We investigate the interplay of population dynamics and adaptive dynamics v
ia the timing of reproduction, in the context of a caricatural discrete-tim
e model. We find that semelparity can cause co-existence of different popul
ation-dynamical attractors and that resonance of lifespan relative to popul
ation-dynamical fluctuations can have a profound effect on invasibility and
the resulting evolutionarily stable life-history. Different local attracto
rs of the resident population dynamics can have different invasion properti
es. Successful invasion in one attractor can be followed by extinction of t
he former invader, ultimately leading the resident to the same attractor, b
ut phase-shifted, or to another attractor. So a strategy can be 'invasible,
yet invincible'. In addition, our analysis emphasizes that, for a fluctuat
ing population, one must carefully distinguish between polymorphisms and mi
xed strategies.