Impact of climate change on biological invasions and population distributions

The purpose of this BIRS workshop was to generate, develop and apply new tools for the analysis of invasions and population distributions under environmental change. Thus the mathematical problems that we addressed were intrinsically spatial. Not only do temperatures vary with latitude, the very processes of population spread and shifts in range boundary are modelled using equations with spatial operators. Hence the mathematical and scientific challenges are significant, but the potential payoffs are large, making this significant as a BIRS workshop. The workshop focused on the following issues: Shifts in species range boundaries under climate change: As temperatures continue to increase, temperature isoclines will move quickly, particularly in northern countries, at rates predicted to be in excess of 1000 meters per year. Which species will keep up with shifting temperature isoclines and which will fall behind, and how can this be determined using dynamical systems? Initial attempts to solve this problem have used nonlinear reaction diffusion equations in a fixed moving coordinate frame for temperature. However, the meeting provided the opportunity to discuss and develop more realistic models that include integral operators that allow for long-distance dispersal, variable-speed coordinate frames for temperature, and changing external environmental conditions. Other approaches included slowly decaying initial conditions, which can appear as the result of a colonization-retraction event, and then may lead to accelerating rates of spread. Mathematical analysis of such systems requires gradually varying travelling waves. However, most current approaches focus on asymptotic behavior with constant parameters and these applications will require time varying parameters and responses on similar time scales. Applications range from understanding the spread of mountain pine beetle from western to central Canada, to analyzing the potential for loss of endangered plant species due to climate warming to tracking the advance of pine processionary moth as it moves across Europe. Thus, many types of biological invasions are induced by climate change. Several challenging mathematical questions are related to such biological invasions in general and require new, sophisticated, mathematical developments. The meeting was the occasion to evaluate the state of the art in mathematical modelling as well as to identify the key mathematical challenges that arise or that are required for further progress. One of aims was to bring together modelers, mathematicians and ecologists with this goal in mind.