How to validate phylogenetic trees? A stepwise procedure

  • François-Joseph Lapointe
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


In this paper, I review some of the methods and tests currently available to validate trees, focussing on phylogenetic trees (dendrograms and cladograms). I first present some of the more commonly used techniques to compare a tree with the data it is derived from (internal validation), or compare a tree to another tree or to more than one (external validation). I also discuss some of the advantages of performing combined (total evidence) versus separate analyses (consensus) of independent data sets for validation purposes. A stepwise validation procedure defined across all levels of comparison is introduced, along with a corresponding statistical test: A phylogeny will be said to be globally validated only if it satisfies all the tests. An application to the phylogeny of kangaroos is presented to illustrate the stepwise procedure.


Phylogenetic Tree Systematic Biology Consensus Tree Distance Matrice Random Data 


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  1. Adams, F. N., III. (1972): Consensus techniques and the comparison of taxonomic trees Systematic Zoology, 21, 390–397.Google Scholar
  2. Alroy. J. (1994): Four permutation tests for the presence of phytogenetic structure, Systematic Biology, 43, 430–437.Google Scholar
  3. Anderbcrg, A. and Tehler, A. (1990): Consensus trees, a necessity in taxonomic practice, Cladistics, 6, 399–402.CrossRefGoogle Scholar
  4. Archie, J. W. (1989a): A randomization test for phytogenetic information in systematic data Systematic Zoology, 38, 219–252.Google Scholar
  5. Archie, J. W. (1989b): Homoplasy excess ratios: New indices for measuring levels of homoplasy in phytogenetic systematics and a critique of the consistency index, Systematic Zoology, 38, 253–269.CrossRefGoogle Scholar
  6. Archie, J. W. (1989c): Phylogenies of plant families: A demonstration of phylogenetic randomness in DNA sequence data derived from proteins, Evolution, 43, 1796–1800.CrossRefGoogle Scholar
  7. Archie, J. W. (1990): Homoplasy excess statistics and retention indices: A reply to Farris Systematic Zoology, 39, 169–174.Google Scholar
  8. Archie, J. W. and Felsenstein, J. (1993): The number of evolutionary steps on random and minimum lengths trees for random evolutionary data. Theoretical Population Biology, 43, 52–79.MATHCrossRefGoogle Scholar
  9. Bandelt. H. J. (1995): Combination of data in phylogenetic analysis Plant Systematics and Evolution Supplementum 9, 355–361.Google Scholar
  10. Barrett, M. et al. (1991): Against consensus Systematic Zoology 40, 486–493.Google Scholar
  11. Barrett, M. et al. (1993): Crusade’? A response to Nelson Systematic Biology 42, 216–217.Google Scholar
  12. Barthélemy, J.-P. and McMorris, F. R. (1986): The median procedure for n-trees Journal of Classification 3, 329–334.Google Scholar
  13. Baum, B. R. (1992): Combining trees as a way of combining data for phylogenetic inference, and the desirability of combining gene trees, Taxon, 41, 3–10.CrossRefGoogle Scholar
  14. Baum, B. R. and Ragan, M. A. (1993): Reply to A. G. Rodrigo’s “A comment on Baum’s method for combining phylogenetic trees, Taxon, 42, 637–640.CrossRefGoogle Scholar
  15. Baverstock, P. R. et al. (1989): Albumin immunologic relationships of the Macropodidae (Marsupialia) Systematic Zoology 38, 38–50.Google Scholar
  16. Berry, V. and Gascuel, O. (1996): On the interpretation of bootstrap trees: Appropriate threshold of clade selection and induced gain, Molecular Biology and Evolution, 13, 999–1011.CrossRefGoogle Scholar
  17. Bledsoe, A. H. and Raikow, R. J. (1990): A quantitative assessment of congruence between molecular and nonmolecular estimates of phylogeny, Journal of Molecular Evolution, 30, 247–259.CrossRefGoogle Scholar
  18. Bleiweiss, R. et al. (1994): DNA-DNA hybridization-based phylogeny of “higher nonpasserines: Reevaluating a key portion of the avian family tree, Molecular Phylogenetics and Evolution, 3, 248–255.CrossRefGoogle Scholar
