Abstracts Mathematics

Dynamical Systems Analysis in Adaptive and Metapopulation Ecology with Applications to Conservation Management

by Guenchik Grosklos

The ability for a species to persist largely relies on how well they adapt to the environment and their interactions with local and global communities. Specifically, if adaptation occurs quickly enough or nearby communities sufficiently promote growth rates, populations at risk of extinction may persist. In this dissertation, we first develop a method that estimates and compares rates of change in time series data of population densities and measurable traits (phenotypes). Additionally, we compare between genetic (evolutionary) and non-genetic (plastic) trait change to determine whether phenotypes change faster when driven by evolutionary or plastic change. We then focus on metapopulation models to understand system dynamics and viability metrics in amphibian populations. We start by investigating a two patch model with 1, 2, and 3 life history stages to understand how dispersal affects population dynamics and synchrony. We categorize dispersal based on the magnitude of dispersal probabilities and degree of symmetry to understand how different dispersal types affect population fluctuations and synchrony. Finally, we use habitat contribution metrics to investigate viability in a seven pond Columbia spotted frog population located in western Montana. We classify each pond based on their relative importance to the global community and use sensitivity analysis to measure how habitat management affects pond size, total population size, and the degree of habitat importance. These results provide a means to understand how species respond to environmental and anthropogenic disturbances for habitat management efforts.