Collaborative Research: Mathematical and Experimental Analysis of Competitive Ecological Models: Patches, Landscapes, Stage Structure, and Conditional Dispersal on the Boundary

University Of North Carolina Greensboro, Greensboro NC

Investigators

Abstract

In our increasingly fragmented world, dispersal between habitat fragments is essential for the long-term survival of a species. This project will integrate mathematical modeling and experimental analysis of an insect commonly found in stored grains to describe the effects of habitat fragmentation, conditional dispersal (e.g. an organism?s decision to leave a fragment depends upon competitor presence) and interspecific competition on population dynamics from the patch level to the landscape level. Results from this project will answer key ecological questions including: What effects do competitors have on the emigration behavior of species at patch boundaries? How do relationships between density and emigration affect regional population dynamics and competitor coexistence? How does conditional dispersal affect competition-dispersal tradeoffs that are thought to be a key to competitor coexistence? The project will advance the analysis of mathematical models created to answer these questions and better understand model dynamics. Finally, results from this study will apply to conservation programs and habitat reserve design. Graduate and undergraduate students will be trained through PI-hosted workshops and mentorship of independent research projects. Project results will be disseminated to both ecological and mathematical communities through peer-reviewed journals, national and international conference talks, and a user-friendly website. Additionally, an app that estimates key dispersal parameters from field data will be created and made publicly available. This project is funded jointly by the Division of Mathematical Sciences Mathematical Biology program and the Division of Environmental Biology Population and Community Ecology program. This collaborative project will integrate reaction-diffusion models, mathematical analysis, and experimental analysis to explore the effects of habitat fragmentation, conditional dispersal and interspecific competition on the population dynamics and species coexistence from the patch to the landscape level. The PIs will use diffusive Lotka-Volterra competition systems with nonlinear boundary conditions modeling density dependent emigration (DDE) both at the patch and landscape levels and stage structure. Ongoing research suggests that life-history traits, such as whether a species is solitary or gregarious, can provide cues as to the form of DDE for particular species. Knowledge of species' life histories, coupled with our predictions regarding how different forms of DDE can affect species coexistence and connectivity among habitat patches, can help determine whether existing reserves are adequate for species coexistence. Dispersal experiments will be performed using two Tribolium flour beetle species to parameterize the models and compare model predictions about coexistence and stability with results from long-term experiments. Innovative contributions will be made by providing (1) experimental evidence that interspecific competitors affect within-patch redistribution, boundary behavior and the strength and form of the DDE relationship; (2) the first theoretical framework and empirical evidence for the effects of conditional dispersal on the population dynamics and coexistence of competing species in fragmented landscapes; and (3) novel analysis of elliptic boundary value problems with nonlinear boundary conditions. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.