Global redistribution and local migration in semi-discrete host–parasitoid population dynamic models

2021

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We model population dynamics of two host species attacked by a common parasitoid using a discrete-time formalism that captures their population densities from year to year. It is well known starting from the seminal work of Nicholson and Bailey that a constant parasitoid attack rate leads to an unstable host-parasitoid interaction. However, a Type III functional response, where the parasitoid attack rate accelerates with increasing host density stabilizes the population dynamics. We first consider a scenario where both host species are attacked by a parasitoid with the same Type III functional response. Our results show that sufficient fast acceleration of the parasitoid attack rate stabilizes the population dynamics of all three species. For two symmetric host species, the extent of acceleration needed to stabilize the three-species equilibrium is exactly the same as that needed for a single host-parasitoid interaction. However, asymmetry can lead to scenarios where the removal of a host species from a stable interaction destabilizes the interaction between the remaining host species and the parasitoid. Next, we consider a situation where one of the host species is attacked at a constant rate (i.e., Type I functional response), and the other species is attacked via a Type III functional response. We identify parameter regimes where a Type III functional response to just one of the host species stabilizes the three species interaction. In summary, our results show that a generalist parasitoid with a Type III functional response to one or many host species can play a key role in stabilizing population dynamics of host-parasitoid communities in apparent competition.

Section: Type III Functional Response Results In a Host-density Dmentioning

confidence: 99%

Population dynamics of multi-host communities attacked by a common parasitoid

2021

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“…To capture such effects of populations changing continuously within the larval stage of each year, a semi-discrete or hybrid formalism has been proposed to mechanistically formulate the corresponding discrete-time model. This semi-discrete approach relies on solving a continuous-time differential equation describing population interaction during the host’s vulnerable stage to derive update functions connecting population densities across consecutive years [20], [34]–[37]. For an attack rate cL m this leads to the model (1) with escape response that depends on both host and parasitoid population densities [20].…”

Section: Stability Arising Through a Type III Functional Responsementioning

confidence: 99%

Fluctuations in population densities inform stability mechanisms in host-parasitoid interactions

2021

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Population dynamics of host-parasitoid interactions has been traditionally studied using a discrete-time formalism starting from the classical work of Nicholson and Bailey. It is well known that differences in parasitism risk among individual hosts can stabilize the otherwise unstable equilibrium of the Nicholson-Bailey model. Here, we consider a stochastic formulation of these discrete-time models, where the host reproduction is a random variable that varies from year to year and drives fluctuations in population densities. Interestingly, our analysis reveals that there exists an optimal level of heterogeneity in parasitism risk that minimizes the extent of fluctuations in the host population density. Intuitively, low variation in parasitism risk drives large fluctuations in the host population density as the system is on the edge of stability. In contrast, high variation in parasitism risk makes the host equilibrium sensitive to the host reproduction rate, also leading to large fluctuations in the population density. Further results show that the correlation between the adult host and parasitoid densities is high for the same year, and gradually decays to zero as one considers cross-species correlations across different years. We next consider an alternative mechanism of stabilizing host-parasitoid population dynamics based on a Type III functional response, where the parasitoid attack rate accelerates with increasing host density. Intriguingly, this nonlinear functional response makes qualitatively different correlation signatures than those seen with heterogeneity in parasitism risk. In particular, a Type III functional response leads to uncorrelated adult and parasitoid densities in the same year, but high cross-species correlation across successive years. In summary, these results argue that the cross-correlation function between population densities contains signatures for uncovering mechanisms that stabilize consumer-resource population dynamics.

“…Similarly, to derive the mean dynamics of the prey’s population density we use m 2 = 1, m 1 = m 3 = 0 to obtain where the right-hand-side now consists of higher-order moments. This problem of unclosed moment dynamics, where the time evolution of lower-order moments depends on higher-order moments has been well described for nonlinear stochastic systems, and often arises in the modeling of biochemical and ecological processes [15], [61]–[77]. Typically, different closure schemes are employed to approximate moment dynamics and we use one such approach known as the Linear Noise Approximation (LNA) [78]–[82].…”

Section: Stochastic Formulation Of the Generalized Lotka-volterra Modelmentioning

confidence: 99%

“…Finally, each predator dies at a rate γ. In addition to predator-prey systems, ecological examples of such consumer-resource dynamics include host-parasitoid interactions that have tremendous application in biological control of pest species [8]–[15]. In a typical interaction, parasitoid wasps search and attack their host insect species by laying an egg within the body of the host.…”

Section: Introductionmentioning

confidence: 99%

Stochastic dynamics of consumer-resource interactions

2021

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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 20th century starting from the seminal work of Lotka and Volterra. 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. 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. Analysis shows that increasing the sensitivity of the attack rate to the prey density attenuates the magnitude of stochastic fluctuations in the population densities. 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. Interestingly, our systematic study of the predator-prey correlations reveals distinct signatures depending on the form of the density-dependent attack rate. In summary, stochastic dynamics of nonlinear Lotka-Volterra models can be harnessed to infer density-dependent mechanisms regulating consumer-resource interactions. 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.