A unified approach is presented for the construction and analysis of m
odels 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 simple
r 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 equa
tions, non-linear Leslie matrices and reaction-diffusion equations. Th
e 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 mod
els and patch models are given in the Appendix.