Abstract not found

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 max-imally separated. The eigenvalues produced by CCA measure this separation. As its name suggests, CCA is also a correspondence analysis technique, but one in which the ordination axes are constrained to be linear combinations of environmental variables. The ordination diagram generated by CCA visualizes not only a pattern of community variation (as in standard ordination) but also the main features of the distributions of species along the environmental variables. Applications demonstrate that CCA can be used both for detecting species-environment relations, and for investigating specific questions about the response of species to environmental variables. Questions in community ecology that have typically been studied by 'indirect ' gradient analysis (i.e. ordination followed by external interpretation of the axes) can now be answered more directly by CCA.

1 Canonical community ordination comprises a collection of methods that relate species assemblages to their environment, in both observational studies and designed experiments. Canonical ordination differs from ordination sensu stricto in that species and environment data are analyzed simultaneously. Part I reviews the theory in a non-mathematical way with emphasis on new insights for the interpretation of ordination diagrams. The interpretation depends on the ordination method used to create the diagram. After the basic theory, Part I is focused on the ordination diagrams in linear methods of canonical community ordination, in particular principal components analysis, redundancy analysis and canonical correlation analysis. Special attention is devoted to the display of qualitative environmental variables. Key words: principal components analysis, redundancy analysis, canonical correlation analysis, biplot, ordination diagram, species-environment relations. 2

: Metric Scaling is a well--known method to represent a finite set with respect to a given Euclidean distance matrix. Several methods to represent rows and columns of a two--way contingency table are available: Correspondence Analysis, Dual Scaling, Canonical Coordinates, etc. We show that metric scaling provides a similar representation by using Hellinger or Rao distances together with Gower's add--a--point formula and discuss its relationship with the other approaches. The present approach suggests an alternative to Multiple Correspondence Analysis for multivariate categorical data. Keywords: Categorical data; Correspondence Analysis; Distances between observations; Multidimensional scaling; Biplot. AMS Subject Classification: 62H25, 62H20, 62-09. 1 Introduction The statistical methodology dealing with categorical data currently has an increasing interest. Under the name Correspondence Analysis (CA), the data analyst recognizes a method of graphical representation of categorical ...

The indicator value and ecological amplitude of a species with respect to a quantitative environmental vari-able can be estimated from data on species occurrence and environment. A simple weighted averaging (WA) method for estimating these parameters is compared by simulation with the more elaborate method of Gaus-sian logistic regression (GLR), a form of the generalized linear model which fits a Gaussian-like species re-sponse curve to presence-absence data. The indicator value and the ecological amplitude are expressed by two parameters of this curve, termed the optimum and the tolerance, respectively. When a species is rare and has a narrow ecological amplitude- or when the distribution of quadrats along the environmental variable is reasonably even over the species ' range, and the number of quadrats is small- then WA is shown to ap-proach GLR in efficiency. Otherwise WA may give misleading results. GLR is therefore preferred as a practi-cal method for summarizing species ' distributions along environmental gradients. Formulas are given to cal-culate species optima and tolerances (with their standard errors), and a confidence interval for the optimum from the GLR output of standard statistical packages.

OF THE DISSERTATION A Markov Chain Monte Carlo Method for Approximating 2-Way Contingency Tables with Applications in the Stability Analysis of Ecological Ordination by Stanley S. Bentow Doctor of Philosophy in Statistics University of California, Los Angeles, 1999 Professor N. Donald Ylvisaker, Chair This dissertation develops a Markov Chain Monte Carlo method for approximating 2-way contingency tables with an eye toward assessing the stability of ecological ordination. Ecology is a part of biology that deals with the interrelationships between populations, communities and ecosystems and their environment. It draws on knowledge from many other disciplines such as climatology, physical geography, agronomy, and pedology [52]. Odum [75] prefers the de nition \ Ecology is the study of structure and function of nature," and stresses the role of ecosystem research in relation to the use of nature by man. Krebs [58] prefers to think of Ecology as the scienti c study of the interactions t...