Nikolay Strigul, Denis Pristinski, Drew W Purves, Jonathan Dushoff, and Stephen W Pacala
Individual-based forest simulators, such as TASS and SORTIE, are spatial stochastic processes that predict properties of populations and communities by simulating the fate of every plant throughout its life cycle. Although they are used for forest management, and able to predict dynamics of real forests, they are also analytically intractable, which limits their usefulness to basic scientists. We have developed a new spatial individual-based forest model that includes a new formulation for the plasticity of crown shape. Its structure allows us to derive an accurate approximation for the individual-based model that predicts mean densities and size structures using the same parameter values and functional forms, and, also, is analytically tractable. The approximation is represented by a system of Von Foerster partial differential equations coupled with an integral equation that we call the Perfect Plasticity Approximation (PPA). We have derived a series of analytical results including equilibrium abundances for trees of different crown shapes, stability conditions, transient behaviors, such as the constant yield law and self-thinning exponents, and two species coexistence conditions.
In Ecological Monographs