POPULATION-DYNAMICS WITH SEQUENTIAL DENSITY-DEPENDENCIES

We analyse the importance of sequential density-dependent processes to population dynamics of single species. We divide a year into several processes of density-dependent reproduction and/or mortality. A sequen ce of n processes can be arranged in n! different sequences. However, only (n - 1)! of these represent unique relative orderings that have d ifferent stability properties and dynamics. Models with several sequen tial density-dependent processes have a much wider repertoire of dynam ics than, e.g., ordinary models based on the logistic equation. Stable equilibrium density and the maximum density of cycles and unstable dy namics do not necessarily increase with increasing b (maximum per capi ta birth rate). The maps of density at time t + 1 (x(t+1)) versus dens ity at time t (x(t)) can have more than one hump, i.e., be bi- or mult imodal. with multiple equilibria. In this type of system, chaos is not the only inevitable outcome of increased b. Instead stable equilibriu m and/or periodic solutions may occur beyond the chaotic region as b i ncreases. It is suggested that this type of model may apply to many ki nds of organisms in seasonal environments. The explicit consideration of sequential density-dependence may be of critical importance for res ource and conservation managers, to avoid switches between multiple eq uilibria or extinction due to poorly timed harvest or pest control.