A Comparison of Some Cotswold Beechwoods Using Multiple-Discriminant Analysis

Abstract

In many plant ecological studies information is available about the performance of species at a number of sites, either in the form of simple 0/1 data or with additional measures of cover/abundance or frequency. The applicability of multivariate methods to the study of such data has been shown by the many uses of ordination and classification in the recent literature. The general aim is to discover grouping or an underlying structure within the data, which is considered as a single multivariate statistical universe. A different problem arises when there are several multivariate statistical universes which have already been defined as distinct by the investigator on some external criterion; the internal structure of any of these, separately or all together, may have been examined previously. The concern now, however, is how these groups may be compared and hypotheses generated about the reasons for their differences. A method suitable for this is Multiple-Discriminant Analysis (MDA), a term we prefer to canonical analysis as used by Seal (1964) and others since it is more explicit and avoids possible confusion with the method of canonical correlation. We know of no report on the use of MDA in the plant ecological literature, but it has been used by Buzas (1967) to compare faunal areas, Healy (1965) to compare groups of mice, Horton, Russell & Moore (1968) to examine differences between soil types in a gilgaied area, and others. This paper reports the application of MDA to ground flora data from some Cotswold beechwoods. There are thirteen groups, each corresponding to a woodland area defined as distinct on the ground. In the initial stages of this work the data of the thirteen woods were considered together and analysed by Association-Analysis and Principal Components Analysis. From these results (Barkham 1968) it appeared that the woodland might be of interest as an ecological unit and within-wood variation was considered first. Thus in investigating the between-wood variation in the present report the results of the previous series of analyses have been taken into account. The differences between woods may be due to differences inherent in varying physical site conditions. But if the latter are similar for two or more woods then the differences in vegetation may be accounted for by variation in management practices. Whichever group of factors may be found most significant it is important to assess differences between woods because the wood is the most frequent unit in forestry and conservation management. In each of the w woods the presence and cover, or absence, of the same species is recorded at a number of sites. Each wood can be represented by its vector of species means (on the measure chosen, see below) and located in m-dimensional space. The discriminant functions, or axes, are a new set of orthogonal axes in this fixed space positioned so that the first accounts for as much as possible of the difference between the wood* Present address: School of Environmental Sciences, University of East Anglia.