DELAYED MATURATION IN TEMPORALLY STRUCTURED POPULATIONS WITH NONEQUILIBRIUM DYNAMICS

In this paper we study the evolutionary dynamics of delayed maturation in semelparous individuals. We model this in a two-stage clonally rep roducing population subject to density-dependent fertility. The popula tion dynamical model allows multiple - cyclic and/or chaotic - attract ors, thus allowing us to illustrate how (i) evolutionary stability is primarily a property of a population dynamical system as a whole, and (ii) that the evolutionary stability of a demographic strategy by nece ssity derives from the evolutionary stability of the stationary popula tion dynamical systems it can engender, i.e., its associated populatio n dynamical attractors. Our approach is based on numerically estimatin g invasion exponents or ''mutant fitnesses''. The invasion exponent is defined as the theoretical long-term average relative growth rate of a population of mutants in the stationary environment defined by a res ident population system. For some combinations of resident and mutant trait values, we have to consider multi-valued invasion exponents, whi ch makes the evolutionary argument more complicated (and more interest ing) than is usually envisaged. Multi-valuedness occurs (i) when more than one attractor is associated with the values of the residents' dem ographic parameters, or (ii) when the setting of the mutant parameters makes the descendants of a single mutant reproduce exclusively either in even or in odd years, so that a mutant population is affected by e ither subsequence of the fluctuating resident densities only. Non-equi librium population dynamics or random environmental noise selects for strategists with a non-zero probability to delay maturation. When ther e is an evolutionarily attracting pair of such a strategy and a popula tion dynamical attractor engendered by it, this delaying probability i s a Continuously Stable Strategy, that is an Evolutionarily Unbeatable Strategy which is also Stable in a long term evolutionary sense. Popu lation dynamical coexistence of delaying and non-delaying strategists is possible with non-equilibrium dynamics, but adding random environme ntal noise to the model destroys this coexistence. Adding random noise also shifts the CSS towards a higher probability of delaying maturati on.