This project will focus on the development and analysis of deterministic structured population models, which will be applied to describe the dynamics of a frog population in an urban area. A combination of analytical and computational methods will be used to understand the population dynamics. New theories on well-posedness, long-time behavior, numerical methods, and parameter estimation techniques will be established. Based on capture-mark-recapture field data, statistical techniques will be employed to approximate weekly frog population sizes. These approximate population sizes will then be compared with the output of the structured population models via the least-squares approach to provide estimates for the model parameters. Furthermore, stochastic population models based on the deterministic ones will be developed and numerically analyzed. These models will be useful for obtaining information about the expected time to population extinction.
This research will advance the understanding of the dynamics of anuran populations in urban systems. By intensively studying a relatively isolated population, information on survivorship and life history patterns will be produced. Because the field study site is a habitat island in an urban interface, an insight into the processes that affect anurans in an anthropomorphic landscape will be gained from the models' theoretical and numerical analyses. The analytical and computational methods developed will provide alternatives to the existing methods that are used to study structured population models. The statistical methods using appropriate probability distributions on the field data provide an effective technique to fine tune the deterministic models for an improved understanding of the dynamics of the anuran population. These mathematical and statistical approaches not only can be used as instructional tools in biomathematics graduate studies, but also will enhance the multidisciplinary research combining population ecology, mathematics, and statistics.
