Mathematics Colloquium: Scaling in Ecological Systems: Macroscopic Equations for Forest Dynamics
4:10 PM; Neill Hall 5W
Abstract: One of the challenges in modern ecology is to understand and predict the emergence of macroscopic patterns of ecological systems as a result of self-organization on multiple temporary and spatial scales. The major challenge is that numerous individual processes in ecological systems are interdependent and occur simultaneously at different levels of biological organization, starting from microscopic scales and ending at the ecosystem level. In physical systems, macroscopic equations for the dynamics of fluids can be derived from stochastic models of the random collisions and transformations of individual molecules. Using a similar approach we have developed a new scaling method to predict forest dynamics using individual-based parameters (Strigul et al., 2008, Ecological monographs, 78: 523-545). At the first stage a new spatial individual-based forest simulator incorporating plasticity of crown shape has been developed. This individual-based simulator is a spatial stochastic process that predicts community properties by simulating the fate of every plant throughout its life cycle. Unfortunately, such non-linear spatial stochastic processes are notoriously intractable. They also require too much computer power to be used at large scale, such as in global models; one cannot simulate every tree on the Earth. However, we were able to derive analytically tractable macroscopic equations approximating the individual-based forest simulator. This approximation is represented by a system of McKendrick-Von Foerster partial differential equations coupled with an integral equation that we call the Perfect Plasticity Approximation (PPA). Certain macroscopic patterns were analytically investigated including equilibrium abundances of different trees, transient behaviors, and coexistence conditions. The PPA accurately predicts dynamics of forest stands on different soil types in practical applications. New unpublished results include a generalization of the PPA approach to model aboveground and belowground competitions for light, water and nutrients.