  19. Bock, II. H. (1985): On some significance tests in cluster analysis, Journal of Classification, 2, 77–108. Bosibud, H. M. and Bosibud, L. E. (1972): A metric for classifications, Taxon, 21, 607–613.Google Scholar
  20. Bourque, M. (1978): Arbres de Steiner et réseaux dont varie l’emplacement de certains sommets. Ph. D. Thesis, Département d’Informatique et de Recherche Operatiouelle, Unversité de Montréal, Montréal.Google Scholar
  21. Bremer, K. (1990): Combinable component consensus, Cladistics, 6, 369–372. Bremer, K. (1995): Branch support and tree stability, Cladistics, 10, 295–304. Brown, J. K. M. (1994): Probabilities of evolutionary trees, Systematic Biology, 43, 78–91.Google Scholar
  22. Bryant, H. N. (1992): The role of permutation tail probability tests in phylogenetic systematics Systematic Biology 41, 258–263.Google Scholar
  23. Bull, J. J. et al. (1993): Partitioning and combining data in phylogenetic analysis, Systematic Biology, 42, 384–397.Google Scholar
  24. Buneman, P. (1971): The recovery of trees from measures of dissimilarity. In: Mathematics in Archeological and Historical Sciences, Hodson, F. R. et al. (eds.), 387–395, Edinburgh University Press, Edinburgh.Google Scholar
  25. Buneman, P. (1974): A note on the metric properties of trees, Journal of Combinatorial Theory (B), 17, 48–50.MathSciNetMATHCrossRefGoogle Scholar
  26. Carpenter, J. M. (1992): Random cladistics Cladistics 8, 147–153.Google Scholar
  27. Carter, M. et al. (1990): On the distribution of lengths of evolutionary trees SIAM Journal of Discrete ai’lathematics 3, 38–47.Google Scholar
  28. Chìppindale, P. T. and Wiens, J. J. (1994): Weighting, partitioning, and combining characters in phylogenetic analysis, Systematic Biology, 43, 278–287.Google Scholar
  29. Colless, D. H. (1980): Congruence between morphometric and allozyme data for Menidia species: A reappraisal Systematic Zoology 29, 288–299 .Google Scholar
  30. Critchlow, D. E. et al. (1996): The triples distance for rooted bifurcating phylogenetic trees Systematic Biology 45, 323–334.Google Scholar
  31. Cucumel, G. and Lapointe, F.-J. (1997): Un test de la pertinence du consensus par une méthode de permutations. In: Actes des XXIXe journées de statistique 299–300, Carcassonne.Google Scholar
  32. Davis, J. I. (1993): Character removal as a means for assessing stability of clades, Cladistics, 9, 201–210.CrossRefGoogle Scholar
  33. Day, W. H. E. (1983a): The role of complexity in comparing classifications, Mathematical Biosciences, 66, 97–114.MathSciNetMATHCrossRefGoogle Scholar
  34. Day, W. H. E. (1983b): Distributions of distances between pairs of classifications. In: Numerical Taxonomy Felsenstein, J. (ed.), 127–131, Springer-Verlag, Berlin.Google Scholar
  35. Day, W. H. E. (1983c): Computationally difficult parsimony problems in phylogenetic systematics Journal of Theoretical Biology 103, 429–438.Google Scholar
  36. Day, W. H. E. (1986): Analysis of quartet dissimilarity measures between undirected phylogenetic trees Systematic Zoology 35, 325–333.Google Scholar
  37. Day, W. H. E. (1987): Computational complexity of inferring phylogenies from dissimilarity matrices Bulletin of Mathematical Biology 49, 461–467.Google Scholar
  38. Day, W. H. E. and McMorris, F. R. (1985): A formalization of consensus index methods Bulletin of Mathematical Biology 47, 215–229.Google Scholar
  39. de Queiroz, A. (1993): For consensus (sometimes) Systematic Biology 42, 368–372.Google Scholar
  40. de Queiroz, A. et al. (1995): Separate versus combined analysis of phylogenetic evidence Annual Review of Ecology and Systematics 26, 657–681.Google Scholar
  41. Dopazo, J. (1994): Estimating errors and confidence intervals for branch lengths in phylogenetic tres by a bootstrap approach. Journal of Molecular Evolution, 38, 300–304.CrossRefGoogle Scholar
  42. Dubes, R. and Jain, A. K. (1979): Validity studies in clustering methodologies, Pattern Recognition, 11, 235–254.MATHCrossRefGoogle Scholar
