Maxwell Institute Colloquium Lecture
Brownian bugs, superprocesses and the Fisher-Kolmogorov equation
W R Young
(Scripps Institution of Oceanography, University of San Diego)The talk will review the connection between two types of mathematical model, both motivated by population biology and ecology. The most detailed description is an individual-based models. An example is the Brownian Bug Model (BBM), in which a collection of reproducing and dying random walkers interacts via competition between neighbours. The older approach, originating with Fisher and Kolmogorov (FK), uses continuous population densities and partial differential equations to model the same biological processes as the BBM. The BBM shows the spontaneous emergence of clusters of related individuals; many biological systems also exhibit clustering, some perhaps for the same reasons as the BBM. However spontaneous clustering does not occur in the FK model. I will discuss the underlying reasons for this failure of FK, and recent attempts using techniques from statistical physics to derive more satisfactory continuum descriptions.
Associated event: a one-day meeting on Geophysical Fluid Dynamics will be held on 8th April, 9.30 am-3.30 pm at the International Centre for Mathematical Sciences. See details here.
