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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.

Two new methods for inferring pH from diatoms are presented. Both are based on the observation that the relationships between diatom taxa and pH are often unimodal. The first method is maximum likelihood calibration based on Gaussian logit response curves of taxa against pH. The second is weighted averaging. In a lake with a particular pH, taxa with an optimum close to the lake pH will be most abundant, so an intuitively reasonable estimate of the lake pH is to take a weighted average of the pH optima of the species present. Optima and tolerances of diatom taxa were estimated from contemporary pH and proportional diatom counts in littoral zone samples from 97 pristine soft water lakes and pools in Western Europe. The optima showed a strong relation with Hustedt’s pH preference groups. The two new methods were then compared with existing calibration methods on the basis of differences between inferred and observed pH in a test set of 62 additional samples taken between 1918 and 1983. The methods were ranked in order of performance as follows (between brackets the standard error of inferred pH in pH units); maximum likelihood (0.63)> weighted averaging (0.71) = multiple regression using pH groups (0.71) = the Gasse & Tekaia method (0.71)> Renberg & Hellberg’s Index B (0.83) % multiple regression

Classical multidimensional scaling (MDS) is a method for visualizing high-dimensional point clouds by mapping to low-dimensional Euclidean space. This mapping is defined in terms of eigenfunctions of a matrix of interpoint dissimilarities. In this paper we analyze in detail multidimensional scaling applied to a specific dataset: the 2005 United States House of Representatives roll call votes. Certain MDS and kernel projections output “horseshoes” that are characteristic of dimensionality reduction techniques. We show that, in general, a latent ordering of the data gives rise to these patterns when one only has local information. That is, when only the interpoint distances for nearby points are known accurately. Our results provide a rigorous set of results and insight into manifold learning in the special case where the manifold is a curve. 1. Introduction. Classical

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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...

This article develops a model to relate a multivariate compositional response to a number of covariates and proposes a new graphical model, called the Random Effects Discrete Regression (REDR) model, which allows for examination of the complex conditional relationships between a set of covariates and multiple discrete response variables. The approach offers a number of advantages over previous approaches and allows for a wide range of inferences. Relationships between compositional observations can be evaluated through a set of interaction parameters and inference about the influence of covariates is possible through a set of regression coefficients. The model also allows for examination of relationships between the covariates via another set of interactions. Parameter inference via Bayesian methods and MCMC is discussed. The proposed model and MCMC methods are used to examine the relationship between compositional observations of two characteristics of fish species and a number of covariates. These relationships are of interest to the U.S. Environmental Protection Agency for stream monitoring. 1.

Canonical correspondence analysis (CCA) is perhaps the most popular multivariate technique used by environmental ecologists for constrained ordination; it is an approximation to the maximum likelihood solution of the Gaussian response model. In this article, we look at the constrained ordination problem from a slightly different point of view and argue that it is this particular point of view that CCA implicitly adopts. This gives us additional insights into the nature of CCA. We then exploit the new perspective to generalize the Gaussian response model to incorporate more flexible response functions. A real example is presented to illustrate the use of the more flexible model.