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.