DELAYED DENSITY-DEPENDENCE AND THE STABILITY OF INTERACTING POPULATIONS AND SUBPOPULATIONS

Theoretical investigations of the dynamics of populations with discret e generations have traditionally been based on simple models of the fo rm Nt+1=f[N-t]. However, recent studies of the dynamics of natural pop ulations indicate that density-dependent population regulation probabl y takes place over many generations (Nt+1=f[N-t, Nt-1,...]). In this p aper, explore the stability properties of interacting populations and contrast the predictions of discrete-generation models of population g rowth which do and do not include delayed density dependence. Relative to non-delayed models, inclusion of delayed density dependence change s the shape of population cycles (flip vs Hopf bifurcations) and decre ases the range of parameters which predict stable equilibria. I also e xplore extensions of these models that include interspecific competiti on and coupling of spatially isolated patches. In both cases, delayed density dependence significantly changes the way in which demographic parameters scale to overall dynamics. For example, when delayed densit y dependence does not differ between two species, the asymptotic stabi lity of both species is determined by a weighted average of the popula tion growth rates of the two species. However, when species differ in time delay, some pairs of species that would both exhibit cyclical or chaotic dynamics in isolation can stably coexist. Analogous conclusion s hold for the effects of deterministic spatial environmental variatio n among coupled patches. This implies that inclusion of delayed densit y dependence in investigations of population dynamics can dramatically change the inferences we draw from mathematical models and that furth er investigations of the effects of deterministic differences in demog raphic parameters and of delayed density dependence are warranted. (C) 1997 Academic Press.