Variation in the abundance of species in space and/or time can be caused by a wide range of underlying processes. Before such causes can be analysed we need simple mathematical models which can describe the observed response patterns. For this purpose a hierarchical set of models is presented. These models are applicable to positive data with an upper bound, like relative frequencies and percentages. The models are fitted to the observations by means of logistic and non-linear regression techniques. Working with models of increasing complexity allows us to choose for the simplest possible model which sufficiently explains the observed pattern. The models are particularly suited for description of responses in time or over major environmental gradients. Deviations from these temporal or spatial trends may be statistically ascribed to, for example, climatic fluctuations or small-scale spatial heterogeneity. The applicability of this approach is illustrated by examples from recent research. A combination of simple, descriptive models like those presented in this paper and causal models as developed by several others, is advocated as a powerful tool towards a fuller understanding of the dynamics and patterns of vegetational change.