Statisticians Perspective:
Bruce Kendall

I originally arrived in ecology through an interest in nonlinear dynamics and chaos, and am still entranced by the mathematical beauty of population models. My experience using quantitative techniques to fit nonlinear population models to fit time series data demonstrates that it is possible to use these models to distinguish among potential biological causes of population dynamics. However, I have come to see that "noise," that pesky thing we love to gripe about, is of central importance, and that we need to think about the bio-physical processes that give rise to stochasticity in ecological dynamics. I believe that it is only by explicitly including the mechanisms of ecological stochasticity (which are themselves often nonlinear) into population models that we can expect these models to provide quantitative insight and predictions. My answer is a qualified "yes", provided they are the right models which can be connected to experimental data.

In order for nonlinear dynamics to be successful as a working hypothesis in ecology, the mathematical models should be based on known mechanisms that determine ecological change. Furthermore, the nonlinear deterministic model must form the "skeleton" of a stochastic model. Stochasticity should be added not as an afterthought; consideration should also be given as to the mechanisms that produce ecological uncertainty. Nonlinear stochastic models of this type can be used to estimate model parameters from data, to obtain confidence intervals around parameter estimates, to evaluate the ability of the model to explain existing data, and to generate testable predictions.