Analysing Ecological Data

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1 Alain F. Zuur Elena N. Ieno Graham M. Smith Analysing Ecological Data University- una Landesbibliothe;< Darmstadt Eibliothek Biologie tov.-nr. 4y Springer

2 Contents Contributors xix 1 Introduction Part 1: Applied statistical theory Part 2: The case studies Data, software and flowcharts 6 2 Data management and software Introduction, Data management Data preparation Statistical software 13 3 Advice for teachers Introduction 17 4 Exploration The first steps : Outliers, transformations and standardisations A final thought on data exploration 47 5 Linear regression Bivariate linear regression Multiple linear regression Partial linear regression 73 6 Generalised linear modelling Poisson regression Logistic regression 88 7 Additive and generalised additive modelling Introduction The additive model Example of an additive model Estimate the smoother and amount of smoothing Additive models with multiple explanatory variables 108

3 xii Contents 7.6 Choosing the amount of smoothing Model selection and validation Generalised additive modelling Where to go from here Introduction to mixed modelling Introduction.: The random intercept and slope model Model selection and validation A bit of theory Another mixed modelling example Additive mixed modelling Univariate tree models Introduction Pruning the tree.' Classification trees A detailed example: Ditch data Measures of association Introduction Association between sites: Q analysis Association among species: R analysis Q and R analysis: Concluding remarks Hypothesis testing with measures of association Ordination First encounter Bray-Curtis ordination Principal component analysis and redundancy analysis The underlying principle of PCA PCA: Two easy explanations PCA: Two technical explanations Example of PCA The biplot General remarks Chord and Hellinger transformations Explanatory variables Redundancy analysis Partial RDA and variance partitioning PCA regression to deal with collinearity Correspondence analysis and canonical correspondence analysis Gaussian regression and extensions..: Three rationales for correspondence analysis From RGR to CCA 238

4 Contents xiii 13.4 Understanding the CCA triplot When to use PCA, CA, RDA or CCA Problems with CA and CCA : Introduction to discriminant analysis Introduction Assumptions Example The mathematics : The numerical output for the sparrow data Principal coordinate analysis and non-metric multidimensional scaling Principal coordinate analysis Non-metric multidimensional scaling ^ Time series analysis Introduction Using what we have already seen before Auto-regressive integrated moving average models with exogenous variables L Common trends and sudden changes Repeated LOESS smoothing Identifying the seasonal component Common trends: MAFA Common trends: Dynamic factor analysis Sudden changes: Chronological clustering ;..: Analysis and modelling of lattice data Lattice data... : Numerical representation of the lattice structure Spatial correlation.....= Modelling lattice data More exotic models...'...-..! ^6 Summary Spatially continuous data analysis and modelling Spatially continuous data : Geostatistical functions and assumptions Exploratory variography analysis : Geostatistical modelling: Kriging A full spatial analysis of the bird radar data Univariate methods to analyse abundance of decapod larvae Introduction The data : Data exploration 377

5 xiv Contents 20.4 Linear regression results Additive modelling results How many samples to take? Discussion Analysing presence and absence data for flatfish distribution in the Tagus estuary, Portugal Introduction Data and materials, Data exploration Classification trees Generalised additive modelling Generalised linear modelling Discussion Crop pollination by honeybees in Argentina using additive mixed modelling Introduction Experimental setup Abstracting the information First steps of the analyses: Data exploration Additive mixed modelling Discussion and conclusions Investigating the effects of rice farming on aquatic birds with mixed modelling Introduction ".'.' The data : Getting familiar with the data: Exploration Building a mixed model. : The optimal model in terms of random components Validating the optimal linear mixed model More numerical output for the optimal model Discussion Classification trees and radar detection of birds for North Sea wind farms Introduction From radars to data Classification trees A tree for the birds A tree for birds, clutter and more clutter Discussion and conclusions Fish stock identification through neural network analysis of parasite fauna 449

6 Contents xv 25.1 Introduction : Horse mackerel in the northeast Atlantic Neural networks Collection of data i;! Data exploration Neural network results..= Discussion.:: Monitoring for change: Using generalised least squares, non-metric multidimensional scaling, and the Mantel test on western Montana grasslands Introduction The data Data exploration Linear regression results Generalised least squares results...: Multivariate analysis results Discussion..' Univariate and multivariate analysis applied on a Dutch sandy beach community Introduction The variables Analysing the data using univariate methods Analysing the data using multivariate methods Discussion and conclusions ': : Multivariate analyses of South-American zoobenthic species spoilt for choice Introduction and the underlying questions Study site and sample collection Data exploration, The Mantel test approach The transformation plus RDA approach Discussion and conclusions Principal component analysis applied to harbour porpoise fatty acid data Introduction The data Principal component analysis Data exploration Principal component analysis results Simpler alternatives to PCA Discussion..526

7 xvi Contents 30 Multivariate analyses of morphometric turtle data size and shape Introduction The turtle data Data exploration Overview of classic approaches related to PCA 534,3.0.5 Applying PCA to the original turtle data Classic morphometric data analysis approaches A geometric morphometric approach ; Redundancy analysis and additive modelling applied on savanna tree data, Introduction Study area Methods Results Discussion Canonical correspondence analysis of lowland pasture vegetation in the humid tropics of Mexico Introduction The study area The data, Data exploration Canonical correspondence analysis results African star grass Discussion and conclusion Estimating common trends in Portuguese fisheries landings Introduction '..rr., The time series data MAFA and DFA : MAFA results DFA results v......; Discussion Common trends in demersal communities on the Newfoundland-Labrador Shelf Introduction Data Time series analysis, Discussion Sea level change and salt marshes in the Wadden Sea: A time series analysis Interaction between hydrodynamical and biological factors The data 603

8 Contents xvii 35.3 Data exploration Additive mixed modelling Additive mixed modelling results Discussion Time series analysis of Hawaiian waterbirds Introduction Endangered Hawaiian waterbirds Data exploration Three ways to estimate trends Additive mixed modelling Sudden breakpoints Discussion Spatial modelling of forest community features in the Volzhsko-Kamsky reserve Introduction Study area Data exploration Models of boreality without spatial auto-correlation Models of boreality with spatial auto-correlation Conclusion 646 References 649 Index 667

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