C.J.F. ter Braak

Bio: C.J.F. ter Braak is an academic researcher. The author has contributed to research in topics: Ordination & Software. The author has an hindex of 1, co-authored 1 publications receiving 3651 citations.

Ecologically meaningful transformations for ordination of species data

Abstract: 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.

Towards a functional classification of the freshwater phytoplankton

Abstract: This paper considers the structure of freshwater phytoplankton assemblages and promotes a scheme of vegetation recognition', based upon the functional associations of species represented in the plankton. These groups are often polyphyletic, recognizing commonly shared adaptive features, rather than common phylogeny, to be the key ecological driver. Thirty-one such associations are outlined and the basic pattern of their distinctive ecologies is outlined. An invitation to other plankton scientists to assist in the development of this scheme is issued.

Permutation tests for univariate or multivariate analysis of variance and regression

Abstract: The most appropriate strategy to be used to create a permutation distribution for tests of individual terms in complex experimental designs is currently unclear. There are often many possibilities, including restricted permutation or permutation of some form of residuals. This paper provides a summary of recent empirical and theoretical results concerning available methods and gives recommendations for their use in univariate and multivariate applications. The focus of the paper is on complex designs in analysis of variance and multiple regression (i.e., linear models). The assumption of exchangeability required for a permutation test is assured by random allocation of treatments to units in experimental work. For observational data, exchangeability is tantamount to the assumption of independent and identically distributed errors under a null hypothesis. For partial regression, the method of permutation of residuals under a reduced model has been shown to provide the best test. For analysis of variance, o...