  43. Dwass, M. (1957): Modified randomization tests for nonparametric hypotheses Annals of Mathematics and Statistics 28, 181–187.Google Scholar
  44. Edgington, E. S. (1995): Randomization tests, 3rd Edition, Revised and Expanded. Marcel Dekker, New York.Google Scholar
  45. Eernisse, D. J. and Kluge, A. G. (1993): Taxonomic congruence versus total evidence, and the phylogeny of amniotes inferred from fossils, molecules and morphology, Molecular Biology and Evolution, 10, 1170–1195.Google Scholar
  46. Efron, B. (1979): Bootstrapping methods: Another look at the jackknife Annals of Statistics 7, 1–26.Google Scholar
  47. Efron, B. and Gong, G. (1983): A leisurely look at the bootstrap, the jackknife, and cross-validation American Statistician 37, 36–48.Google Scholar
  48. Efron, B. and Tibshirani, R. J. (1993): An introduction to the bootstrap, Chapman and Hall, New York.Google Scholar
  49. Efron, B. et al. (1996): Bootstrap confidence levels for phylogenetic trees Proceedings of the National Academy of Sciences USA93, 13429–13434.Google Scholar
  50. Estabrook, G. F. (1992): Evaluating undirected positional congruence of individual taxa between two estimates of the phylogenetic tree for a group of taxa, Systematic Biology, 41, 172–177.Google Scholar
  51. Estabrook, G. F. et al. (1985): Comparison of undirected phylogenetic trees based ou subtrees of four evolutionary units, Systematic Zoology, 34, 193–200.CrossRefGoogle Scholar
  52. Faith, D. P. (1991): Cladistic permutation tests for monophyly and nonmonophyly, Systematic Zoology, 40, 366–375.CrossRefGoogle Scholar
  53. Faith, D. P. (1992): Ou corroboration: A reply to Carpenter Cladistics 8, 265–273.Google Scholar
  54. Faith, D. P. and Ballard, J. W. O. (1994): Length differences topology-dependent tests: A response to Källersjö et al, Cladistics, 10, 57–64.CrossRefGoogle Scholar
  55. Faith, D. P. and Belbin, L. (1986): Comparison of classifications using measures intermediate between metric dissimilarity and consensus similarity, Journal of Classification, 3, 257–280.MATHCrossRefGoogle Scholar
  56. Faith, D. P. and Cranston, P. S. (1991): Could a cladogram this short have arisen by chance alone? on permutation tests for cladistic structure, Cladistics, 71–28.CrossRefGoogle Scholar
  57. Faith, D. P. and Trueman, J. W. H. (1996): When the topology-dependent permutation test (T-PTP) for monophyly returns significant support for monophyly, should that be equated with (a) rejecting a null hypothesis of nonmonophyly, (b) rejecting a null hypothesis of “no structure,” (c) failing to falsify a hypothesis of monophyly, or (d) none of the above? Systematic Biology, 45, 580–586.CrossRefGoogle Scholar
  58. Farris, J. S. (1989a): The retention index and the resealed consistency index, Cladistics, 5, 417–419. Farris, J. S. (1989b): The retention index and homoplasy excess, Systematic Zoology, 38, 406–407. Farris, J. S. (1991): Excess homoplasy ratios, Cladistics, 7,81–91.CrossRefGoogle Scholar
  59. Farris, J. S. et al. (1995a): Constructing a significance test for incongruence Systematic Biology44, 570572.Google Scholar
  60. Farris, J. S. et al. (1995b): Testing significance of incongruencies, Cladistics, 10, 315–370. Felsenstein, J. (1978): The number of evolutionary trees, Systematic Zoology, 27, 27–33.Google Scholar
  61. Felsenstein, J. (1985): Confidence limits on phylogenies: An approach using the bootstrap, Evolution, 39, 783–791.CrossRefGoogle Scholar
  62. Felsenstein, J. (1993): PHYLIP: Phylogeny inference package, version 3.5c, distributed by the author, University of Washington, Seattle.Google Scholar
  63. Felsenstein, J. and Kishino, H. (1993): Is there something wrong with the bootstrap on phylogenies? A reply to Hillis and Bull, Systematic Biology, 42, 193–200.Google Scholar
  64. Finden, C. R. and Gordon, A. D. (1985): Obtaining common pruned trees Journal of Classification 2, 225–276.Google Scholar
  65. Fowlkes, E. B. and Mallows, C. L. (1983): A method for comparing two hierarchical clusterings, Journal.Google Scholar
