From spatial individuals and populations to correlation equations

David Rand

In this talk I want to discuss how to go from discrete individuals distributed in space to continuum equations in systems in ecology, evolution and epidemiology where the micro correlations are much more important than fluctuations. I will consider both the underlying mathematical formalism for deriving and closing correlation equations and a range of examples from ecology, evolution and epidemiology. In particular, I want to consider (a) how to use correlation equations to handle invasions in individual-based spatial models and (b) the role of micro-correlations in determining critical community size, fade-out scaling in epidemics and evolutionary velocity in host-parasite systems.

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