This paper presents a new and simple method to find indicator species and species assemblages characterizing groups of sites The novelty of our approach lies in the way we combine a species relative abundance with its relative frequency of occurrence in the various groups of sites This index is maximum when all individuals of a species are found in a single group of sites and when the species occurs in all sites of that group; it is a symmetric indicator The statistical significance of the species indicator values is evaluated using a randomization procedure Contrary to TWINSPAN, our indicator index for a given species is independent of the other species relative abundances, and there is no need to use pseudospecies The new method identifies indicator species for typologies of species releves obtained by any hierarchical or nonhierarchical classification procedure; its use is independent of the classification method Because indicator species give ecological meaning to groups of sites, this method provides criteria to compare typologies, to identify where to stop dividing clusters into subsets, and to point out the main levels in a hierarchical classification of sites Species can be grouped on the basis of their indicator values for each clustering level, the heterogeneous nature of species assemblages observed in any one site being well preserved Such assemblages are usually a mixture of eurytopic (higher level) and stenotopic species (characteristic of lower level clusters) The species assemblage approach demonstrates the importance of the ''sampled patch size,'' ie, the diversity of sampled ecological combinations, when we compare the frequencies of core and satellite species A new way to present species-site tables, accounting for the hierarchical relationships among species, is proposed A large data set of carabid beetle distributions in open habitats of Belgium is used as a case study to illustrate the new method

/pdf/species-assemblages-and-indicator-species-the-need-for-a-11brlxhd4r.pdf

Species assemblages and indicator species:the need for a flexible asymmetrical approach

https://www.wsl.ch/staff/niklaus.zimmermann/papers/ecomod135_147.pdf

Predictive habitat distribution models in ecology

A new multivariate analysis technique, developed to relate community composition to known variation in the environment, is described. The technique is an extension of correspondence analysis (reciprocal averaging), a popular ordination technique that extracts continuous axes of variation from species occurrence or abundance data. Such ordination axes are typically interpreted with the help of external knowledge and data on environmental variables; this two—step approach (ordination followed by environmental gradient identification) is termed indirect gradient analysis. In the new technique, called canonical correspondence analysis, ordination axes are chosen in the light of known environmental variables by imposing the extra restriction that the axes be linear combinations of environmental variables. In this way community variation can be directly related to environmental variation. The environmental variables may be quantitative or nominal. As many axes can be extracted as there are environmental variables. The method of detrending can be incorporated in the technique to remove arch effects. (Detrended) canonical correspondence analysis is an efficient ordination technique when species have bell—shaped response curves or surfaces with respect to environmental gradients, and is therefore more appropriate for analyzing data on community composition and environmental variables than canonical correlation analysis. The new technique leads to an ordination diagram in which points represent species and sites, and vectors represent environmental variables. Such a diagram shows the patterns of variation in community composition that can be explained best by the environmental variables and also visualizes approximately the "centers" of the species distributions along each of the environmental variables. Such diagrams effectively summarized relationships between community and environment for data sets on hunting spiders, dyke vegetation, and algae along a pollution gradient.

/pdf/canonical-correspondence-analysis-a-new-eigenvector-4kvv4zh7ls.pdf

Canonical Correspondence Analysis: A New Eigenvector Technique for Multivariate Direct Gradient Analysis

Multivariate analyses are well known and widely used to identify and understand structures of ecological communities. The ade4 package for the R statistical environment proposes a great number of multivariate methods. Its implementation follows the tradition of the French school of "Analyse des Donnees" and is based on the use of the duality diagram. We present the theory of the duality diagram and discuss its implementation in ade4. Classes and main functions are presented. An example is given to illustrate the ade4 philosophy.

