A theory of gradient analysis

This chapter concerns data analysis techniques that assist the interpretation of community composition in terms of species' responses to environmental gradients in the broadest sense. All species occur in a characteristic, limited range of habitats; and within their range, they tend to be most abundant around their particular environmental optimum. The composition of biotic communities thus changes along environmental gradients. Direct gradient analysis is a regression problem—fitting curves or surfaces to the relation between each species' abundance, probability of occurrence, and one or more environmental variables. Ecologists have independently developed a variety of alternative techniques. Many of these techniques are essentially heuristic, and have a less secure theoretical basis. This chapter presents a theory of gradient analysis, in which the heuristic techniques are integrated with regression, calibration, ordination and constrained ordination as distinct, well-defined statistical problems. The various techniques used for each type of problem are classified in families according to their implicit response model and the method used to estimate parameters of the model. Three such families are considered. The treatment shown here unites such apparently disparate data analysis techniques as linear regression, principal components analysis, redundancy analysis, Gaussian ordination, weighted averaging, reciprocal averaging, detrended correspondence analysis, and canonical correspondence analysis in a single theoretical framework.