Project Overview
Understanding the mechanisms promoting stability of predator-prey/parasitoid-host interactions has been a fertile and critically important area of theoretical and empirical research for the past century. Age (stage) structure, differential vulnerability of prey life stages, and variability in development times of life stages are ubiquitous features of predator-prey systems. Theoretical studies have demonstrated that stability is enhanced by invulnerable host stages, that the interaction between parasitoid and host can induce generation cycles in the host, and recently that variability in host (or parasitoid) development can strongly enhance stability. To date, there has NEVER been an unambiguous test of these theoretical predictions. Using the cowpea weevil Callosobruchus maculatus and its parasitoid Anisopteromalus calandrae as a model predator-prey system (Fig. 1), we are testing whether a change in the mean and/or variability in development time of specific host stages can affect host-parasitoid stability and dynamical behavior.

Fig. 1. The (A) host C. maculatus and (B) parasitoid A. calandrae

This project involves my long-time collaborator, John Reeve (Fig. 2), and two mathematicians at Southern Illinois University, Dashun Xu and MingQing Xiao. We have recently been awarded an NSF grant (Population and Community Ecology/Mathematical Biology; August, 2010) to pursue the research outlined below.

Research Objectives
This research project, still in its infancy, has two objectives. (1) Conduct the first experimental tests of whether a change in the mean duration of the juvenile invulnerable host stage or variability in the development time of the vulnerable host stage can affect host-parasitoid stability and long term population dynamics. (2) Combine mathematics and empirical data to develop more realistic and applicable models describing complex parasitoid-host interactions. 

Fig. 2. John Reeve observing planthopper boundary behavior

Research Plan
1. Model predictions. We developed a stage-structured model tailored to the C. maculatus – A. calandrae system. The model was used to guide our experimental plan (see below). For unmanipulated microcosms, our model predicts long-period cycles of both species (Fig. 3A). An experimental increase in the duration of the invulnerable H1 stage (TH1), from the norm of 16.8 d to 26.8 d, results in the emergence of generation cycles on the order of 42 d (Fig. 3B). Our model also suggests that population dynamics are strongly affected by variability in development time of the vulnerable H2 stage (σTH2). When we fix TH1 at 10.5 d and make mean duration of the H2 stage equal 3 d, we obtain long-period cycles when σTH2 is low (Fig. 3C) and dampening oscillations and point stability when σTH2 is high (Fig 3D).

Fig. 3. Numerical solutions of a C. maculatus – A. calandrae model with fixed developmental delays showing (A) longer period cycles for the natural value of TH1 vs. (B) generation cycles for increased TH1. Solutions for gamma distributed TH2 showing (C) unstable dynamics for low variability and (D) stable dynamics for high variability in TH2.

Fig. 4. Experimental microcosm containing mung beans, weevils and parasitoids

2. Experiments. In laboratory microcosms (Fig. 4), under normal conditions, hosts and parasitoids exhibit relatively complex population dynamics (Fig. 5). In the latter third of the time series, long-period cycles appear to be emerging, as predicted by our models (see Fig. 3A). In the first of two experiments, the duration of the invulnerable juvenile host stage (H1; (Fig. 6) will be experimentally lengthened by 60% above natural levels, and we will quantify its effects on the long term population dynamics of C. maculatus and A. calandrae. This manipulation changes the parasitoid-to-host ratio of generation times from 0.71 for the control to 0.54 for the long-duration treatment. The latter ratio is at the theoretical expectation for host generation cycles (our predicted outcome for this manipulation; Fig. 3B).

In the second experiment , we enhance variability in the distribution of TH2 by making it bimodal, which is predicted to make the host-parasitoid system point stable (see Fig. 3D).

Fig. 5. Representative population dynamics for the host and parasitoid in unmanipulated experimental microcosms.

Fig. 6. Weevil larva developing in mung bean

3. Model development. The modeling phase of this study is being spearheaded by the Southern Illinois group (Reeve, Xu and Xiao). Here, the main objective is to develop mathematical models describing the population dynamics of C. maculatus and A. calandrae and study their qualitative mathematical properties. The models and analysis will address two questions: (1) How does variability in development time influence the stability and persistence time of the host-parasitoid system? (2) What happens if additional complexities of the system (e.g., competition among weevil larvae, age-specific (density-dependent) fecundity) are explicitly incorporated into a mathematical model?