Dr. Ratnasingham Shivaji, the H. Barton Excellence Professor in the Department of Mathematics and Statistics, has received an $80,000 grant from the National Science Foundation to continue research on the project: “Collaborative Research: Mathematical and Experimental Analysis of Competitive and Predator-Prey Models: Conditional Dispersal on Patches to Landscapes.” Dr. Shivaji is the lead principal investigator on the collaborative project. His colleagues Dr. James Cronin of Louisiana State University and Dr. Jerome Goddard of Auburn University at Montegomery also received grants to carry out their work on the project.
This research seeks to understand the impact of habitat fragmentation and inter-species competition on species in a predator-prey system by creating mathematical models that allow scientists to analyze and understand the impact of ecological and geographical variables. Dr. Shivaji and his team expect their findings can ultimately inform the design of conservation programs and biological reserves.
The abstract below, retrieved from the NSF website, provides more information about this research.
Long-term survival and coexistence of species in the face of habitat loss and fragmentation is among the most critical concerns faced by ecologists today. This project is an integration of mathematical modeling and experimental analysis of an insect herbivore and predator system to explore the effects of habitat fragmentation, interspecific competition, and predation on the population dynamics and coexistence of species from the patch to the landscape level. Results from this project aim to answer two key ecological questions: (1) For competing species, what effect does the density of the same or different species have on dispersal-reproduction and dispersal competition tradeoffs arising from the evolution of dispersal in fragmented habitats? (2) How does the presence of a shared predator affect the relationship between density and emigration, tradeoffs involving dispersal? The project will also provide significant contributions towards the analysis of mathematical models created to study this behavior via development of new mathematical tools to better understand model dynamics. Finally, results from this study are expected to be applicable to conservation programs and reserve design. This project will involve the training of graduate and undergraduate students through PI-hosted workshops and mentorship of independent research projects. Moreover, an app that estimates key dispersal parameters from field data will be created and made publicly available.
This collaborative project comprises integrated reaction-diffusion modeling, mathematical analysis, and experimental research to explore the effects of habitat fragmentation, conditional dispersal, interspecific competition, and predation on the population dynamics and species coexistence from the patch to the landscape level. The Investigators will use diffusive Lotka-Volterra competition and predator-prey systems with nonlinear boundary conditions modeling density dependent emigration (DDE) at the patch and landscape levels. Experiments will be performed using two Tribolium flour beetle species to examine how the DDE relationship and life-history tradeoffs are affected by a shared predator (Xylocoris flavipes). This project is expected to be novel and significant by providing (1) experimental evidence that interspecific competitors and predators affect boundary behavior, the strength and form of DDE, and important life-history tradeoffs linked to species coexistence; (2) the first theoretical framework for the effects of conditional dispersal on the population dynamics and coexistence of competing species and a shared predator in fragmented landscapes; and (3) a significant contribution toward the analysis of systems of elliptic boundary value problems with nonlinear boundary conditions, as new mathematical tools will be developed to better understand the models’ dynamics. Knowledge of species’ life histories, coupled with predictions regarding how competitors and predators can alter the magnitude and form of DDE and life history tradeoffs, can help determine whether existing reserves are adequate for species long-term coexistence.