  66. of the American Statistical Association,78, 553–569.Google Scholar
  67. Pumas, G. W. (1984): The generation of random, binary unordered trees Journal of Classification 1 187–233.Google Scholar
  68. Goloboff, P. (1991a): Homoplasy and the choice among cladograms,•Cladistics, 7, 215–232. Goloboff, P. (1991b): Random data, homoplasy and information, Cladistics,7 395–406.CrossRefGoogle Scholar
  69. Gordon, A. D. (1986): Consensus supertrees: the synthesis of rooted trees containing overlapping sets of labeled leaves, Journal of Classification, 3, 335–348.MathSciNetMATHCrossRefGoogle Scholar
  70. Gordon, A. D. (1987): A review of hierarchical classifications Journal of the Royal Statistical Society (A)150, 119–137.Google Scholar
  71. Gower, J. C. (1983): Comparing classifications. In: Numerical Taxonomy, Felsenstein, J. (ed.), 137–155, Springer-Verlag, Berlin.CrossRefGoogle Scholar
  72. Graham, R. L. and Foulds, L. R. (1982): Unlikelihood that minimal phylogenies for a realistic biological study can be constructed in reasonable computational time, Mathematical Biosciences, 60, 133–142.Google Scholar
  73. Hall, P. and Martin, M. A. (1988): On bootstrap resampling and iterations Biometrika 75, 661–671.Google Scholar
  74. Harding, E. F. (1971): The probabilities of rooted tree-shapes generated by random bifurcations Advances in Applied Probability 4, 44–77.Google Scholar
  75. -Iarshman, J. (1994): The effect of irrelevant characters on bootstrap values, Systematic Biology, 43, 419–424.Google Scholar
  76. Hartigan, J. A. (1967): Representation of similarity matrices by trees Journal of the American Statistical Association 62, 1140–1158.Google Scholar
  77. Hedges, S. B. (1992): The number of replications needed for accurate estimation of the bootstrap P value in phylogenetic studies, Molecular Biology and Evolution, 9, 366–369.Google Scholar
  78. Hendy, M. D. et al. (1984): Comparing trees with pendant vertices labelled SIAM Journal in Applied Mathematics 44, 1054–1065.Google Scholar
  79. Hillis, D. M. (1987): Molecular versus morphological approaches to systematics Annual Review of Ecology and Systematics 18, 23–42.Google Scholar
  80. Hillis, D. M. (1991): Discriminatin g between phylogenetic signal and random noise in DNA sequences, In: Phylogenetic analysis of DNA sequences, Miyamoto, M. M. and Cracraft, J. (eds.), 278–294, Oxford University Press, New York.Google Scholar
  81. Hillis, D. M. (1995): Approaches for assessing phylogenetic accuracy Systematic Biology 44, 3–16.Google Scholar
  82. Hillis, D. M. and Bull, J. J. (1993): An empirical test of bootstrapping as a method for assessing confidence in phylogenetic analysis, Systematic Biology, 42, 182–192.Google Scholar
  83. Hubert, L. J. and Baker, F. B. (1977): The comparison and fitting of given classification schemes Journal of Mathematical Psychology 16, 233–253.Google Scholar
  84. uelsenbeck, J. P. (1995): Performance of phylogenetic methods in simulation, Systematic Biology, 44, 17–48.Google Scholar
  85. Huelsenbeck, J. P. and Bull, J. J. (1996): A likelihood ratio test for detection of conflicting phylogenetic signal, Systematic Biology, 45, 92–98.CrossRefGoogle Scholar
  86. Huelsenbeck, J. P. et al. (1994): Is character weighting a panacea for the problem of data heterogeneity in phylogenetic analysis?, Systematic Biology, 43, 288–291.Google Scholar
  87. Huelsenbeck, J. P. et al. (1995): Parametric bootstrapping in molecular phylogenetics: Applications and performance, In: Molecular Zoology: Strategies and Protocols, Ferraris, J and Palumbi, S. (eds.), Wiley, New York.Google Scholar
  88. Huelsenbeck, J. P. et al. (1996): Combining data in phylogenetic analysis, Trends in Ecology and Evolution, 11, 152–158.CrossRefGoogle Scholar
  89. Jardine, C. J. et al. (1967): The structure and construction of taxonomic hierarchies Mathematical Biosciences 1, 173–179.Google Scholar
  90. Källersjö, M. et al. (1992): Skewness and permutation Cladistics8, 275–287.Google Scholar
