Comparisons of three ordination techniques

Summary Simulated coenoclines were used to test performance of several techniques for ordinating samples by species composition: Wisconsin polar or Bray-Curtis ordination with Euclidean distance (ED) and the complements of percentage similarity (PD) and coefficient of community (CD) as distance measures, Principal components analysis, and polar and non-polar or indirect use of Discriminant function analysis. In general the Bray-Curtis technique gave the best ordinations, and PD was the best distance measure. Euclidean distance gave greater distortion than PD in all tests; CD may be better than PD only for some sample sets of high alpha and beta diversity and high levels of noise or sample error. Principal components ordinations are increasingly distored as beta diversity increases, and are highly vulnerable to effects of both noise and sample clustering. Discriminant function analysis was found generally unsuitable for ordination of samples by species composition, but likely to be useful for sample classification.     

A generalized standardization procedure in ecological ordination: Tests with Principal Components Analysis

Abstract. Standardization by norms of sample position vectors as well as by sample totals has been used frequently in vegetation ecology. Both standardizations are only special cases of the Generalized Standardization Procedure (GSP) described in this paper. The general procedure allows a wide choice of data transformations simply by varying values of a single standardization parameter. Principal Components Analysis (PCA) often involutes opposite ends of a coenospace, producing results that may be difficult to interpret. Experiments with simulated as well as field data sets revealed that involuted gradients can be unfolded if GSP is applied prior to PCA. Compared to Correspondence Analysis, GSP-PCA was superior in recovering the structure of analysed coenoclines.     

Gradient analysis of dry grassland vegetation in Denmark

Abstract. We present a gradient analysis of 620 vegetation samples covering most of the floristic and environmental variation in semi‐natural grassland vegetation on well‐drained soils in Denmark. Vegetation was sampled using frequency in subplots. Explanatory variables were surface inclination, aspect, pH, geographical co‐ordinates together with indications of soil type. Detrended Correspondence Analysis revealed four floristic gradients that could be interpreted in ecological terms by measured variables supplemented with site calibrations based on weighted averaging of Ellenberg's indicator values. All four axes were interpreted using rank correlation statistics, and linear and non‐linear multiple regression of sample scores on explanatory variables. The first gradient was from dry calcareous to humid acidic grasslands; the second reflected an underlying gradient in fertility; the third reflected regional differentiation and the fourth was associated with variation in intensity of competition as indicated by association with calibrated Grime‐CSR values for the plots. We applied subset ordination to the data as a supplement to traditional permutation and correlation statistics to assess the consistency of ordination results. DCA axes 1 and 2 were consistent in space and time. This gradient analysis is discussed in a context of plant strategy theory and species diversity models. Ecocline patterns lend support to the view that grazing not only favours the ruderal strategy but also the stress‐tolerant strategy. The low rank of competition as an explanatory variable for the floristical gradients supports the notion that competitive effects play a subordinate role for species composition compared to microclimate and soil conditions in infertile semi‐natural grasslands.     

Ordination and classification in the upland Rugege forest (Rwanda,Central Africa)

Summary Quantitative data on habitat and vegetation from 42 releves of the Rugege forest have been submitted to different ordination and classification methods.The habitat factors which have an important effect upon vegetation are: hydromorphy, abundance of tree layer and depth of soil.The different ordination (principal components analysis and reciprocal averaging) and numerical classification methods applied to the same set of data lead to consistent results. The numerical classification seems better than the Braun-Blanquet's method.Four groupings have been defined.The future developments of ecological studies in the Rugege forest are discussed in relation to the forest conservation.All data presented in this work were collected during my stay in the National Institute of Scientific Research of Rwanda, 1971 – 1972. Part of the computations (numerical analysis and principal components analysis) was carried out at the Nijmegen University's IBM 370/155; I am happy to thank Dr. E. van der Maarel and Dr. J.G.M. Janssen for their welcome and assistance. The reciprocal averaging ordinations and the principal components analysis on the basis of correlation between relevés were performed on the Louvain-La-Neuve University's IBM 370/158; I am very grateful to Professeur Berthet for this important assistance.This paper corresponds to part of a thesis presented at the Liège University on 7th November 1973.     

Altitudinal pattern of vegetation variation on Tenerife

Abstract. The variation in structure and floristic composition of the vegetation of Tenerife is related to different environmental factors. 200 sample plots, stratified according to altitude, exposure to wind, kind and age of parent rock, inclination and degree of disturbance were analysed throughout the island. The resulting data were analysed using univariate statistics (altitudinal distribution profiles of the more frequent species) and multivariate methods (Correspondence, Cluster and Pattern Analysis). Altitude, exposure to wind and, to a lesser extent, disturbance were found to be the major determinants of vegetational variation, whereas parent rock and inclination were less important. Ordination results show a continuum in structural and floristic variation of the vegetation with species distributions varying continually along the altitudinal gradient. Nevertheless, altitudinally bound plant community types were recognized with Cluster Analysis. Vegetational discontinuities, which were also detected by pattern analysis, are more evident on the windward slope of the island; they have been attributed to the existence of a major underlying environmental discontinuity the ‘cloud sea’-which is associated with a climatic inversion. On the leeward slope, beyond the influence of the cloud sea, discontinuities are less evident and vegetational variation seems to be closer to a coenocline, i.e. a vegetational continuum.     

Simulation of community patterns

Programs are described for the simulation of coenoplanes-mathematically defined, two-dimensional community patterns characterized by scattered and broadly overlapping Gaussian reponse surfaces for species populations. Field data have been studied to derive a set of assumptions regarding realistic properties of coenoplanes and ways in which some of these properties should be variable. Additional assumptions define properties of samples and sets of samples taken from coenoplanes. The programs thus provide a basis for tests of different ordination techniques and effects of characteristics of sample sets on these.