Open Collections

Predicting species spread in heterogeneous landscapes with IDEs

Banff International Research Station for Mathematical Innovation and Discovery

Characterising the spread of biological populations is crucial in responding to both species invasions and the shifting of habitat under climate change. Spreading speeds can be studied through mathematical models such as the discrete-time integro-difference equation (IDE) framework. The usual approach in implementing IDE models has been to ignore spatial variation in the demographic and dispersal parameters and to assume that these are spatially homogeneous. On the other hand, real landscapes are rarely spatially uniform with environmental variation being very important in determining biological spread. In this talk we will demonstrate two new analytical methods for approximating the wavespeed of species invasion for different types of heterogeneous landscapes, which depend on landscape and dispersal scales. Finally, we will show a new efficient simulation technique for predicting species spread in 2D heterogeneous landscapes. Our technique, an adaptive algorithm, leads to an order of magnitude improvement in computational efficiency (RAM and CPU) over non-adaptive algorithms. We will demonstrate the user-friendly interface which is adaptable to many types of large scale IDE problems. Our algorithm enables the investigation of scientific questions that would have previously been impossible due to computational resource constraints, and allows large simulations to be carried out on a desktop or laptop rather than on a computer cluster.

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

video/mp4

Author affiliation: Centre for Ecology & Hydrology

2017-03-22

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60972

Unreviewed

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