  91. Kim, J. (1993): Improving the accuracy of phylogenetic estimation by combining different methods, Systematic Biology, 42, 331–340.Google Scholar
  92. Kirsch, J. A. W. et al. (1995): Resolution of portions of the kangaroo phylogeny (Marsupialia: Macropodidae) using DNA hybridization Biological Journal of the Linnean Society 55, 309–328.Google Scholar
  93. Kirsch, J. A. W. et al. (1997): DNA-hybridisation studies of marsupials and their implications for metatherian classification. Australian Journal of Zoology, in press.Google Scholar
  94. Klassen, G. J. et al. (1991): Consistency indices and random data Systematic Zoology 40, 446–457.Google Scholar
  95. Kluge, A. G. (1989): A concern for evidence and a phylogenetic hypothesis of relationships among Epicrates (Boidae, Serpentes) Systematic Biology 38, 7–25.Google Scholar
  96. Kluge, A. G. and Farris, J. S. (1969): Quantitative phyletics and the evolution of anurans Systematic Zoology 18, 1–32.Google Scholar
  97. Krajewski, C. and Dickerman, A. W. (1990): Bootstrap analysis of phylogenetic trees derived from DNA hybridization matrices, Systematic Zoology, 39, 383–390.CrossRefGoogle Scholar
  98. Lanyon, S. (1985): Detecting internal inconsistencies in distance data Systematic Zoology 34, 397–403.Google Scholar
  99. Lanyon, S. (1993): Phylogenetic frameworks: Towards a firmer foundation for the comparative approach Biological Journal of the Linnean Society 49, 45–61.Google Scholar
  100. Lapointe, F.-J. and Cucumel, G. (1997): The average consensus procedure: combination of weighted trees containing identical or overlapping sets of objects, Systematic Biology, 46, 306–312.CrossRefGoogle Scholar
  101. Lapointe, F.-J. and Legendre, P. (1990): A statistical framework to test the consensus of two nested classifications, Systematic Zoology, 39, 1–13.CrossRefGoogle Scholar
  102. Lapointe, F.-J. and Legendre, P. (1991): The generation of random ultrametric matrices representing dendrograms, Journal of Classification, 8, 177–200.CrossRefGoogle Scholar
  103. Lapointe, F.-J. and Legendre, P. (1992a): A statistical framework to test the consensus among additive trees (cladograms), Systematic Biology, 41, 158–171.Google Scholar
  104. Lapointe, F.-J. and Legendre, P. (1992b): Statistical significance of the matrix correlation coefficient for comparing independent phylogenetic trees, Systematic Biology, 41, 378–384.Google Scholar
  105. Lapointe, F.-J. and Legendre, P. (1994): A classification of pure. malt Scotch whiskies Applied Statistics 43, 237–257.Google Scholar
  106. Lapointe, F.-J. and Kirsch, J. A. W. (1995): Estimating phylogenies from lacunose distance matrices, with special reference to DNA hybridization data, Molecular Biology and Evolution, 12, 266–284.Google Scholar
  107. Lapointe, F.-J. and Legendre, P. (1995): Comparison tests for dendrograms: A comparative evaluation Journal of Classification 12, 265–282.Google Scholar
  108. Lapointe, F.-J. et al. (1994): Jackknifing of weighted trees: Validation of phylogenies reconstructed from distances matrices, Molecular Phylogenetics and Evolution, 3, 256–267.CrossRefGoogle Scholar
  109. Leclerc, B. and Cucumel, G. (1987): Consensus en classification: Une revue bibliographique Mathématiques et Sciences Humaines 100, 109–128.Google Scholar
  110. Lecointre, G. H. et al. (1993): Species sampling has a major impact on phylogenetic inference Molecular Phylogenetics and Evolution 2, 205–224.Google Scholar
  111. Lefkovitch, L. P. (1985): Euclidean consensus dendrograms and other classification structures Mathematical Biosciences 74, 1–15.Google Scholar
  112. Le Quesne, W. (1989): Frequency distributions of lengths of possible networks from a data matrix Cladistics 5, 395–407.Google Scholar
  113. Li, W.-H. and Guoy, M. (1991): Statistical methods for testing phylogenies, In: Phylogenetic analysis of DNA sequences Miyamoto, M. M. and Cracraft, J. (eds.), 249–277, Oxford University Press, New York.Google Scholar
