Open Collections

Will transient dynamics help or hurt species during climate change?

Banff International Research Station for Mathematical Innovation and Discovery

Climate change is moving many species’ suitable habitats, forcing populations to either track their habitats using dispersal, adapt in place, or face extinction. Most mathematical models of species’ climate responses focus on asymptotic population dynamics. In contrast, most management decisions occur on the time scale of short-term (transient) dynamics. Transient behavior can often differ greatly from asymptotic dynamics, leading to poor management decisions. In this talk, I will use an integrodifference equation to explore the transient dynamics of a population tracking its moving habitat. Although transient dynamics are usually studied in the context of non-spatial models of multiple species or stage-structured populations, I will show that (and why) transient dynamics can occur in unstructured, single-species spatial models. Using the endangered Fender’s blue butterfly subspecies (lcaricia icarioides fenderi) as a model species, I will highlight three results with strong management implications. First, transient dynamics can only occur under a certain set of biological and environmental conditions, which can serve as indicators of possible transients. Second, the model pinpoints the optimal location to place individuals within the habitat so that short-term survival is greatest. Third, the model offers an explanation for critical slowing-down—the observation that systems near a tipping point often exhibit long transient dynamics. I will close with a discussion of future extensions, such as transients in stage-structured integrodifference equations.

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

video/mp4

Author affiliation: University of Washington

2017-03-24

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60986

Unreviewed

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