An An Introduction to Mathematical Taxonomy

Overview


Students of mathematical biology discover modern methods of taxonomy with this text, which introduces taxonomic characters, the measurement of similarity, and the analysis of principal components. Other topics include multidimensional scaling, cluster analysis, identification and assignment techniques, more. A familiarity with matrix algebra and elementary statistics are the sole prerequisites.
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An Introduction to Mathematical Taxonomy

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Overview


Students of mathematical biology discover modern methods of taxonomy with this text, which introduces taxonomic characters, the measurement of similarity, and the analysis of principal components. Other topics include multidimensional scaling, cluster analysis, identification and assignment techniques, more. A familiarity with matrix algebra and elementary statistics are the sole prerequisites.
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Product Details

  • ISBN-13: 9780486435879
  • Publisher: Dover Publications
  • Publication date: 1/15/2004
  • Pages: 160
  • Product dimensions: 5.36 (w) x 8.44 (h) x 0.35 (d)

Table of Contents

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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