  114. Li, W.-H. and Zharkikh, A. (1994): What is the bootstrap technique?, Systematic Biology, 43, 424–430. Li, W.-H. and Zharkikh, A. (1995): Statistical tests of DNA phylogenies, Systematic Biology, 44, 49–63.Google Scholar
  115. Ling, R. F. (1973): A probability theory of cluster analysis Journal of the American Statistical Association 68, 159–164.Google Scholar
  116. Mantel, N. (1967): The detection of disease clustering and a generalized regression approach Cancer Research 27, 209–220.Google Scholar
  117. Margush, T. (1982): Distances between trees Discrete Applied Mathematics 4, 281–290.Google Scholar
  118. Margush, T. and McMorris, F. R. (1981): Consensus n-trees, Bulletin of Mathematical Biology, 43, 239244.Google Scholar
  119. Marshall, C. R. (1991): Statistical tests and bootstrapping: Assessing the reliability of phylogenies based on distance data, Molecular Biology and Evolution, 8, 386–391.Google Scholar
  120. Mason-Gamer, R. J. and Kellogg, E. K. (1996): Testing for phylogenetic conflict among molecular data.Google Scholar
  121. sets in the tribe Triticeae (Gramineae), Systematic Biology,45 524–545.Google Scholar
  122. McMorris, F. R. (1985): Axioms for consensus functions ou undirected phylogenetic trees Mathematical Biosciences 74 17–21.Google Scholar
  123. McMorris, F. R. et al. (1983): A view of some consensus methods for trees. In: Numerical Taxonomy Felsenstein, J. (ed.), 122–126, Springer-Verlag, Berlin.Google Scholar
  124. McMorris, F. R. and Neumann, D. (1983): Consensus functions defined on trees Mathematical Social Sciences 4 131–136.Google Scholar
  125. Meier, R. et al. (1991): Homoplasy slope ratio: A better measurement of observed homoplasy in cladistic analyses, Systematic Zoology, 40, 74–88.CrossRefGoogle Scholar
  126. Mickevich, M. F. (1978): Taxonomic congruence, Systematic Zoology, 27, 143–158.CrossRefGoogle Scholar
  127. Milligan, G. W. (1981): A Monte-Carlo study of 30 internal criterion measures for cluster-analysis, Psychometrika, 46, 187–195.MathSciNetMATHCrossRefGoogle Scholar
  128. Miyamoto, M. M. (1985): Consensus cladograms and general classifications Cladistics 1186–189.Google Scholar
  129. Miyamoto, M. M. et al. (1994): A congruence test of reliability using linked mitochondria) DNA sequences, Systematic Biology, 43, 236–249.Google Scholar
  130. Miyamoto, M. M. and Fitch, W. M. (1995): Testing species phylogenies and phylogenetic methods with congruence, Systematic Biology, 44, 64–76.Google Scholar
  131. Mueller, L. D. and Ayala, F. J. (1982): Estimation and interpretation of genetic distances in empirical studies, Genetical Research, 40, 127–137.CrossRefGoogle Scholar
  132. Murtagh, F. (1984): Counting dendrograms: A survey, Discrete Applied Mathematics, 7, 191–199.MathSciNetMATHCrossRefGoogle Scholar
  133. Nelson, G. (1979): Cladistic analysis and synthesis: Principles and definitions, with a historical note on Adauson’s Famille des Plantes (1763–1764), Systematic Zoology, 28, 1–21.CrossRefGoogle Scholar
  134. Nelson, G. (1993): Why crusade against consensus? A reply to Barrett, Donoghue, and Sober Systematic Biology 42 215–216.Google Scholar
  135. Nemec, A. F. L. and Brinkburst, R. O. (1988): The Fowlkes-Mallows statistic and the comparison of two independently determined dendrograms, Canadian Journal of Fisheries and Aquatic Sciences, 45, 97 1975.Google Scholar
  136. Neumann, D. A. (1983): Faithful consensus methods for n-trees, Mathematical Biosciences, 63, 271–287. Nixon, K. C. and J. M. Carpenter. (1996): On simultaneous analysis, Cladistics, 12, 221–241.Google Scholar
  137. Oden, N. L. and Shao, K. T. (1984): An algorithm to equiprobably generate all directed trees with k labeled terminal nodes and unlabeled interior nodes, Bulletin of Mathematical Biology, 46, 379–387.MathSciNetMATHGoogle Scholar
  138. Olmstead, R. G. and Sweere, J. A. (1994): Combining data in phylogenetic systematics: An empirical approach using three molecular data sets in the Solanacae, Systematic Biology, 43, 467–481.CrossRefGoogle Scholar
