There is rich literature on using continuous-time and discrete-time models for studying population dynamics of consumer-resource interactions. The continuous-time framework is generally used to model populations with overlapping generations and all year-round reproduction. In contrast, discrete-time models are more suited for populations with non-overlapping generations that reproduce in a discrete pulse determined by season. Inspired by the Nicholson-Bailey/Lotka-Volterra modeling formalisms in discrete-time/continuous-time, respectively, we consider host-parasitoid interactions with an arbitrary parasitoid attack rate that is a function of both the host and parasitoid population densities. We characterize and compare stability regimes in both modeling frameworks for analogous host reproduction and attack rates. Our analysis shows that a Type II functional response is stabilizing in both modeling frameworks only when combined with other mechanisms, such as mutual interference between parasitoids. This stability regime related to a Type II functional response is smaller in the discrete-time framework compared to continuous-time, and shrinks with increasing host reproduction. A Type III functional response is by itself stabilizing, but the extent of attack-rate acceleration needed is much higher in the discrete-time framework, and its stability regime expands with increasing host reproduction. Finally, our results show that while mutual parasitoid interference can stabilize population dynamics, cooperation between parasitoids to handle hosts is destabilizing in both frameworks. However, a combination of a Type III functional response together with parasitoid cooperation can create stability. In summary, our comparative analysis systematically characterizes diverse ecological processes driving stable population dynamics in discrete-time and continuous-time consumer-resource models.
Analytical Discrete-Time Models of Insect Population Dynamics
