Analysis of Time-Dependent Integrodifference Population Models

• Main Author: McAdam, Taylor J
• Format: Others
• Published: Scholarship @ Claremont 2013
• Subjects: Analysis; Dynamic Systems
• Online Access: http://scholarship.claremont.edu/hmc_theses/44; http://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1052&context=hmc_theses

The population dynamics of species with separate growth and dispersal stages can be described by a discrete-time, continuous-space integrodifference equation relating the population density at one time step to an integral expression involving the density at the previous time step. Prior research on this model has assumed that the equation governing the population dynamics remains fixed over time, however real environments are constantly in flux. We show that for time-varying models, there is a value Λ that can be computed to determine a sufficient condition for population survival. We also develop a framework for analyzing persistence of a population for which growth and dispersal behavior alternate predictably throughout time. Finally, we consider a number of time-varying models that include randomness.