Note: Intro -- Tracking Environmental Change Using Lake Sediments -- Preface -- Structure of the Book -- About The Editors -- Contents -- Contributors -- Part I Introduction, Numerical Overview, and Data-Sets -- Chapter 1: The March Towards the Quantitative Analysis of Palaeolimnological Data -- Palaeolimnology -- Types of Palaeolimnological Data -- Different Temporal Scales: From Surface-Sediment Calibration Sets to Detailed Sediment-Core Studies -- Opportunities and Challenges -- Outline of the Book -- References -- Chapter 2: Overview of Numerical Methods in Palaeolimnology -- Introduction -- Types of Palaeolimnological Data -- The Role of Quantification in Palaeolimnology -- Overview of Numerical Methods -- Identification, Classification, and Assignment -- Exploratory Data Analysis -- Regression Analysis and Statistical Modelling -- Introduction to Regression Analysis and Statistical Modelling -- General Linear Models -- Extending the General Linear Model -- Introduction -- Generalised Linear Models -- Mixed-Effects Models -- Non-parametric Regression Models -- Classification and Regression Trees (CARTs) -- Artificial Neural Networks (ANNs) and Self-Organising Maps (SOMs) -- Multivariate Regression -- Model Selection and Shrinkage -- Quantitative Environmental Reconstruction, Calibration, and Inverse Regression -- Temporal-Series Analysis -- Confirmatory Data Analysis -- Conclusions -- References -- Chapter 3: Data-Sets -- Introduction -- The Round Loch of Glenhead Data-Set -- The SWAP Data-Set -- Data Availability -- References -- Part II Numerical Methods for the Analysis of Modern and Stratigraphical Palaeolimnological Data -- Chapter 4: Introduction and Overview of Part II -- Introduction -- Data Collection and Data Assessment -- Identification -- Error Estimation -- Data Storage and Data-Bases -- Exploratory Data Analysis -- Data Summarisation. , Data Analysis -- Gradient Lengths and Compositional Turnover in Palaeolimnological Data -- Estimating Richness from Palaeolimnological Data -- Estimating Species Optima and Tolerances Using Palaeolimnological Data -- Comparison of Clusterings and Ordinations of Palaeolimnological Data -- Data Interpretation -- Conclusions -- References -- Chapter 5: Exploratory Data Analysis and Data Display -- Introduction -- Exploring Univariate Distributions -- Graphical Tools -- Data Transformation -- Graphical Techniques for Categorical (Nominal and Ordinal) Data -- Exploring Bivariate Relationships -- Multivariate Techniques -- Time-Series Data -- Outlier Detection and Treatment -- Missing Values -- Graph Drawing -- Software -- Conclusions -- References -- Chapter 6: Assessment of Uncertainties Associated with Palaeolimnological Laboratory Methods and Microfossil Analysis -- Introduction -- Single Parameter Estimates -- Microfossil Counts -- Percentages (Taxa as Proportions of an Overall Sum) -- Treating Taxa as Ratios of Types (Counting Outside the Sum) -- Treating Taxa as Numbers of Individuals Per Volume or Weight (Microfossil Concentrations) -- Treating Taxa as Numbers of Individuals Per Unit Surface Per Year (Accumulation Rates, Influx) -- Artificial Count Data to Assess the Errors Associated with Low Microfossil Counts -- Inter-laboratory Comparisons -- Software Availability -- Estimating Varve-Counting Errors -- Multi-core Studies -- Conclusions -- References -- Chapter 7: Clustering and Partitioning -- Introduction -- Artificial Example -- Basic Concepts in Clustering -- Unconstrained Agglomerative Clustering Methods -- K-Means Partitioning -- Example: The SWAP-UK Data -- Constrained Clustering in One Dimension -- Example: The Round Loch of Glenhead (RLGH) Fossil Data -- Constrained Clustering in Two Dimensions -- Example: The SWAP-UK Data. , Clustering Constrained by Canonical Analysis -- Indicator Species Analysis -- Example: The Round Loch of Glenhead (RLGH) Fossil Data -- Two-Way Indicator Species Analysis -- Example: The SWAP-UK Data -- Multivariate Regression Trees -- Example: The SWAP-UK Data -- Conclusions -- References -- Chapter 8: From Classical to Canonical Ordination -- Introduction -- Basic Concepts in Simple Ordination -- Transformation of Physical Data -- Transformation of Assemblage Composition Data -- Choice of an Appropriate Distance Function -- Euclidean or Cartesian Space, Euclidean Representation -- Metric or Non-metric Ordination? -- How Many Axes Are Required? -- Simple Ordination Methods: PCA, CA, PCoA, NMDS -- Introduction to Canonical Ordination -- Canonical Ordination Methods -- Linear RDA -- Linear CCA -- Other Forms of Asymmetric Canonical Analyses -- Spatial or Temporal Analysis Through Variation Partitioning -- Modelling