The effects of endogenous ecological memory on population stability and resilience in a variable environment

Abstract

Endogenous ecological memory (EEM) refers to the phenomenon where past states of a system (i.e. population density) can influence present states. In this paper, we address the effects of EEM on qualitative changes in population dynamics over time. The goal was to determine the effects of EEM on the stability and resilience of a population. Since natural populations do not live in isolation, we analyze the discrete-time Ricker model S t+1 = S t exp ( R) exp (− RS t / K) with environmental stochasticity. We explore the model when time-delays are restricted to the density-dependent exp( −RS t / K) component of the model and lognormal multiplicative noise is incorporated as well. Simulation results show that population stability, as measured by the standard deviation of population density about the carrying capacity, decreases as the duration of EEM increases. We observe boom–bust cycles in population density for significantly long time-delays in density-dependence. These cycles become more extreme as the regulating effects of density-dependence are increasingly delayed, resulting in decreased population stability. Simulation results also show that population resilience, as measured by the return time to equilibrium after perturbation ( T r), decrease with increasing fecundity R in a pattern that differs from the predictions of some theoretical work where memory is absent. Finally, the presence of environmental stochasticity changes the resilience properties of the model, relative to the equivalent noise-free model.