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 sequence of n processes can be arranged in n! different sequences. However, only (n - 1)! of these represent unique relative orderings that have different stability properties and dynamics. Models with several sequential density-dependent processes have a much wider repertoire of dynamics than, e.g., ordinary models based on the logistic equation. Stable equilibrium density and the maximum density of cycles and unstable dynamics do not necessarily increase with increasing b (maximum per capita birth rate). The maps of density at time t + 1 (x(t+1)) versus density at time t (x(t)) can have more than one hump, i.e., be bi- or multimodal. with multiple equilibria. In this type of system, chaos is not the only inevitable outcome of increased b. Instead stable equilibrium and/or periodic solutions may occur beyond the chaotic region as b increases. It is suggested that this type of model may apply to many kinds of organisms in seasonal environments. The explicit consideration of sequential density-dependence may be of critical importance for resource and conservation managers, to avoid switches between multiple equilibria or extinction due to poorly timed harvest or pest control.