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

This project is an integration of mathematical modeling and experimental analysis of an invertebrate predator-prey system to explore the effects of habitat fragmentation, conditional dispersal, predation, and interspecific competition on herbivore population dynamics from the patch level to the landscape level. It represents a unique collaboration between two mathematicians, and ecologist, and undergraduate and PhD students. This project is expected to provide much-needed information in population ecology on the consequences of conditional dispersal to population dynamics of species in fragmented landscapes. Results from this project will answer several key ecological questions such as will the presence of density dependent dispersal help to moderate potentially detrimental factors as habitat fragmentation or worse, exacerbate their effects. The project will also provide a significant contribution towards the analysis of elliptic boundary value problems with nonlinear boundary conditions, as new mathematical tools will be developed to better understand the dynamics of these population models. Finally, the project will provide clear guidelines for how empirical studies should be constructed to evaluate the presence and consequences of density dependent dispersal in light of the predictions of these theoretical models. The investigators will disseminate the results of this project to both the ecological and mathematical communities through various media including peer-reviewed mathematical and ecological journals, talks at national and international conferences, and a user-friendly website showcasing the research. An important aspect of this project will involve the training of graduate and undergraduate students through workshops hosted by the investigators and mentorship of independent research projects. Moreover, a population dynamics curriculum covering basic population ecology through mathematical tools and interesting examples for exploring population models related to density dependent dispersal will be developed targeting undergraduate and advanced level high school students and freely available to the public via the project's website.

The purpose of this collaborative project between will be an integration of modeling of population dynamics via reaction diffusion models, mathematical analysis, and experimental analysis of an invertebrate system to explore the effects of habitat fragmentation, conditional dispersal, predation, and interspecific competition on herbivore population dynamics from the patch level to the landscape level. This study will help answer important biological questions such as 1) what patch level effects can be expected from density dependent dispersal, specifically of positive, negative or U-shaped density dependent dispersal, 2) does density dependent dispersal moderate or even exacerbate the effects of habitat fragmentation, Allee effects, interspecific competition, or predation on local or regional stability/persistence of a population, and 3) how should empirical studies be constructed to evaluate the presence and consequences of density dependent dispersal in light of the predictions of these theoretical models. A more comprehensive understanding of the patch and landscape level consequences of density dependent dispersal in the presence of such complicating factors as predation, interspecific competition, and habitat fragmentation is important by itself, but may also lead to the development of better population management strategies, especially in an environment where populations face diverse ecological challenges due to predation, habitat fragmentation, and global climate change. This project is expected to be significant by providing much-needed information in population ecology on the consequences of conditional dispersal (i.e., as a function of the density of conspecifics, interspecific competitors, and predators) to population dynamics of species in fragmented landscapes. The research is novel because, to date, theoretical and empirical studies in fragmented systems have ignored other forms of density dependent dispersal (negative or U-shaped) that are commonly found in nature. Results from this project will answer several key ecological questions as to whether the presence of negative or U-shaped density dependent dispersal helps to moderate potentially detrimental factors as habitat fragmentation or worse, exacerbate their effects. The project will also provide a significant contribution towards the analysis of elliptic boundary value problems with nonlinear boundary conditions, as new mathematical tools will be developed to better understand the dynamics of these population models. Further, development of a true landscape level modeling framework built on reaction diffusion equations will serve as a foundation for enhanced study of landscape dynamics in theoretical models. The investigators plan to disseminate the results of this project to both the ecological and mathematical communities through various media including: the ArXiv, peer-reviewed mathematics, mathematical biology, and ecology journals, and in talks at mathematical biology and ecological conferences.