The Use of Fractal and Chaos Theory to Verify, Simplify, and Extend Forest Ecosystem Models

Drs. Cohen and Pastor propose to study output from the model LINKAGES for the purpose of identifying a strange attractor. The LINKAGES model simulates feedback responses of a forested ecosystem to atmospheric and soil changes. It also simulates births, growth, and deaths of individual trees and the decay and N dynamics of annual cohorts in litter of a 1/2 ha plot. The model is one of the most widely used and verified models of its kind. Preliminary results indicate that the model produces a low-dimensional strange attractor and therefore reflects a chaotic dynamical system. Cohen and Pastor found that some essential properties of the model as a dynamical system are lost when outputs are averaged over several plots. These preliminary findings have profound implications for the use and further development of the LINKAGES model: 1) because of sensitivity to initial conditions, long-term model predictions cannot be trusted, 2) the investigators contend that extending the model to include spatial considerations is essential, and 3) the fact that the model produces a low-dimensional strange attractor means that there are few basic mechanisms that control the macroscopic behavior of the model. By extending the model to include spatial mechanisms, Cohen and Pastor will investigate the fractal dimension of plant species distributions over the landscape as they are produced by the model. The investigators will then used data on spatial distributions of plant species in a relevant area, and compare the fractal dimension of the real distribution to that produced by the model. Drs. Cohen and Pastor are innovative and productive scientists who are experienced with the problems of the development and validation of large, complex ecosystem models. These models are used for predicting the effects of climate change on the biosphere and may be essential tools for managing resources in the future. This research is an essential test of the behavior of these models. The institutional support for this research is outstanding.