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

The Theory of Island Biogeography

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

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Experimental Design and Data Analysis for Biologists

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

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

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.

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Principal component analysis

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Modern Applied Statistics With S

http://rbasicsworkshop.weebly.com/uploads/1/8/6/0/18603232/peres-neto_etal_2005.pdf

How many principal components? stopping rules for determining the number of non-trivial axes revisited

We compared the von Bertalanffy growth function (VBGF) and five polynomial functions (PF) in modelling fish growth for 16 populations comprising six species of freshwater fishes. Ranked results of the variance explained by each growth function indicated that VBGF described growth data better than three- and four-parameter polynomial functions. Log-transforming length and age greatly improved the goodness-of-fit of the three-parameter polynomial function. Statistical comparison of growth between populations or sexes was done using a general linear model for polynomial functions. An analysis of residual sum of squares was proposed to compare the resultant VBGFs because the nonlinear formulation of the VBGF prevented traditional analysis of covariance procedures. Fitting of different growth functions to the same growth data set yielded the same result in the intra-species growth comparisons for three species (eight populations) but different results for two species (seven populations). Where ages of the fish...

A Comparison of von Bertalanffy and Polynomial Functions in Modelling Fish Growth Data

A multivariate measure of the concordance or association between matrices of species abundances and environmental variables was generally lacking in ecology until recently. Traditional statistical ...

PROTEST: A PROcrustean Randomization TEST of community environment concordance

Principal component analysis (PCA) is one of the most commonly used tools in the analysis of ecological data. This method reduces the effective dimensionality of a multivariate data set by producing linear combinations of the original variables (i.e., com- ponents) that summarize the predominant patterns in the data. In order to provide meaningful interpretations for principal components, it is important to determine which variables are associated with particular components. Some data analysts incorrectly test the statistical significance of the correlation between original variables and multivariate scores using standard statistical tables. Others interpret eigenvector coefficients larger than an arbitrary absolute value (e.g., 0.50). Resampling, randomization techniques, and parallel analysis have been applied in a few cases. In this study, we compared the performance of a variety of approaches for assessing the significance of eigenvector coefficients in terms of type I error rates and power. Two novel approaches based on the broken-stick model were also evaluated. We used a variety of simulated scenarios to examine the influence of the number of real dimensions in the data; unique versus complex variables; the magnitude of eigen- vector coefficients; and the number of variables associated with a particular dimension. Our results revealed that bootstrap confidence intervals and a modified bootstrap confidence interval for the broken-stick model proved to be the most reliable techniques.

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Giving meaningful interpretation to ordination axes: assessing loading significance in principal component analysis

Data on the presence or absence of 25 fish species in a survey of 52 lakes from the watersheds of the Black and Hollow rivers of south-central Ontario were analyzed with eight similarity coefficien...

Donald A. Jackson

Papers

How many principal components? stopping rules for determining the number of non-trivial axes revisited

A Comparison of von Bertalanffy and Polynomial Functions in Modelling Fish Growth Data

PROTEST: A PROcrustean Randomization TEST of community environment concordance

Giving meaningful interpretation to ordination axes: assessing loading significance in principal component analysis

Similarity Coefficients: Measures of Co-Occurrence and Association or Simply Measures of Occurrence?