Open Collections

Integrodifference equation models for populations in dynamic habitats

Banff International Research Station for Mathematical Innovation and Discovery

Dynamic changes in habitat sizes and locations have important consequences for their residents. In this talk, I will present two integrodifference equation models. The first model describes the dynamics of a population whose habitat shifts under climate warming. The second model describes a population whose habitat expands and contracts seasonally. For both models, I will show that the persistence metric for compact integral operators on a bounded domain extends to that of an unbounded domain. I will then present the ecological insight gained from the mathematical analysis. For the first model, I will demonstrate that the population will lag behind the shifting habitat and carry a â climatic debtâ , especially when the climate warming is accelerating. For the second model, I will explain how the concept of critical habitat size is extended to that of a "lower minimal limit size" in a two-season scenario. 

Mathematics; Dynamical systems and ergodic theory; Difference and functional equations

video/mp4

Author affiliation: Lafayette College

2019-03-05

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/68478

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/