Donald A. Jackson

Bio: Donald A. Jackson is an academic researcher from University of Toronto. The author has contributed to research in topics: Principal component analysis & Species richness. The author has an hindex of 50, co-authored 124 publications receiving 13486 citations. Previous affiliations of Donald A. Jackson include Queen's University.

Stopping rules in principal components analysis: a comparison of heuristical and statistical approaches'

Abstract: Approaches to determining the number of components to interpret from principal components analysis were compared. Heuristic procedures included: retaining components with eigenvalues (Xs) > 1 (i.e., Kaiser-Guttman criterion); components with bootstrapped Xs > 1 (bootstrapped Kaiser-Guttman); the scree plot; the broken-stick model; and components with Xs totalling to a fixed amount of the total variance. Statistical ap- proaches included: Bartlett's test of sphericity; Bartlett's test of homogeneity of the cor- relation matrix, Lawley's test of the second X; bootstrapped confidence limits on successive Xs (i.e., significant differences between Xs); and bootstrapped confidence limits on eigen- vector coefficients (i.e., coefficients that differ significantly from zero). All methods were compared using simulated data matrices of uniform correlation structure, patterned ma- trices of varying correlation structure and data sets of lake morphometry, water chemistry, and benthic invertebrate abundance. The most consistent results were obtained from the broken-stick model and a combined measure using bootstrapped Xs and associated eigen- vector coefficients. The traditional and bootstrapped Kaiser-Guttman approaches over- estimated the number of nontrivial dimensions as did the fixed-amount-of-variance model. The scree plot consistently estimated one dimension more than the number of simulated dimensions. Bartlett's test of sphericity showed inconsistent results. Both Bartlett's test of homogeneity of the correlation matrix and Lawley's test are limited to testing for only one and two dimensions, respectively.

What controls who is where in freshwater fish communities — the roles of biotic, abiotic, and

Abstract: We examine evidence for the structuring of fish communities from stream and lake systems and the roles of biotic, abiotic, and spatial factors in determining the species composition. Piscivory by fish is a dominant factor in both stream and lake systems whereas evidence for the importance of competition appears less convincing. Within small streams or lakes, the impact of predation may exclude other species, thereby leading to mutually exclusive distributions and strong differences in community composition. Within a geographic region, abiotic effects frequently dictate the rel - ative importance of piscivory, thereby indirectly influencing the composition of prey species present. The spatial scale of studies influences our perceived importance of biotic versus abiotic factors, with small-scale studies indicating a greater importance of competition and large-scale studies emphasizing abiotic controls. The scale of the individual sites considered is critical because smaller systems have higher variability and wider extremes of conditions than larger lakes and rivers. The stability of physical systems and degree of spatial connectivity contribute to increased diversity in both larger stream and larger lake systems. We identify challenges and needs that must be addressed both to advance the field of fish community ecology and to face the problems associated with human-induced changes.

What controls who is where in freshwater fish communities the roles of biotic, abiotic, and spatial factors

Abstract: We examine evidence for the structuring of fish communities from stream and lake systems and the roles of biotic, abiotic, and spatial factors in determining the species composition. Piscivory by fish is a dominant factor in both stream and lake systems whereas evidence for the importance of competition appears less convincing. Within small streams or lakes, the impact of predation may exclude other species, thereby leading to mutually exclusive distributions and strong differences in community composition. Within a geographic region, abiotic effects frequently dictate the relative importance of piscivory, thereby indirectly influencing the composition of prey species present. The spatial scale of studies influences our perceived importance of biotic versus abiotic factors, with small-scale studies indicating a greater importance of competition and large-scale studies emphasizing abiotic controls. The scale of the individual sites considered is critical because smaller systems have higher variability and ...

How well do multivariate data sets match? The advantages of a Procrustean superimposition approach over the Mantel test.

Abstract: The Mantel test provides a means to test the association between distance matrices and has been widely used in ecological and evolutionary studies. Recently, another permutation test based on a Procrustes statistic (PROTEST) was developed to compare multivariate data sets. Our study contrasts the effectiveness, in terms of power and type I error rates, of the Mantel test and PROTEST. We illustrate the application of Procrustes superimposition to visually examine the concordance of observations for each dimension separately and how to conduct hypothesis testing in which the association between two data sets is tested while controlling for the variation related to other sources of data. Our simulation results show that PROTEST is as powerful or more powerful than the Mantel test for detecting matrix association under a variety of possible scenarios. As a result of the increased power of PROTEST and the ability to assess the match for individual observations (not available with the Mantel test), biologists now have an additional and powerful analytical tool to study ecological and evolutionary relationships.

The Theory of Island Biogeography

Abstract: Preface to the Princeton Landmarks in Biology Edition vii Preface xi Symbols Used xiii 1. The Importance of Islands 3 2. Area and Number of Speicies 8 3. Further Explanations of the Area-Diversity Pattern 19 4. The Strategy of Colonization 68 5. Invasibility and the Variable Niche 94 6. Stepping Stones and Biotic Exchange 123 7. Evolutionary Changes Following Colonization 145 8. Prospect 181 Glossary 185 References 193 Index 201

Experimental Design and Data Analysis for Biologists

Abstract: An essential textbook for any student or researcher in biology needing to design experiments, sample programs or analyse the resulting data The text begins with a revision of estimation and hypothesis testing methods, covering both classical and Bayesian philosophies, before advancing to the analysis of linear and generalized linear models Topics covered include linear and logistic regression, simple and complex ANOVA models (for factorial, nested, block, split-plot and repeated measures and covariance designs), and log-linear models Multivariate techniques, including classification and ordination, are then introduced Special emphasis is placed on checking assumptions, exploratory data analysis and presentation of results The main analyses are illustrated with many examples from published papers and there is an extensive reference list to both the statistical and biological literature The book is supported by a website that provides all data sets, questions for each chapter and links to software

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

Abstract: 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

Principal component analysis

Abstract: Principal component analysis PCA is a multivariate technique that analyzes a data table in which observations are described by several inter-correlated quantitative dependent variables. Its goal is to extract the important information from the table, to represent it as a set of new orthogonal variables called principal components, and to display the pattern of similarity of the observations and of the variables as points in maps. The quality of the PCA model can be evaluated using cross-validation techniques such as the bootstrap and the jackknife. PCA can be generalized as correspondence analysis CA in order to handle qualitative variables and as multiple factor analysis MFA in order to handle heterogeneous sets of variables. Mathematically, PCA depends upon the eigen-decomposition of positive semi-definite matrices and upon the singular value decomposition SVD of rectangular matrices. Copyright © 2010 John Wiley & Sons, Inc.

Modern Applied Statistics With S

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