  139. Omland, K. E. (1994): Character congruence between a molecular and a morphological phylogeny for dabbling ducks (Arras), Systematic Biology, 43, 369–386.Google Scholar
  140. Page, R. D. M. (1988): Quantitative cladistic biogeography: Constructing and comparing area cladograms, Systematic Zoology, 37, 254–270.CrossRefGoogle Scholar
  141. Page, R. D. M. (1991): Random dendrograms and null hypotheses in cladistic biogeography Systematic Zoology 40 54–62.Google Scholar
  142. Patterson, C. et al. (1993): Congruence between molecular and morphological phylogenies Annual Review of Ecology and Systematics 24 153–188.Google Scholar
  143. Penny, D. and Hendy, M. D. (1985a): The use of tree comparison metrics, Systematic Zoology, 34, 75–82. Penny, D. and Hendy, M. D. (1985b): Testing methods of evolutionary tree construction, Cladistics, 1, 266–278.CrossRefGoogle Scholar
  144. Penny, D. et al. (1982): Testing the theory of evolution by comparing phylogenetic trees constructed from five different protein sequences, Nature, 297, 197–200.CrossRefGoogle Scholar
  145. Penny, D. et al. (1992): Progress with methods for constructing evolutionary trees Trends in Ecology and Evolution 7, 73–79.Google Scholar
  146. Phillips, C. and Warnow, T. J. (1996): The asymmetric median tree–A new model for building consensus trees, Discrete Applied Mathematics, 71, 311–335.MathSciNetMATHCrossRefGoogle Scholar
  147. Phipps, J. B. (1975): The numbers of classifications, Canadian Journal of Botany, 54, 686–688.CrossRefGoogle Scholar
  148. Podani, J. and Dickinson, T. A. (1984): Comparison of dendrograms: A multivariate approach Canadian Journal of Botany 62 2765–2778.Google Scholar
  149. Poe, S. 1996. Data set incongrence and the phylogeny of Crocodilians, Systematic Biology, 45, 393–414.CrossRefGoogle Scholar
  150. Prager, E. M. and Wilson, A. C. (1976): Congruency of phylogenies derived from different proteins, Journal of Molecular Evolution, 9, 45–57.CrossRefGoogle Scholar
  151. Proskurowski, A. (1980): On the generation of binary trees Journal of the Association of Computing Machinery 27 1–2.Google Scholar
  152. Purvis, A. (1995a): A modification to Baum and Ragan’s method for combining phylogenetic trees, Systematic Biology, 44, 251–255.Google Scholar
  153. Purvis, A. (1995b): A composite estimate of primate phylogeny Philosophical Transactions of the Royal Society of London (B) 348 405–421.Google Scholar
  154. Quiroz, A. J. (1989): Fast random generation of binary, t-ary and other types of trees Journal of Classification 6 223–231.Google Scholar
  155. Ragan, M. A. (1992): Phylogeuetic inference based on matrix representation of trees Molecular Phylogenetics and Evolution 1 53–58.Google Scholar
  156. Robinson, D. F. (1971): Comparison of labeled trees with valency Three Journal of Combinatorial Theory 11 105–119.Google Scholar
  157. Robinson, D. F. and Foulds, L. R. (1979): Comparison of weighted labelled trees. In: Lecture Notes in Matehmatics Volume 748, 119–126, Springer-Verlag, Berlin.Google Scholar
  158. Robinson, D. F. and Foulds, L. R. (1981): Comparison of phylogenetic trees, Mathematical Biosciences, 53, 131–147.MathSciNetMATHCrossRefGoogle Scholar
  159. Rodrigo, A. G. (1993a): Calibrating the bootstrap test of monophyly, International Journal of Parasitology, 23, 507–514.CrossRefGoogle Scholar
  160. Rodrigo, A. G. (19936): A comment on Baum’s method for combining phylogenetic trees, Taxon, 42, 63 1636.Google Scholar
  161. Rodrigo, A. G. et al. (1993): A randomisation test of the null hypothesis that two cladograms are sample estimates of a parametric phylogenetic tree, New Zealand Journal of Botany, 31, 257–268.CrossRefGoogle Scholar
  162. Rohlf, F. J. (1974): Methods of comparing classifications, Annual Review of Ecology and Systematics, 5, 101–113.CrossRefGoogle Scholar
  163. Rohlf, F. J. (1982): Consensus indices for comparing classifications, Mathematical Biosciences, 59, 13 1144.Google Scholar
  164. Ronquist, F. (1996): Matrix representations of trees, redudancy and weighting, Systematic Biology, 45, 247–253.CrossRefGoogle Scholar
