Jim Cronin - Development Time and Predator-Prey Population Dynamics

Development Time and Predator-Prey Population Dynamics

Project Overview

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

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. 2. John Reeve observing planthopper boundary behavior.

This project involves my long-time collaborator, John Reeve (Fig. 2), and two fantastic mathematicians at Southern Illinois University, Dashun Xu and MingQing Xiao. The research is funded by a grant from NSF (Population and Community Ecology/Mathematical Biology).

Research Objectives

This research project has five objectives.

(1) Conduct the first experimental tests of whether variability in development time of the vulnerable host stage can affect host-parasitoid stability and long term population dynamics.

(2) Test the long-standing theoretical prediction that the mean duration of an invulnerable host stage affects host-parasitoid stability and long term population dynamics.

(3) Experimentally test how changes in the pulse addition of food resources affects host-parasitoid stability and long-term population dynamics.

(4) Evaluate how changes in the duration and variability in development time of prey life stages influences the evolution of predator morphological and life-history traits.

(5) Develop more realistic mathematics models to describe complex parasitoid-host interactions.

Fig. 3. Experimental microcosm containing mung beans, weevils and parasitoids

Variance in vulnerable host stage experiment:

Cronin, J. T., J. D. Reeve, D. Xu, M. Xiao and H. N. Stevens. 2016. Variable prey development time suppresses predator-prey cycles and enhances stability. Ecology Letters 19:318-327.

For two years (≈ 27 host generations), replicate host-parasitoid microcosms (Fig. 3) were subjected to two treatments, natural levels of variation (Normal variance) and high levels of variation (High variance) in the duration of the vulnerable host stage. We opted for an artificial means of changing development time that targets a specific life stage, the vulnerable stage of the host (H2 stage; Fig. 4), without altering any other aspects of the host’s demography. This was accomplished by manually replacing beans with weevils just prior to entering the vulnerable stage with weevils that have been in the vulnerable host stage for different lengths of time. Specifically, variability in the duration of the vulnerable host stage was increased by replacing weevils entering the vulnerable stage with equal numbers of weevils at the beginning and near the end of the vulnerable stage.

diagram of treatment effects — Fig. 4. Diagram of the experimental treatment and its effect on the average development times of the weevil life stages. For the adult weevil life stage (H4), the mean duration is based on the females. Inset histograms show the distribution of H2 weevil ages used in the High- and Low-variance treatments (Cronin et al. 2016).

In unmanipulated control and Normal-variance microcosms, hosts and parasitoids exhibited distinct population cycles with a periodicity of 1 or 2 host generations, respectively (Figs. 5, 6). In contrast, microcosms in the High-variance treatment exhibited much more stable population dynamics (Fig. 6), in strong support of theoretical predictions above (Fig. 3). Adult host and parasitoid abundances were 18 and 24% less variable, respectively, in the High-variance than Normal-variance microcosms. More significantly, periodicity in host and parasitoid population dynamics all but disappeared. This study suggests that developmental variability is not simply noise in the system but is critical to predator-prey population dynamics. We suggest that variability in development times could be exploited in the development of pest-management programs. A manuscript from this research is currently in review for publication.

time series and wavelet analysis — Fig. 5. Time series and wavelet analysis for the host and parasitoid in a representative unmanipulated experimental microcosm. Spanning the two-year study, there is clear evidence of period-two oscillations (note the region in red in the wavelet analysis.)

Simulations using our stage-structured models for the host and parasitoid provided additional support that increasing variability in the duration of the vulnerable host stage, H₂, promotes increased system stability; i.e., reduced amplitude fluctuations and long-term persistence of the host-parasitoid interaction. We first estimated the parameters in the models using the data from the Unmanipulated controls, and found that the model readily generated period 2 oscillations similar to the microcosms (Fig. 7A) and found that the Normal-variance microcosms were prone to extinction whereas the High-variance microcosms were persistent, illustrating the stabilizing effect of variability. Fig. 7B-C shows the model output for these two treatments where stability was increased by adding more parasitoid aggregation, sufficient for the Normal-variance treatment to persist. The standard deviation in host population sizes was 60% higher for the Normal-variance as compared to the High-variance treatments. Standard deviation in parasitoid abundances between treatments was similar.

The simulations suggest that variability in the vulnerable host stage enhances stability because it allows some hosts to escape parasitism when parasitoid densities are high, allowing additional host cohorts to arise and thereby smoothing the oscillations.

model simulations — Fig. 7. Model simulations were tailored for each of the three treatments: Unmanipulated control (A), Normal variance (B) and High variance (C). In the Normal- and High-variance simulations, k (the clumping parameter from the negative-binomial model) was reduced to achieve long-term persistence in the Normal-variance treatment.

Duration of invulnerable host stage experiment:

LDSD diagram — Fig. 8. Diagram of the experimental treatment of H₁ development time and its effect on the average development times of the weevil life stages. For the adult weevil life stage (H₄), the mean duration is based on the females.

In this experiment, our approach to manipulating the duration of the invulnerable host stage (TH1), while affecting no other life stage of the host or parasitoid, involved replacing beans with weevils of a known H₁ age and replacing them with an equivalent number of beans containing weevils in a younger or older H₁ stage. Using this approach, we were able to increase or decrease the duration of the H₁ stage by approximately 60% relative to unmanipulated levels (16.8 ± 0.3 d) (Fig. 8). As the H₁ stage is the longest of all host stages, these changes in H₁ significantly altered the host generation time while having no effect on parasitoid generation time. Specifically, the parasitoid:host generation time is 0.71 for the control, 0.54 for the long-duration treatment, and 0.98 for the short-duration treatment. According to theory, the long-duration treatment should promote greater host-parasitoid stability (e.g. Godfray & Hassell 1989; Reeve et al. 1994).

Although the two-year study is complete, we are still analyzing the time series data. However, our initial analyses suggest that our short- and long-duration treatments did not change the periodicity in host and parasitoid time series in comparison to unmanipulated controls. However, the amplitude of cycles was greatly diminished in the short-duration treatment, suggesting that, in contrast to theory, stability is enhanced by having similar host-parasitoid generation times.

LDSD time series — Fig. 9. Representative time series for each treatment, the unmanipulated control (CTRL-1), Short-duration treatment (SD-1) and Long-duration treatment (LD-1).

Objectives 3-5 are currently in progress. The modeling phase of this study (objective 5) has been spearheaded by the Southern Illinois group (Reeve, Xu and Xiao). Development of the stage-structured mathematical models for C. maculatus and A. calandrae are complete and have been used to address objective 1 (see Cronin et al. 2016).