At the other end of the spectrum are predator-dependent attack rates. That initially accelerates with increasing prey density and then saturates to 1/ T h. The steady-state prey and predator equilibrium densities corresponding to the Lotka-Volterra model (1) are given by Once fully developed, the parasitoid emerges from the dead host to repeat the life cycle. The egg hatches into a juvenile parasitoid that develops within the host by eating it from the inside out. In a typical interaction, parasitoid wasps search and attack their host insect species by laying an egg within the body of the host. In addition to predator-prey systems, ecological examples of such dynamics include host-parasitoid interactions that have tremendous application in biological control of pest species. Predators consume prey with a constant rate f that we refer to as the attack rate, and each attacked prey leads to a new predator. Here r represents the prey’s growth rate and h( t) grows exponentially over time in the absence of the predator. Moreover, these mechanisms can have contrasting consequences on population density fluctuations, with predator-dependent attack rates amplifying stochasticity, while prey-dependent attack rates countering to buffer fluctuations.Ĭaptures the dynamics of a predator-prey system, where h( t) and p( t) are the average population densities (number of individuals per unit area) of the prey, and the predator at time t. In summary, stochastic dynamics of nonlinear Lotka-Volterra models can be harnessed to infer density-dependent mechanisms regulating predator-prey interactions. Interestingly, our systematic study of the predator-prey correlations reveals distinct signatures depending on the form of the density-dependent attack rate. In contrast, these fluctuations vary non-monotonically with the sensitivity of the attack rate to the predator density with an optimal level of sensitivity minimizing the magnitude of fluctuations. Analysis shows that increasing the sensitivity of the attack rate to the prey density attenuates the magnitude of stochastic fluctuations in the population densities. Here, we consider a stochastic formulation of the Lotka-Volterra model where the prey’s reproduction rate is a random process, and the predator’s attack rate depends on both the prey and predator population densities. While the Lotka-Volterra predator-prey model predicts a neutrally stable equilibrium with oscillating population densities, a density-dependent predator attack rate is known to stabilize the equilibrium. The interaction between a consumer (such as, a predator or a parasitoid) and a resource (such as, a prey or a host) forms an integral motif in ecological food webs, and has been modeled since the early 20 th century starting from the seminal work of Lotka and Volterra.
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