Studies by ourselves and others (Swan 1970, Austin & Noy-Meir 1972, Beals 1973, Hill 1973, 1974, Austin 1976a, b, Fasham 1977, Gauch Whittaker & Wentwarth 1977, Noy-Meir & Whittaker 1977, Orloci 1978, Gauch, Whittaker & Singer 1979) have found faults with all ordination techniques currently in use, at least when applied to ecological data specifying the occurrences of species in community samples. These faults certainly do not make existing techniques useless; but they mean that results must be interpreted with caution. Even with the best techniques, the underlying structure of the data is often poorly expressed.

Detrended correspondence analysis: an improved ordination technique

2 Foreword This textbook provides study materials for the participants of the course named Multivariate Analysis of Ecological Data that we teach at our university for the third year. Material provided here should serve both for the introductory and the advanced versions of the course. We admit that some parts of the text would profit from further polishing, they are quite rough but we hope in further improvement of this text. We hope that this book provides an easy-to-read supplement for the more exact and detailed publications like the collection of the Dr. Ter Braak' papers and the Canoco for Windows 4.0 manual. In addition to the scope of these publications, this textbook adds information on the classification methods of the multivariate data analysis and introduces some of the modern regression methods most useful in the ecological research. Wherever we refer to some commercial software products, these are covered by trademarks or registered marks of their respective producers. This publication is far from being final and this is seen on its quality: some issues appear repeatedly through the book, but we hope this provides, at least, an opportunity to the reader to see the same topic expressed in different words.

https://esajournals.onlinelibrary.wiley.com/doi/pdf/10.1890/0012-9623%282006%2987%5B193%3AMAOED%5D2.0.CO%3B2

Multivariate Analysis of Ecological Data

We shall, in this last chapter, treat the floristic-sociological or Braun-Blanquet approach to classification and interpretation of communities.

The Braun-Blanquet Approach

The numerical treatment of phytosociological data is often based on estimates of cover and/or abundance according to the Braun-Blanquet and Domin scales. Since Schwickerath (1931, 1938, 1940) and Tuxen & Ellenberg (1937) published their transformations there has been discussion on the way the scale values should be used in calculations Qualitative approaches, i.e. based on presence and absence have also been favoured (e.g. Williams & Lambert 1959, van der Maarel 1966) Dagnelie (I960) proposed a pseudoqualitative basis for various calculations by means of a ‘coupure’. A coupure includes the deletion of lower values, usually according to a fixed criterion, e.g. the number of occurrences in a phytosociological table to be remained should be as close as possible to 50%. Dagnelie’s approach remained largely unknown and apparently it has never been tested.

https://www.jstor.org/stable/info/20145666

Transformation of Cover-Abundance Values in Phytosociology and its Effects on Community Similarity

Publisher Summary Ordination implies an abstract space in which the entities form a constellation. In the Bray–Curtis ordination, the entities are samples and the attributes are species values in those samples. The aim of this method is to (1) calculate a distance matrix, (2) select two reference points (either real or synthetic samples) for determining direction of each axis, and (3) project all samples onto each such axis by their relationship to the two reference points. There are two major problems common to all ordination techniques, which include a function of the β-diversity or heterogeneity of the data set—that is, how different the samples are from one another. All ordinations distort the original multivariate data set and information is inevitably lost. Distortion in ordination has two kinds of consequences. The first is compressing and stretching distances in the ordination, compared with the original distance measures and relative to one another. The second consequence is the curvature of environmental axes, and this relates to Orloci's types A and C. Some of the alternatives to Bray–Curtis ordination are principal component analysis, reciprocal averaging, and iterative-stress minimization techniques.

Bray-curtis ordination: an effective strategy for analysis of multivariate ecological data

Q-type ordination methods are emphasized in general phytosociological studies. A new modification of the simple ordination method is introduced as principal axes ordination. Its relation to the theoretically preferred principal components analysis is discussed. A new simple similarity coefficient based on both similarity and disimilarity components is proposed.

On the use of ordination models in phytosociology

This contribution presents a review of the development of the study of vegetation dynamics since 1979, in the framework of a jubilee meeting on progress in the study of vegetation. However, an exhaustive review is both impossible and unnecessary. It is impossible within the few pages available because of the vast literature published, and it is unnecessary because there are several review papers and textbooks available. To start with the year 1979 itself, two important papers appeared (White 1979; Huston 1979), and a symposium on advances in vegetation science was held in Nijmegen (Van der Maarel 1980a,b). Further publications consulted for this paper include Pickett & White (1985), Pickett et al. (1987), Gray et al. (1987), Burrows (1990), Van Andel et al. (1993), Glenn-Lewin et al. (1992) and Agnew et al. (1993). In 1979 a similar special meeting was held (Werger 1979), where I contributed with a review-like paper on numerical methods in vegetation science. Since this important aspect of vegetation science was not covered at this jubilee meeting, some developments of this branch have been included here, mainly so far as they apply to vegetation dynamics. Since I am involved in one particular branch of vegetation dynamics, i.e. gap dynamics, extra attention will be paid to recent work in Uppsala, perhaps at the expense of other new developments.

/pdf/vegetation-dynamics-and-dynamic-vegetation-science-vv6wgxw87t.pdf

Vegetation dynamics and dynamic vegetation science

Most of the methods used in the multivariate analysis of data on vegetation and environment, or transformations implied in such methods, put disproportionate emphasis on species with a relatively wide ecological amplitude occurring with relatively high cover-abundance values, and/or rare species. This problem can be overcome to some extent by reducing the cover-abundance values to presence-absence data, but this means a severe loss of information. A standardization of values by species maxima as is done automatically in some programs, may lead to an undesirable emphasis on species represented with low values only.

Optimum-transformation of plant species cover-abundance values

Current methods for the determination of the minimal area of a phytocoenosis are compared. A new method is described. It is based on the increase in average quantitative similarity between plots in series of nested plots of increasing size in relation to species richness and dominance relations. A simulation model composed of coenotic molecules sensu Moravec is developed from which these relations can be deduced. Both a quantita tive and a qualitative minimal area are derived in this way. The analytical minimal area is then defined in relation to the largest of the two minimal area values, because in this way both the species richness and the dominance relations will be represented.

E. van der Maarel

Papers

Transformation of Cover-Abundance Values in Phytosociology and its Effects on Community Similarity

On the use of ordination models in phytosociology

Vegetation dynamics and dynamic vegetation science

Optimum-transformation of plant species cover-abundance values

A new approach to the minimal area of a plant community