Statisticians Perspective:
R. A. Desharnais

Do Mathematical Models Really Work After All? 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.