The interplay between multiple control mechanisms in a host-parasitoid system: a discrete-time stage-structured modelling approach

We propose a discrete-time host-parasitoid model with stage structure in both species. For this model, we establish conditions for the existence and global stability of the extinction and parasitoid-free equilibria as well as conditions for the existence and local stability of an interior equilibrium and system persistence. We study the model numerically to examine how pesticide spraying may interact with natural enemies (parasitoids) to control the pest (host) species. We then extend the model to an impulsive difference system that incorporates both periodic pesticide spraying and augmentation of the natural enemies to suppress the pest population. For this system, we determine when the pest-eradication periodic solution is globally attracting. We also examine how varying the control measures (pesticide concentration, natural enemy augmentation and the frequency of applications) may lead to different pest outbreak or persistence outcomes when eradication does not occur.

Rapid phenological change differs across four trophic levels over 15 years

The success of consumers often depends on synchronizing with their resources; however, recent climate change has affected the phenology of many species, resulting in mismatches and leading to community-wide changes. Field studies chronicling both the dynamics and behavior of four trophic levels seldom run for more than a few years, thereby bringing into question the longer term trajectories of these phenological shifts at multiple levels. Do these shifts between trophic levels remain constant over time, or do they continue to move apart? To address these questions, in 2004, I initiated a long-term study of the phenological relationships of two ferns, a host caterpillar (and its moth), its principal primary parasitoid wasp, and hyperparasitoid wasp. The study involves only a few species at each level, but they make up nearly all the members of the community. Ferns emerged progressively earlier in the spring, at rates exceeding one day per year, while moths eclosed roughly 0.6 days earlier per year, the primary parasitoid at 0.8 days earlier per year, and the hyperparasitoid fluctuated widely. Each of these changes fostered significant mismatches. Year-to-year changes of the moth and primary parasitoid varied much more than those of the ferns. In each instance, dates of last eclosions moved earlier more rapidly than did early eclosion dates, truncating their seasons. The extremely rapid, though variable, changes in phenology of the various trophic levels follow the unprecedentedly rapid temperature increase of the immediately adjacent Gulf of Maine.

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

Host-parasitoid population dynamics is often probed using a semi-discrete/hybrid modeling framework. Here, the update functions in the discrete-time model connecting year-to-year changes in the population densities are obtained by solving ordinary differential equations that mechanistically describe interactions when hosts become vulnerable to parasitoid attacks. We use this semi-discrete formalism to study two key spatial effects: local movement (migration) of parasitoids between patches during the vulnerable period; and yearly redistribution of populations across patches outside the vulnerable period. Our results show that in the absence of any redistribution, constant density-independent migration and parasitoid attack rates are unable to stabilize an otherwise unstable host-parasitoid population dynamics. Interestingly, inclusion of host redistribution (but not parasitoid redistribution) before the start of the vulnerable period can lead to stable coexistence of both species. Next, we consider a Type-III functional response (parasitoid attack rate increases with host density), where the absence of any spatial effects leads to a neutrally stable host-parasitoid equilibrium. As before, density-independent parasitoid migration by itself is again insufficient to stabilize the population dynamics and host redistribution provides a stabilizing influence. Finally, we show that a Type-III functional response combined with density-dependent parasitoid migration leads to stable coexistence, even in the absence of population redistributions. In summary, we have systematically characterized parameter regimes leading to stable/unstable population dynamics with different forms of spatial heterogeneity coupled to the parasitoid's functional response using mechanistically formulated semi-discrete models.

Structural dynamics in the host-parasitoid system of the pine needle gall midge (Thecodiplosis japonensis) during invasion

The structural dynamics of host–parasitoid populations play a key role in the mechanism of natural community development with invasive species. Species invading new habitats experience coevolution with their newly acquired natural enemies, and their population dynamics are driven by a complex interaction between biological and environmental factors. We examined the biological and environmental factors which potentially influence a community of parasitoids throughout the 25-year invasion history of the pine needle gall midge (PNGM), Thecodiplosis japonensis, an important pest of pines in eastern Asia. We found that differences in establishment sequence and competitive ability among the parasitoids attacking this species determined the parasitoid community’s structure and dynamics. In particular, the timing for the initial establishment of the host–parasitoid association, incomplete superiority in competition among parasitoids, and indirect competition by a combination of the parasitoids were important factors for determining community’s structure and dynamics. Finally, the history of change in the community composition could be explained by the phenology differences in its member species, mediated by environmental factors.

Hydra effects in discrete-time models of stable communities

A species exhibits a hydra effect when, counter-intuitively, increased mortality of the species causes an increase in its abundance. Hydra effects have been studied in many continuous time (differential equation) multispecies models, but only rarely have hydra effects been observed in or studied with discrete time (difference equation) multispecies models. In addition most discrete time theory focuses on single-species models. Thus, it is unclear what unifying characteristics determine when hydra effects arise in discrete time models. Here, using discrete time multispecies models (where total abundance is the single variable describing each population), I show that a species exhibits a hydra effect in a stable system only when fixing that species' density at its equilibrium density destabilizes the system. This general characteristic is referred to as subsystem instability. I apply this result to two-species models and identify specific mechanisms that cause hydra effects in stable communities, e.g., in host--parasitoid models, host Allee effects and saturating parasitoid functional responses can cause parasitoid hydra effects. I discuss how the general characteristic can be used to identify mechanisms causing hydra effects in communities with three or more species. I also show that the condition for hydra effects at stable equilibria implies the system is reactive (i.e., density perturbations can grow before ultimately declining). This study extends previous work on conditions for hydra effects in single-species models by identifying necessary conditions for stable systems and sufficient conditions for cyclic systems. In total, these results show that hydra effects can arise in many more communities than previously appreciated and that hydra effects were present, but unrecognized, in previously studied discrete time models.

The effects of host-feeding on stability of discrete-time host-parasitoid population dynamic models

Discrete-time models are the traditional approach for capturing population dynamics of a host-parasitoid system. Recent work has introduced a semi-discrete framework for obtaining model update functions that connect host-parasitoid population levels from year-to-year. In particular, this framework uses differential equations to describe the host-parasitoid interaction during the time of year when they come in contact, allowing specific behaviors to be mechanistically incorporated. We use the semi-discrete approach to study the effects of host-feeding, which occurs when a parasitoid consumes a potential host larva without ovipositing. We find that host-feeding by itself cannot stabilize the system, and both populations exhibit behavior similar to the Nicholson-Bailey model. However, when combined with stabilizing mechanisms such as density-dependent host mortality, host-feeding contracts the region of parameter space that allows for a stable host-parasitoid equilibrium. In contrast, when combined with a density-dependent parasitoid attack rate, host-feeding expands the non-zero equilibrium stability region. Our results show that host-feeding causes inefficiency in the parasitoid population, which yields a higher population of hosts per generation. This suggests that host-feeding may have limited long-term impact in terms of suppressing host levels for biological control applications.