A firm understanding of the mechanisms that allow multiple species to coexist is necessary in order to explain patterns of biodiversity. Several researchers have addressed this challenge by developing theory, while others have collected natural history or experimental data. This creative project joins these two separate approaches by explicitly addressing the intersection of theory and data. The proposed projects focus on the interactions between a beetle and its parasitoid wasp; parasitoids can play an important role in limiting insect populations in natural and agricultural habitats. First, the theoretical prediction that heterogeneity in parasitoid attack rates can promote coexistence of predator and prey will be tested experimentally. Second, new theory will be developed to pursue the idea that interactions between demographic stochasticity and resource heterogeneity promote population persistence. Third, the intersection of theory with data will be addressed through the development of efficient experimental designs, with an emphasis on response surface experimental designs. Through simulations, the investigators will study relative efficiencies of alternative experimental designs for quantifying the functional relationships that underlie species interactions.
This project is potentially transformative in that it will accelerate the use of new experimental designs and analyses to compare alternative model structures, as opposed to the standard practice of rejecting null hypotheses. The investigator will develop open-source software to evaluate experimental designs in specific contexts. This project will contribute to the training of undergraduate and graduate students in research techniques, data analysis, computer programming, and in independent research. Florida State University serves a diverse undergraduate population, and the investigator plans to recruit students from groups currently under-represented in science and mathematics.
This award had two primary objectives: to study ways that experiments can more efficiently provide the data necessary to parameterize mathematical models, and to apply some of these methods to gain a better understanding of ways that heterogeneity in interaction strengths affects the spatial and temporal population dynamics of beetle, both in the presence and absence of a parasitoid wasp. Progress was made on both fronts. I used simulation studies to explore alternative experimental designs that can provide greater information content per data point (in an information theoretic context) and reduce the level of uncertainty in parameter estimates. Recommendations include using (i)partial derivatives of functions with respect to parameters, as opposed to independent variables, and (ii)using patterns of divergence in alternative functions to plan data collection. The optimal number of discrete treatments for estimating a function's parameter values is just slightly more than the number of parameters in the function, a result that runs counter to existing recommendations of regression-type designs with many treatment values. The empirical work explored how populations invade new habitat, how populations are affected by variation in sex ratios, and how resource heterogeneity affects the stability of host-parasitoid dynamics. Variation in a population's sex ratio, whether due to demographic stochasticity or to sex-based differences in dispersal behaviors, can interact with other factors to affect rates of population growth and spread. Heterogeneity in resources affects the stability of host-parasitoid population dynamics. Although the effects of resource heterogeneity are in broad qualitative agreement with predictions from theory, population dynamics are also affected by behaviors that are not captured by simple mathematical models. The grant also helped to support the training of three graduate students and a postdoctoral scholar. The trainees extended some of the research themes to include additional insect species, and to conduct field work that complements the model system that was used in the lab. This award has resulted in eight peer-reviewed journal publications to date, all co-authored with the graduate students, postdoc, and other colleagues, a manuscript in review and several more still in preparation.
