Abstract
Resource pulses are well documented and have important consequences for population dynamics relative to continuous inputs. However, pulses of top-down factors (e.g. predation) are less explored and appreciated in the ecological literature. Here, we use a simple differential equation population model to show how pulsed removals of individuals from a population alter population size relative to continuous dynamics. Pulsed removals result in lower equilibrium population sizes relative to continuous removals, and the differences are greatest at low population growth rates, high removal rates, and with large, infrequent pulses. Furthermore, the timing of the removal pulses (either stochastic or cyclic) affects population size. For example, cyclic removals are less likely than stochastic removals to result in population eradication, but when eradication occurs, the time until eradication is shorter for cyclic than with stochastic removals.
Highlights
Temporal variability in both-bottom up and-top down processes is likely the norm for most ecological systems, yet the consequences of top-down pulses on ecological dynamics are rarely explored
While the effects and interactions of top-down and bottom-up factors have been frequently explored in the ecological literature, the effects of temporal variability have only been well explored from the bottom-up[2,17]
Just as resource pulses affect community dynamics and trophic interactions via changes to growth and reproduction rates[18], prey switches[19], and coexistence among competitors[20], it is likely that variation in prey abundance that results from pulses of predation could have important effects on food web interactions[21,22]
Summary
To explore the effects of pulsed removals on prey population dynamics, we expand on the Schaefer harvest model[13], which is a basic ordinary differential equation (ode) population model (Eq 1) that assumes logistic population growth, where the rate of change in population N (dN/dt) is dN dt. In the case of the discrete removals, δ is a Dirac-delta function with magnitude H that occurs at intervals of γ We compared these three population models using simulations where the same number of individuals were removed from a population and subsequent effects on the mean equilibrium population size was recorded. Less frequent pulses produce the greatest differences between continuous and pulsed removals when population growth rates are low (Fig. 1b) or removal rates are large (Fig. 1c) This relationship is governed by the timing of pulses. While we did not explicitly model continuous removals, cyclic removals over short time intervals are very similar to continuous dynamics (compare pink and green lines at low intervals between pulses in Fig. 1a) as expected, and in eradication simulations, cyclic pulses that are temporally close together (pink dashed lines) approximate continuous removal dynamics. These patterns emerge because stochastic pulses that occur in rapid succession have a larger effect (even accounting for occasional longer recovery times) than episodic pulses that typically allow more recovery (see Supplementary Fig. S2)
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