Mat-1.3656 Seminar on numerical analysis and computational science

Monday, Dec 9, 2013, room M233 at 14.15, Eirola & Stenberg

Otso Ovaskainen, University of Helsinki, Department of Biosciences
Markov evolutions in the space of locally finite configurations: applications in ecology and evolution

Spatial and stochastic models are often straightforward to simulate but difficult to analyze mathematically. Most of the mathematical methods available for non-linear stochastic and spatial models are based on heuristic rather than mathematically justified assumptions, so that e.g. the choice of the moment closure can be considered more of an art than a science.
In collaboration with mathematicians from Bielefeld University (Germany), I have utilized recent developments in the field of "Markov evolutions in the space of locally finite configurations", to develop a modelling framework that is widely applicable for theoretical ecology. In particular, the framework allows one to derive spatial moment equations of all orders can be systematically from the underlying individual-based assumptions. Further, we go beyond mean-field theory by expanding spatial moment equations perturbatively around the mean-field model. I illustrate the applications of the framework in the context of ecological and evolutionary models.