Challenges in modeling biological invasions and population distributions in a changing climate 1

Biological invasions and climate change represent important environmental challenges. Climate change makes understanding and predicting biological invasions more difficult because of the changes it can produce in the abiotic environment and species interactions experienced by an invading population. Trying to understand biological invasions in the face of climate change by means of mathematical models raises many challenges in both modeling and analysis. This article will describe some recent work that may be relevant to understanding invasions in a changing world, and points out some specific mathematical challenges that arise in that modeling context.