Abstract
The contribution ofJ. S. L. Gilmour to numerical taxonomy is reviewed. His important concept of natural classification, as being general-purpose classifications with high predictivity, led to the development of ideas of information content, unit characters and equal character-weighting. The concept of predicitivity is extended to taxonomic trees (phenograms or cladograms). Under certain assumption of random sampling of characters it is shown that the probability of recovering the correct tree topology or tree-form may be small if characters are few. There may be very many topologies or tree-forms, every one of which has individually a low probability. It is, however, possible to estimate the aggregate probability of trees which have more than some specified resemblance to the “correct” tree. The practical prospects of estimating the distribution of tree probabilities are discussed.
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References
Adanson, M., 1757: Histoire naturelle du Sénégal. — Paris: Bauche.
—, 1763: Familles des plantes. — Paris: Vincent.
Astolfi, P., Kidd, K. K., Cavalli-Sforza, L. L., 1981: A comparison of methods for reconstructing evolutionary trees. — Syst. Zool.30: 156–169.
Beckner, M., 1959: The biological way of thought. — New York: Columbia University Press.
Cain, A. J., 1958: Logic and memory inLinnaeus's system of taxonomy. — Proc. Linn. Soc. London, 169th session: 144–163.
—, 1958: An analysis of the taxonomist's judgement of affinity. — Proc. Zool. Soc. London131: 85–98.
Cavalli-Sforza, L. L., Edwapds, A. F., 1967: Phylogenetic analysis: models and estimation procedures. — Evolution21: 550–570.
Conover, W. J., 1971: Practical nonparametric statistics. — New York: John Wiley.
Farris, J. S., 1973: A probability model for inferring evolutionary trees. — Syst. Zool.22: 250–256.
—, 1977: On the phenetic approach to vertebrate classification. — InHecht, M. K., Goody, P. C., Hecht, B. M., (Eds.): Major patterns in vertebrate evolution, pp. 823–850. — New York: Plenum Press.
Felsenstein, J., 1973: Maximum likelihood and minimum-steps methods for estimating evolutionary trees from data on discrete characters. — Syst. Zool.22: 240–249.
—, 1983: Parsimony in systematics: biological and statistical issues. — Ann. Rev. Ecol. Syst.11: 333–358.
—, 1985a: Confidence limits on phylogenies with a molecular clock. — Syst. Zool.35: 152–161.
—, 1985b: Confidence limits on phylogenies: an approach using the bootstrap. — Evolution39: 783–791.
Gilmour, J. S. L., 1936: Whither taxonomy? Text of a paper given to Section K (Botany) of the British Association for the Advancement of Science in Blackpool 1936, first published 1976 in The Classification Soc. Bull.3 (4): 3–9; and reprinted in the present volume.
—, 1937: A taxonomic problem. — Nature (London)139: 1040–1042. — Reprinted in The Classification Soc. Bull., 1976,3 (4): 9–15; and in the present volume.
—, 1940: Taxonomy and philosophy. — InHuxley, J., (Ed.): The new systematics, pp. 461–474. — Oxford: Oxford University Press.
Gower, J. C., 1974: Maximal predictive classification. — Biometrics30: 643–654.
Hartigan, J. A., 1967: Representation of similarity matrices by trees. — J. Amer. Statist. Ass.62: 1140–1158.
Holmquist, R., 1979: The method of parsimony: an experimental test and theoretical analysis of the adequacy of molecular restoration studies. — J. Molec. Biol.135: 939–958.
Jardine, N., Sibson, R., 1968: The construction of hierarchic and non-hierarchic classifications. — Computer J.11: 177–184.
Kidd, K. K., Cavalli-Sforza, L. L., 1971: Number of charactes examined and error in reconstruction of evolutionary trees. — InHodson, F. R., Kendall, D. G., Tăutu, P., (Eds).: Mathematics in the archaeological and historical sciences, pp. 335–346. — Edinburgh: Edinburgh University Press.
La Duke, J., Crawford, D. J., 1979: Character compatibility and phyletic relationships in several closely related species ofChenopodium of the Western United States. — Taxon28: 307–314.
MacLaren, M. D., Marsaglia, G., 1965: Uniform random number generators. — J. Assoc. Comp. Mach.12: 83–89.
Michener, C. D., Sokal, R. R., 1957: A quantitative approach to a problem in classification. — Evolution11: 130–162.
Mill, J. S., 1843: A system of logic. 2 vols. — London: Parker.
Penny, D., Hendy, M. D., 1985: The use of tree comparison metrics. — Syst. Zool.34: 75–82.
Phipps, J. B., 1971: Dendrogram topology. — Syst. Zool.20: 306–308.
Sackin, M. J., 1985: Comparisons of classifications. — InGoodfellow, M., Jones, D., Priest, F. G., (Eds.): Computer-assisted bacterial systematics, pp. 21–36. — London: Academic Press.
Sneath, P. H. A., 1957: Some thoughts on bacterial classification. — J. Gen. Microbiol.17: 184–200.
—, 1986: Significance tests for multivariate normality of clusters from branching patterns in dendograms. — Math. Geol.18: 3–32.
—, 1985: Naturalness and predicitivity of classifications. — Biol. J. Linn. Soc.24: 217–231.
—, 1973: Numerical taxonomy: the principles and practice of numerical classification. — San Francisco: Freeman.
Sokal, R. R., Michener, C. D., 1958: A statistical method for evaluating systematic relationships. — Univ. Kansas Sci. Bull.38: 1409–1438.
—, 1963: Principles of numerical taxonomy. — San Francisco: Freeman.
Whewell, W., 1840: The philosophy of the inductive sciences, founded upon their history. 2 vols. — Cambridge: Deighton.
Wichmann, B. A., Hill, I. D., 1982: Algorithm AS183: an efficient and portable pseudorandon number generator. — Appl. Statistics31: 188–190.
Woodger, J. H., 1937: The axiomatic method in biology. — Cambridge: Cambridge University Press.
—, 1945: On biological transformations. — InLe Gros Clark, W. E., Medawar, P. B., (Eds.): Assays on growth and form presented toD'Arcy Wentworth Thompson, pp. 94–120. — Oxford: Clarendon Press.
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Dedicated to the memory of JohnS. L. Gilmour.
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Sneath, P.H.A. Predictivity in taxonomy and the probability of a tree. Pl Syst Evol 167, 43–57 (1989). https://doi.org/10.1007/BF00936546
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DOI: https://doi.org/10.1007/BF00936546