J. Zool. Syst. Evol. Research 40 (2002) 169–194 Received on 5 August 2002 Ó 2002 Blackwell Verlag, Berlin ISSN 0947–5745 1Museum of Comparative Zoology, Harvard University, Cambridge, MA, USA; 2Department of Biological Sciences, Columbian University, NewYork, NY, USA Classifications and other ordering systems Ernst Mayr1 and W. J. Bock2 Abstract 9.5.1. Evidently descended from the same ancestor 1. Introduction 9.5.2. Parallelophyly 2. Why ordering systems should be of interest to the 9.5.3. Reversal philosopher? 9.5.4. Convergence 3. The universality of diversity 9.6. Significance of characters (weighing) 4. Objectives of ordering systems 9.7. Numerical approaches 4.1. Sorting 10. Ordering by using only the criterion of phylogeny – type 5 4.2. Information storage and retrieval is a major objective 10.1. Hennigian cladification of most ordering systems 10.2. Peculiarities of Hennigian terminology 4.3. Identification of an unknown item 10.2.1. Paraphyly 4.4. Inferences about not yet studied properties 10.2.2. Monophyly 4.5. To serve as base line in comparative studies 10.2.3. Relationship 5. Kinds of Ordering Systems 10.2.4. Classification 5.1 General considerations 10.2.5. Taxon 5.2. Ordering of single entities 10.3. Cladistic analysis 5.2.1. Assigning singular entities to a linear sequence 10.4. Recognition of clades (sequential listing) –type 1 11. Upward classification by two criteria, clustering by 5.2.1.1. Arbitrary sequence similarity and by common descent – type 6 5.2.1.2. Alphabetical listing 11.1. Pre-Darwinian classification 5.2.1.3. Chronological listing 11.2. Post-Darwinian classification 5.2.1.4. Listing by rank or achievement 11.3. Genealogy alone does not give a classification 5.2.2. Ordering the chemical elements according to 11.4. Is a biological classification a theory? numerical properties of their atoms – type 2 12. Ecological factors of evolution and classification 6. Ordering by the clustering of entities 12.1. The origin of a new higher taxon (splitting or 6.1. Ordering by a single criterion budding) 6.2. Ordering by special similarity – type 3 12.2. Impact of ecological shifts on classification 6.2.1. Establishing groups by logical division (mostly 13. Phylogenetic or genealogical analysis dichotomy = ‘‘downward classification’’) 13.1. Use in biological classifications 6.2.2. Special purpose ordering 13.2. Translating the phylogenetic analysis into an ordering 6.3. Arrangement of entities into classes based on overall system (comprehensive) similarity– type 4 13.2.1. Darwinian classification 6.4. Ordering by phylogeny or by similarity and phylogeny 13.2.2. Hennigian cladification – types 5 and 6 14. Graphic representations of ordering systems 7. Evolution versus phylogeny 14.1. Phenogram 7.1 Darwinian evolution 14.2. Haeckelian-Darwinian dendrogram 7.2. Haeckelian phylogeny 14.3. Hennigian cladogram 7.3. Hennigian phylogeny 15. Darwinian classification or Hennigian cladification? 8. Class and classification 15.1. Merits and deficiencies of Darwinian classification 8.1. Definition of class 15.1.1. Classification 8.2. Construction of classes (taxa) 15.1.2. Phylogeny 8.3. General definition of classification 15.2. Merits and deficiencies of Hennigian cladification 8.4. Biological classifications as hierarchies 15.2.1. Phylogeny 8.5. Ranking 15.2.2. Classification 9. Similarity 16. Resolution of the conflict 9.1. General concept and use in classification 16.1. Stating the conflict 9.2. Meaning of similarity in biological classification 16.2. Which system is superior? 9.3. How to determine similarity? 16.3. Termination of the conflict 9.4. Overall similarity 17. Glossary 9.5. Sources of similarity in organisms 18. Literature U.S. Copyright Clearance Center Code Statement: 0947–5745/02/4004–0169$15.00/0 www.blackwell.de/synergy 170 Mayr and Bock Abstract The enormous variety of things in nature must be ordered before it can be studied and understood. Unfortunately in spite of their great importance, the methods of ordering have been greatly neglected by the philosophers. In this article, we distinguish six systems of ordering. Classification, in which similar entities are grouped in classes (taxa), is one such ordering system, but not all ordering systems are classifications. The Hennigian system of cladification consists of the ordering of branches of the phylogenetic tree, strictly on the basis of a single criterion, the branching points of the phylogeny (holophyly) (Hennigian phylogeny). It is not a system of classification, as it does not lead to classes of entities possessing similar phenotypic attributes. A Darwinian classification, by using two criteria, similarity and common descent, leads to the recognition of classes (taxa) of similar entities consistent with common descent (monophyly) (Haeckelian phylogeny). Key words: Classification – Hennig – Haeckelian Phylogeny – Cladification – Ordering systems 1. Introduction sequences based on appropriate criteria. Placing entities into Our world is characterized by an almost chaotic diversity of some chosen order is one of the most important methods of things and processes. The basic task of scientists