A Theory of Gradient Analysis

Abstract

The theory of gradient analysis is presented in this chapter, 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 into families according to their implicit response model and the method used to estimate parameters of the model. Three such families are considered. First, the family of standard statistical techniques based on the linear response model is dealt with, because they are conceptually the simplest and provide a basis for what follows, even though their ecological application is restricted. Second, a family of somewhat more complex statistical techniques are outlined which are formal extensions of the standard linear techniques and incorporate unimodal (Gaussian-like) response models explicitly. Finally, the family of heuristic techniques is considered based on weighted averaging. These are not more complex than the standard linear techniques, but implicitly fit a simple unimodal response model rather than a linear one. Ordination diagrams and their interpretation on bi plots and joint plots are also given in the chapter. This chapter has discussed which response model to choose from direct and indirect gradient analysis, and then in direct system, which one to choose from regression and constrained ordination. © 1988, Academic Press Limited