Variability, vagueness and comparison methods for ecological models

A unified approach is presented for the construction and analysis of models for the dynamics of populations and communities in the presence of temporal variability, vague density dependence, chaos or analytical intractability. The approach is based on comparisons involving simpler models which provide ceilings and floors to the densities predicted by the full models. The method is applied to examples of several types of models, including difference equations, ordinary differential equations, non-linear Leslie matrices and reaction-diffusion equations. The models treated describe various ecological phenomena including self-regulation, competition, predator-prey interactions, age structure and spatial structure. Some results needed for the analysis of matrix models and patch models are given in the Appendix.