is to provide science and an indispensable activity of daily life. How could explanations for all aspects of this diversity, while that of we find an item in a large market or a book in a library, if these philosophers of science is to overview the approaches and items were not placed in an order according to some methods used by the scientists in reaching these explanations. principles? Ordering systems, including classifications, are needed to But what are these principles and how are they chosen? reduce this chaotic diversity into understandable, manageable Ordering systems to deal with human artefacts may be arrangements before scientific explanations are possible. At the constructed strictly artificially and for convenience only. But onset, we must emphasize that not all ordering systems are when developing ordering systems for scientific purposes for classifications, as is all too frequently assumed by both existing objects in nature, from biological cell types and species scientists and philosophers. Ordering systems is an overall to chemical elements, minerals and astronomical bodies, one term and includes all schemes that attempt to arrange a must remember that the ordering must be founded on the diversity of objects into particular categorizations. Classifica- fundamental theories in the particular field of inquiry. One tions are a subset of ordering systems that attempt to arrange a should be immediately wary of any claim about the existence diversity of entities into sets of classes based on similarities of theory-free order in nature. There is simply no foundation possessed by the included individual entities. In biology, for the belief that a natural order exists in nature independ- classifications exist of living organisms, but also of organ, cell ently of any theory and that it is ‘out there’ waiting to be and tissue types of diverse organisms, of ecological commu- discovered in the absence of any theory. Because biological nities, etc. These classifications are not all of the same type; classifications and phylogenies of organisms are historical- hence, ‘biological classification’ is not a single concept. Not all narrative explanations, they are dependent on the nomolog- biological classifications are evolutionary classifications of ical-deductive theory of evolution if they are to be scientific organisms, as is all too often erroneously assumed by (Bock 2000b). We disagree strongly with claims, such as are biologists and philosophers alike. Yet other ordering systems made by Brower (2000, p. 143) and many other cladists, ‘… exist in biology, such as phylogenetic trees or dendrograms, Whether a theory of evolution is philosophically antecedent to which are equally useful, but are not classifications. Haecke- systematics or systematics provides evidence that allows lian phylogenies and Hennigian cladifications (¼ cladograms; inference of a scientific theory of evolution. In this paper, I see Glossary and Mayr 1965) are quite different types of will advocate the latter point of view and highlight its utility in ordering systems from Darwinian classifications, as different as the current debate surrounding alternate methods of phylo- clades are from taxa which are respectively units of different genetic inference.’ Osche (2002, pp. 18–20) has discussed in types of ordering systems. Biologists have been so accustomed some detail Hennig’s aversion to base systematic theory and to thinking about all ordering systems as classifications that methods on evolutionary theory. many statements in the literature about classifications are Considering the enormous importance of this process of actually statements about ordering systems in general. More- ordering in the diverse fields of science, it is quite astonishing over, it is difficult to analyse earlier discussions of biological to what extent its analysis has been neglected by philosophers. ordering systems because they may refer to evolutionary In fact, we have been unable to find a treatment of classifi- classifications of organisms, to phylogenies (both Haeckelian cation (and of ordering systems in general) in any philosoph- and Hennigian), to ‘essentialistic’ classifications of tissue, cell ical publication between the 1840s (Whewell 1840; Mill 1843) and other types, and to other types of ordering systems, the and 1997 as comprehensive and aware of ambiguities as that of result being a confused morass. Whewell in his Philosophy of the Inductive Sciences (1840). Ordering systems are important not only for scientists and Whewell very perceptively realized that ordering by the philosophers, but for all humans in most or all activities of methods of logical division was something quite different their daily life. Most essential is that ordering systems, from classifying by grouping (clustering), even though he did including classifications, are above all heuristic schemes and not always clearly separate the two methods. His treatment must be judged primarily on criteria of convenience, whatever also suffered from his pre-evolutionary attempt to apply the these criteria might be for the particular system.