On Objective Functions of Phytosociological Resemblance

Abstract

Different objective functions are reviewed with regard to their intrinsic properties and generic relationshiDs as they relate to the measurement of phytosociological resemblance. These functions may take the form of a distance, probability, or information. Functions of these kinds are best conceived by the phytosociologist as abstractions which are meaningful only when placed within the bounds of a given sample space. In such a space the phytosociological objects, such as the individual stands of vegetation, are represented as points whose relative spatial placement is determined by the resemblance function. The spatial configuration of points, i.e., the manner of their placement relative to one another in sample space, is referred to as sample structure in the present paper. The first part of the paper includes a discussion of the sample space and sample structure, and it also deals with the concept of stochastic and deterministic resemblance functions. This is followed by the description of the different variants of distance, a probability-type coefficient, and several information theory functions. While the distance functions here represent metric divergences, which define the relative placement of objects in sample space, a probability-type coefficient, as a probability divergence, expresses the likelihood that given objects will be more dis-