Temporal Structure in Sediment Cores [and Environmental Structure in Modern Assemblages] -- Testing Hypotheses in (Multi-) Factorial Experiments -- Software -- References -- Chapter 9: Statistical Learning in Palaeolimnology -- Introduction -- Classification and Regression Trees -- Multivariate Regression Trees -- Other Types of Tree-Based Machine-Learning Methods (Bagging, Boosted Trees, Random Forests, Multivariate Adaptive Regression Splines) -- Bagging -- Random Forests -- Boosting -- Multivariate Adaptive Regression Splines -- Artificial Neural Networks and Self-organising Maps -- Artificial Neural Networks -- Self-organising Maps -- Bayesian Networks -- Genetic Algorithms -- Principal Curves and Surfaces -- Shrinkage Methods and Variable Selection -- Discussion and Conclusions -- References -- Part III Numerical Methods for the Analysis of Stratigraphical Palaeolimnological Data -- Chapter 10: Introduction and Overview of Part III. , Introduction -- Data Collection and Data Assessment -- Identification -- Data Assessment and Error Estimation -- Data Summarisation -- Single Stratigraphical Data-Sets -- Two or More Stratigraphical Sequences -- Data Analysis -- Rate-of-Change Analysis -- Population Analysis -- Stratigraphical Changes in Taxonomic Richness -- Temporal-Series Analysis -- Quantifying Recent Change -- Quantitative Palaeoenvironmental Reconstructions -- Data Interpretation -- Community and Assemblage Reconstruction -- Causative Factors -- Conclusions -- References -- Chapter 11: Analysis of Stratigraphical Data -- Introduction -- Zonation -- Techniques -- Determining the Number of Zones -- Software -- Example of Use -- Splitting of Individual Stratigraphical Sequences -- Example of Use -- Summarising Stratigraphical PatternsUsing Ordination Results -- Summarising Palaeoecological PatternsUsing Cluster Analysis -- Quantifying Recent Change -- Rate-of-Change Analysis -- Example of Use -- Future Developments -- Conclusions -- References -- Chapter 12: Estimation of Age-Depth Relationships -- Introduction -- Radiocarbon Dating -- Errors -- The Need for Radiocarbon Calibration -- Calibration Methods -- Reduction to Single Point Estimates -- Age-Depth Models -- Analytical vs. Monte Carlo Age-Depth Models -- Basic Age-Depth Models -- Linear Interpolation -- Polynomials -- Splines -- Other Models -- Mixed-Effects Models -- Implementation -- Bayesian Age-Depth Modelling -- Chronological Ordering -- Wiggle-Match Dating -- Other Models -- Software Packages -- Discussion -- Choice of Model -- Conclusions and Future Developments -- References -- Chapter 13: Core Correlation -- Introduction -- Theory and Method -- Case Studies -- Ice Chronology -- Mountain and Arctic Lakes -- Other Palaeolimnological Applications -- Conclusions -- References. , Chapter 14: Quantitative Environmental Reconstructions from Biological Data -- Introduction -- Training-Set Development -- Numerical Methods -- Introduction -- Classical Methods -- Inverse Methods -- Weighted-Averaging (WA) Regression and Calibration -- Partial Least Squares (PLS) and Weighted-Averaging Partial Least Squares Regression and Calibration (WAPLS) -- Artificial Neural Networks (ANN) -- Modern Analogue Technique (MAT) -- Locally-Weighted Weighted-Averaging (LWWA) Regression and Calibration -- Bayesian Methods -- Model Selection and Evaluation -- Spatial Autocorrelation and Environmental Reconstruction -- Reconstruction Testing, Evaluation, and Validation -- Assessing the Statistical Significance of a Quantitative Reconstruction -- RMSEP and Sample-Specific Error Estimates -- Goodness-of-Fit and Analogue Measures -- Comparison of Reconstructions Using DifferentNumerical Methods -- Comparison of Reconstructions Using Different Proxies -- Case Study -- Assumptions and Limitations -- Software -- Conclusions and Future Work -- References -- Chapter 15: Analogue Methods in Palaeolimnology -- Introduction -- The Modern Analogue Technique (MAT) -- Analogue Matching -- Dissimilarity and Dimensionality -- The Curse of Dimensionality -- How Similar Is Similar Enough? -- Choosing k to Optimise RMSEP -- Choosing k via Dissimilarity Jumps -- Reference Distributions of Dissimilarities -- Monte Carlo Resampling -- Receiver Operating Characteristic (ROC) Curves -- Logistic Regression Modelling -- Evaluation of Environmental Reconstructions -- Software -- Conclusions and Future Work -- References -- Chapter 16: Autocorrelogram and Periodogram Analyses of Palaeolimnological Temporal-Series from Lakes in Central and Western North America to Assess Shifts in Drought Conditions -- Introduction -- Statistical Background -- Time-Domain Approach. , Frequency-Domain Approach.