/pdf/the-ade4-package-implementing-the-duality-diagram-for-r095ij3wwz.pdf

The ade4 Package: Implementing the Duality Diagram for Ecologists

This paper examines how to obtain species biplots in unconstrained or constrained ordination without resorting to the Euclidean distance [used in principal-component analysis (PCA) and redundancy analysis (RDA)] or the chi-square distance [preserved in correspondence analysis (CA) and canonical correspondence analysis (CCA)] which are not always appropriate for the analysis of community composition data. To achieve this goal, transformations are proposed for species data tables. They allow ecologists to use ordination methods such as PCA and RDA, which are Euclidean-based, for the analysis of community data, while circumventing the problems associated with the Euclidean distance, and avoiding CA and CCA which present problems of their own in some cases. This allows the use of the original (transformed) species data in RDA carried out to test for relationships with explanatory variables (i.e. environmental variables, or factors of a multifactorial analysis-of-variance model); ecologists can then draw biplots displaying the relationships of the species to the explanatory variables. Another application allows the use of species data in other methods of multivariate data analysis which optimize a least-squares loss function; an example is K-means partitioning.

https://www.umass.edu/landeco/teaching/multivariate/readings/LegendreandGallagher2001.pdf

Ecologically meaningful transformations for ordination of species data

Canoco is a software package for multivariate data analysis, with an emphasis on dimesional reduction (ordination), regression analysis, and the combination of the two, constrained ordination. Canoco makes effective and powerful ordination methods easilyt accessible for scientists wanting to infer and visualize pattern and structure in complex multivariate data, e.g. biologists researching the relations between plant and animal communities and their environment. Canoco contains linear and unimodal ordination methods, with the possibility to account for background variation specified by covariates. In combination with extensive facilities for permutation tests, these methods have proven to be remarkably effective in solving applied research problems.

CANOCO Reference Manual and CanoDraw for Windows User's Guide: Software for Canonical Community Ordination (version 4.5)

Ecological data has several special properties: the presence or absence of species on a semi-quantitative abundance scale; non-linear relationships between species and environmental factors; and high inter-correlations among species and among environmental variables. The analysis of such data is important to the interpretation of relationships within plant and animal communities and with their environments. In this corrected version of Data Analysis in Community and Landscape Ecology, without using complex mathematics, the contributors demonstrate the methods that have proven most useful, with examples, exercises and case-studies. Chapters explain in an elementary way powerful data analysis techniques such as logic regression, canonical correspondence analysis, and kriging.

/pdf/data-analysis-in-community-and-landscape-ecology-3qatdnu8pv.pdf

Data Analysis in Community and Landscape Ecology

Publisher Summary This chapter concerns data analysis techniques that assist the interpretation of community composition in terms of species' responses to environmental gradients in the broadest sense. All species occur in a characteristic, limited range of habitats; and within their range, they tend to be most abundant around their particular environmental optimum. The composition of biotic communities thus changes along environmental gradients. Direct gradient analysis is a regression problem—fitting curves or surfaces to the relation between each species' abundance, probability of occurrence, and one or more environmental variables. Ecologists have independently developed a variety of alternative techniques. Many of these techniques are essentially heuristic, and have a less secure theoretical basis. This chapter presents a theory of gradient analysis, 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 in families according to their implicit response model and the method used to estimate parameters of the model. Three such families are considered. The treatment shown here unites such apparently disparate data analysis techniques as linear regression, principal components analysis, redundancy analysis, Gaussian ordination, weighted averaging, reciprocal averaging, detrended correspondence analysis, and canonical correspondence analysis in a single theoretical framework.

/pdf/a-theory-of-gradient-analysis-351pq0a6mk.pdf

A Theory of Gradient Analysis

Canoco Reference Manual and User’s Guide: Software for Ordination (version 5.0)

Canonical correspondence analysis (CCA) is introduced as a multivariate extension of weighted averaging ordination, which is a simple method for arranging species along environmental variables. CCA constructs those linear combinations of environmental variables, along which the distributions of the species are maximally separated. The eigenvalues produced by CCA measure this separation.

/pdf/the-analysis-of-vegetation-environment-relationships-by-1t1e62l921.pdf

C.J.F. ter Braak

Papers

CANOCO Reference Manual and CanoDraw for Windows User's Guide: Software for Canonical Community Ordination (version 4.5)

Data Analysis in Community and Landscape Ecology

A Theory of Gradient Analysis

Canoco Reference Manual and User’s Guide: Software for Ordination (version 5.0)

The analysis of vegetation-environment relationships by canonical correspondence analysis