying environment more efficiently than the resident, and invade successfully when the resident is in certain attractors, whereas they cannot invade in the other attractors. When the mutants are inferior to the resident, in the sense that they have lower viability and/or fertility, they still can invade successfully, provided that the amplitude of the oscillations is high enough. Successful invasion can lead to resonance-mediated co-existence of resident and invader, even if the invader is very inferior to the resident. This also depends on the amplitude of the oscillations, and is impossible when the population is in steady state. On the other hand, for mutants that are less inferior to the resident, successful invasion by a mutant strategy from one attractor will inevitably be followed by extinction of the former invader and concurrent re-establishment of the resident. The expulsion of the invader is accompanied by an invasion-induced attractor switch, or phase shift, of the population dynamics. I call this phenomenon ``the resident strikes back''. In other words, the invader seems to dig its own grave and the resident strategy is invasible, yet invincible by these mutants. After the resident has struck back, other mutants can successfully invade again. It is only on a longer time-scale that this might lead to an intermittent co-existence of superior resident and inferior mutant 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 co-existence. The interplay of population- and adaptive dynamics might yield wrong predictions about the outcome of competition when based on a steady-state analysis.