An Introduction to Mathematical Taxonomy

Cover

An Introduction to Mathematical Taxonomy

Copyright © 1982 by Cambridge University Pres
     ISBN 0-486-43587-3

CONTENTS

PREFACE

1  An introduction to the philosophy and aims of numerical taxonomy
     1.1 Introduction
     1.2 Systematics, classification and taxonomy
     1.3 The construction of taxonomic hierarchies by traditional and numerical taxonomy : comparison of methods
     1.4 The philosophy of taxonomy
     1.5 Classification and inferences concerning patterns of evolution
     1.6 Summary

2  Taxonomic characters
     2.1 Introduction
     2.2 Number of characters
     2.3 Type of characters and coding of character states
          2.3.1 Qualitative characters
          2.3.2 Quantitative characters
     2.4 Weighting of characters
     2.5 Homology of characters
     2.6 Summary

3  The measurement of similarity
     3.1 Introduction
     3.2 Similarity measures for binary characters
          3.2.1 The simple matching coefficient
          3.2.2 Jaccard's coefficient
     3.3 Similarity measures for qualitative characters having more than two states
     3.4 Similarity measures for quantitative characters
     3.5 Measures of dissimilarity and distance
     3.6 Gower's similarity coefficient
     3.7 Similarity and distance between populations
          3.7.1 Qualitative characters
          3.7.2 Quantitative characters
     3.8 Summary

4  Principal components analysis
     4.1 Introduction
     4.2 Principal components analysis -geometrical interpretation
     4.3 A brief mathematical account of principal components analysis
     4.4 Examples
     4.5 Principal components plots
     4.6 Factor analysis
     4.7 Summary

5  Multidimensional scaling
     5.1 Introduction
     5.2 Classical multidimensional scaling
          5.2.1 Principal coordinates analysis -technical details
          5.2.2 Principal coordinates analysis-an example
     5.3 Other methods of multidimensional scaling
          5.3.1 Non-metric multidimensional scaling - technical details
          5.3.2 Non-metric multidimensional scaling - examples
     5.4 Minimum spanning trees
     5.5 Summary

6  Cluster analysis
     6.1 Introduction
     6.2 Hierarchical clustering techniques
          6.2.1 Single-linkage clustering
          6.2.2 Complete-linkage clustering
          6.2.3 Group-average clustering
          6.2.4 Centroid clustering
     6.3 Properties of hierarchical techniques
     6.4 Other clustering methods
          6.4.1 Monothetic divisive clustering
          6.4.2 Minimization of trace (W)
          6.4.3. A multivariate mixture model for cluster analysis
          6.4.4 Jardine and Sibson's K-dend clustering method
     6.5 An example
     6.6 The evaluation of results and other problems
          6.6.1 Measuring clustering tendency
          6.6.2 Global fit of hierarchy
          6.6.3 Partitions from a hierarchy
     6.7 What is a cluster?
     6.8 Summary

7  Identification and assignment techniques
     7.1 Introduction
     7.2 Diagnostic keys
          7.2.1 The construction of diagnostic keys
     7.3 Probabilistic assignment techniques
          7.3.1 Fisher's linear discriminant function
          7.3.2 Canonical variate analysis
          7.3.3 An example of canonical variate analysis
     7.4 Summary

8  The construction of evolutionary trees
     8.1 Introduction
     8.2 Evolution as a branching process
     8.3 The principle of minimal evolution
     8.4 The topology of the tree
     8.5 Optimization of trees

     8.6 Reticulate evolution : the problem of hybrids
     8.7 Gene phylogenies
     8.8 Summary

REFERENCES

AUTHOR INDEX

SUBJECT INDEX

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