Historically, ecological models neglected spatial considerations, providing an elegant but fundamentally inadequate understanding of the factors affecting biodiversity. Reaction diffusion theory provided an alternative, and enjoyed a rich and fruitful development after Turing's classic work. But reaction-diffusion theory falls short in ints treatment of spatial patchiness, local stochasticity, and the discreteness of individuals. In the last decade, there has been rapid development of other approaches, especially metapopulations and interacting particle systems, as well as individual-based models of Lagrangian type. This lecture will review these, and relate them.
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