| Preface | vii |
| 1 | An introduction to the philosophy and aims of numerical taxonomy | 1 |
| 1.1 | Introduction | 1 |
| 1.2 | Systematics, classification and taxonomy | 1 |
| 1.3 | The construction of taxonomic hierarchies by traditional and numerical taxonomy: comparison of methods | 2 |
| 1.4 | The philosophy of taxonomy | 4 |
| 1.5 | Classification and inferences concerning patterns of evolution | 7 |
| 1.6 | Summary | 9 |
| 2 | Taxonomic characters | 11 |
| 2.1 | Introduction | 11 |
| 2.2 | Number of characters | 12 |
| 2.3 | Type of characters and coding of character states | 14 |
| 2.3.1 | Qualitative characters | 14 |
| 2.3.2 | Quantitative characters | 18 |
| 2.4 | Weighting of characters | 20 |
| 2.5 | Homology of characters | 21 |
| 2.6 | Summary | 23 |
| 3 | The measurement of similarity | 25 |
| 3.1 | Introduction | 25 |
| 3.2 | Similarity measures for binary characters | 25 |
| 3.2.1 | The simple matching coefficient | 26 |
| 3.2.2 | Jaccard's coefficient | 26 |
| 3.3 | Similarity measures for qualitative characters having more than two states | 29 |
| 3.4 | Similarity measures for quantitative characters | 30 |
| 3.5 | Measures of dissimilarity and distance | 31 |
| 3.6 | Gower's similarity coefficient | 39 |
| 3.7 | Similarity and distance between populations | 41 |
| 3.7.1 | Qualitative characters | 41 |
| 3.7.2 | Quantitative characters | 43 |
| 3.8 | Summary | 45 |
| 4 | Principal components analysis | 46 |
| 4.1 | Introduction | 46 |
| 4.2 | Principal components analysis--geometrical interpretation | 47 |
| 4.3 | A brief mathematical account of principal components analysis | 49 |
| 4.4 | Examples | 51 |
| 4.5 | Principal components plots | 55 |
| 4.6 | Factor analysis | 57 |
| 4.7 | Summary | 58 |
| 5 | Multidimensional scaling | 59 |
| 5.1 | Introduction | 59 |
| 5.2 | Classical multidimensional scaling | 59 |
| 5.2.1 | Principal coordinates analysis--technical details | 61 |
| 5.2.2 | Principal coordinates analysis--an example | 65 |
| 5.3 | Other methods of multidimensional scaling | 68 |
| 5.3.1 | Non-metric multidimensional scaling--technical details | 70 |
| 5.3.2 | Non-metric multidimensional scaling--examples | 71 |
| 5.4 | Minimum spanning trees | 73 |
| 5.5 | Summary | 76 |
| 6 | Cluster analysis | 77 |
| 6.1 | Introduction | 77 |
| 6.2 | Hierarchical clustering techniques | 77 |
| 6.2.1 | Single-linkage clustering | 78 |
| 6.2.2 | Complete-linkage clustering | 80 |
| 6.2.3 | Group-average clustering | 81 |
| 6.2.4 | Centroid clustering | 82 |
| 6.3 | Properties of hierarchical techniques | 85 |
| 6.4 | Other clustering methods | 87 |
| 6.4.1 | Monothetic divisive clustering | 87 |
| 6.4.2 | Minimization of trace (W) | 88 |
| 6.4.3 | A multivariate mixture model for cluster analysis | 89 |
| 6.4.4 | Jardine and Sibson's K-dend clustering method | 89 |
| 6.5 | An example | 91 |
| 6.6 | The evaluation of results and other problems | 94 |
| 6.6.1 | Measuring clustering tendency | 95 |
| 6.6.2 | Global fit of hierarchy | 96 |
| 6.6.3 | Partitions from a hierarchy | 96 |
| 6.7 | What is a cluster? | 101 |
| 6.8 | Summary | 104 |
| 7 | Identification and assignment techniques | 106 |
| 7.1 | Introduction | 106 |
| 7.2 | Diagnostic keys | 107 |
| 7.2.1 | The construction of diagnostic keys | 110 |
| 7.3 | Probabilistic assignment techniques | 112 |
| 7.3.1 | Fisher's linear discriminant function | 115 |
| 7.3.2 | Canonical variate analysis | 116 |
| 7.3.3 | An example of canonical variate analysis | 117 |
| 7.4 | Summary | 121 |
| 8 | The construction of evolutionary trees | 122 |
| 8.1 | Introduction | 122 |
| 8.2 | Evolution as a branching process | 122 |
| 8.3 | The principle of minimal evolution | 125 |
| 8.4 | The topology of the tree | 127 |
| 8.5 | Optimization of trees | 128 |
| 8.6 | Reticulate evolution: the problem of hybrids | 129 |
| 8.7 | Gene phylogenies | 131 |
| 8.8 | Summary | 136 |
| References | 138 |
| Author Index | 145 |
| Subject Index | 147 |
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