Abstract
Population dynamics of host-parasitoid interactions have 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.
Highlights
Population dynamics of host-parasitoid interactions have been traditionally studied using a discrete-time formalism starting from the classical work of Nicholson and Bailey
Discrete-time formalism is a tradition in modeling of hostparasitoid interaction starting from the seminal work of Nicholson and Bailey close to a century ago, and this framework is partly motivated by the univoltine life histories of insects living in the temperate regions of the world
The fact that the simplest Nicholson-Bailey model leads to an unstable interaction with diverging cycles of population densities fueled a rich body of theoretical/experimental work understanding the impact of diverse ecological processes on host-parasitoid population d ynamics[16]
Summary
The first mechanism is when the escape response f (Pt ) only depends on the parasitoid density, and the non-trivial host-parasitoid equilibrium is stable, if and only, if, the equilibrium adult host density is an increasing function of the host reproduction rate R22 This type of stability arises through several related processes, such as, a fraction of the host population being in a refuge (i.e., protected from parasitoid attacks)[16,23], large host-to-host difference in parasitism r isk[22,24,25,26], parasitoid interference[27,28,29], and aggregation in parasitoid attacks[30,31,32]. Parasitoids have tremendous potential for biological control of pest s pecies[36,37,38,39], and a Type III functional response has been shown to suppress the host density to arbitrary low levels while maintaining system stability[35] In this contribution, we consider annual variations in host reproduction that drive fluctuations in the host/ parasitoid population densities[2]. We start by incorporating host-to-host differences in parasitism risk in the Nicholson-Bailey model (2)
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