Evolutionary Biology

, Volume 46, Issue 1, pp 71–89 | Cite as

On the Typology of Relations

  • Evgeny V. MavrodievEmail author
  • David M. Williams
  • Malte C. Ebach
Synthesis Paper


The possibility of undertaking matrix/optimization-free cladistic analysis is one of the most interesting ideas to emerge in the last few decades from within the field of systematics, particularly in the development of cladistics. The purpose of this paper is to design further opportunities and prospects made possible by eliminating the matrix as the primary source of data representation. The main focus of this paper is to outline a supertree approach that, if combined with the methodology of three-taxon statement analysis (3TA), may be seen as a powerful heuristic alternative to the application of conventional matrix/optimization-based methods used for the analysis of systematic data, and which currently forms the mainstream of contemporary phylogenetics. Using the average consensus technique as an example, we demonstrate explicitly that methods of construction of supertrees may be applied to the array of three-taxon statements (3TS), especially if the latter are represented initially as minimal trees, not as binary matrices, as was originally proposed. The 3TA-average consensus procedure recognizes solely ‘reversal’-based clades and is also free from the potential issues of 3TA, such as the data distortion due to inability to handle putative reversals. Thus the main benefit of this new approach over the traditional one is its accuracy and advantages when implementing the Hennigian views on the cladistic analysis that states that all characters must be a priori polarized before the best fitting tree is found. We also found that the average consensus technique (as well as other median supertree calculation techniques) is purely typological and we stressed that this simple point had never been mentioned before. We proposed that the average consensus of 3TSs (as well as any median consensus of 3TSs) may be viewed as a median type and the extended procedure of the traditional 3TA may be treated as a typology of the relations. The connection between median type and phylogeny may be established only indirectly. The heuristic scientific typology may be derived within a completely metaphysics-free context. Goethe’s idea of “Urphenomenon” and Max Weber’s “Ideal Types” are mentioned as examples of heuristic metaphysical-free typological frameworks.


Average consensus method Median supertrees Matrix-free Cladistics Three-taxon statement Three-taxon statement analysis 



The authors wish to thank Prof. Michel Laurin (CNRS/MNHN/UPMC, Sorbonne Universités, Paris, France), Dr. Valentin Rineau (CNRS/MNHN/UPMC, Sorbonne Universités, Paris, France) and an anonymous reviewer for their helpful comments and suggestions.

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Authors and Affiliations

  • Evgeny V. Mavrodiev
    • 1
    Email author
  • David M. Williams
    • 2
  • Malte C. Ebach
    • 3
  1. 1.Florida Museum of Natural HistoryUniversity of FloridaGainesvilleUSA
  2. 2.Department of Life Sciencesthe Natural History MuseumLondonUK
  3. 3.Palaeontology, Geobiology and Earth Archives Research Centre, School of Biological, Earth and Environmental SciencesUNSWKensingtonAustralia

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