stochmodels - Stochastic models in ecology and evolution...

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Stochastic models in ecology and evolution Ben Bolker April 13, 2009 Introduction huge topic (Ulam’s analogy: the study of nonlinear systems as the study of “non-elephant animals”. Ditto for deterministic systems.) stochasticity generally not covered thoroughly in math biology classes (but see Allen (2003), Kot (2001)); harder math, (?) less clear-cut results (?) stochasticity in a model: epistemological rather than an ontological purpose analysis harder . . . especially for nonlinear systems (most of the interesting ones, although there are interesting linear approximations, e.g. during invasions) definitions can be a bit tricky: is a diffusion model a “stochastic” model or not? Not explicitly . . . but implicitly based on a “random walk” or Brownian motion process (movement of individuals in space, or of populations in state space) well-posed stochastic models typically converge to deterministic ones in some limit (e.g. Kurtz (1970)), either in a large-population case or as the expected solution of an ensemble of realizations defs: endogenous ( demographic) vs. exogenous ( environmental) stochasticity state space can get very large (e.g. metapopulation models)
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stochmodels - Stochastic models in ecology and evolution...

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