The Evolutionary Optimality of Oscillatory and Chaotic Dynamics in Simple Population Models

Abstract

The problem is considered of whether natural selection favors genotypes characterized by oscillatory or chaotic population dynamics. This is done with reference to two simple one-dimensional models, which display a variety of dynamical patterns according to the different values of their parameters: the semelparous and iteroparous Ricker models. To lind the optimal genotype (or genotypes) within a given feasibility set, the concept of Continuously Stable Strategy (CSS) and a haploid model of competition between genotypes are used. The parameters subject to evolution are the intrinsic finite rate of increase and respectively the juvenile mortality in the semelparous model and the adult survival in the iteroparous one. In the semelparous case a single feasible CSS exists, while in the other case more than one CSS might exist. The dynamical nature of the optimal genotype (stable equilibrium, stable sustained oscillations or chaos) is basically determined by the shape of the set of feasibility for the parameters defining each genotype. However, if the feasibility set is drawn at random, the probability that the corresponding optimal genotype (or genotypes) be oscillatory or chaotic is quite low. This result, however, might not hold with more complex models.