  165. Russo, C. A. M. et al. (1996): Efficiencies of different genes and different tree-building methods in recovering a known vertebrate phylogeny, Molecular Biology and Evolution, 13, 525–536.CrossRefGoogle Scholar
  166. Sanderson, M. J. (1989): Confidence limits on phylogenies: The bootstrap revisited, (laths es, 5, 113129.Google Scholar
  167. Sanderson, M. J. (1995): Objections of bootstrapping phylogenies: A critique, Systematic Biology, 44, 299–320.Google Scholar
  168. Savage, H. M. (1983): The shape of evolution: Systematic tree topology Biological Journal of the Linneae Society20, 225–244.Google Scholar
  169. Shao, K. and Rohlf, F. J. (1983): Sampling distribution of consensus indices when all bifurcating trees are equally likely. In: Numerical Taxonomy, Felsenstein, J. (ed.), 132–136, Springer-Verlag, Berlin.CrossRefGoogle Scholar
  170. Shoo, K. and Sokal, R. R. (1986): Significance tests of consensus indices, Systematic Zoology, 35, 58 2590.Google Scholar
  171. Simberloff, D. (1987): Calculating probabilities that cladograms match: A method of biogeographic inference, Systematic Zoology, 36, 175–195.CrossRefGoogle Scholar
  172. Simberloff, D. et al. (1981): There have been no statistical tests of cladistics biogeographical hypotheses. In: Vicariance Biogeography: A Critique, Nelson, G. and Rosen, D. E. (eds.), 40–63, Columbia University Press, New York.Google Scholar
  173. Sneath, P. H. A. (1967): Some statistical problems in numerical taxonomy, The Statistician, 17, 1–12.CrossRefGoogle Scholar
  174. Sokal R. R. and Rohlf, F. J. (1962): The comparison of dendrograms by objective methods, Taxon, 9, 3340.Google Scholar
  175. Sokal R. R. and Rohlf, F. J. (1981): Taxonomic congruence in the Leptopodomorpha re-examined Systematic Zoology30, 309–325.Google Scholar
  176. Steel, M. A. (1988): Distribution of the symmetric difference metric on phylogenetic trees SLANI.Journal of Discrete Mathematics1, 541–555.Google Scholar
  177. Steel, M. A. (1992): The complexity of reconstructing trees from qualitative characters and subtrees Journal of Classification9, 91–116.Google Scholar
  178. Steel, M. A. and Penny, D. (1993): Distribution of tree comparison metrics-Some new results Systematic Biology42, 126–141.Google Scholar
  179. Steel., M. A. et al. (1992): Significance of the length of the shortest tree Journal of Classification9, 6370.Google Scholar
  180. Stinebrickuer, R. (1982): S-consensus trees and indices Bulletin of Mathematical Biology46, 923–935.Google Scholar
  181. Stinebrickner, R. (1984): An extension of intersection methods from trees to dendrograms Systematic Zoology33, 381–386.Google Scholar
  182. Sullivan, J. (1996): Combining data with different distributions of among-site variation Systematic Biology45, 375–379.Google Scholar
  183. Swofford, D. L. (1991): When are phylogeny estimates from molecular and morphological data incongruent?, In: Phylogenetic analysis of DNA sequences, Miyamoto, M. M. and Cracraft, J. (eds.), 295–333, Oxford University Press, New York.Google Scholar
  184. Swofford, D. I. et al. (1996a): Phylogenetic inference, In: Molecular Systematics, 2nd edition, Hillis, D. M. et al. (eds.), 407–514, Sinauer, Sunderland.Google Scholar
  185. Swofford, D. L. et al. (19966): The topology-dependent permutation test for monophyly does not test for monophyly, Systeneatic Biology, 45, 575–579.Google Scholar
  186. Waterman, M. S. and Smith, T. F. (1978): On the similarity of dendrograms Journal of Theoretical Biology73, 789–800.Google Scholar
  187. Wiens, J. J. and Chippindale, P. T. (1994): Combining and weighting characters and the prior agreement approach revisited, Systematic Biology, 43, 564–566.CrossRefGoogle Scholar
  188. Wiens, J. J. and Reeder, T. W. (1995): Combining data sets with different numbers of taxa for phylogenetic analysis, Systematic Biology, 44, 548–558.Google Scholar
  189. Wilkinson, M. (1994): Common cladistic information and its consensus representation: Reduced Adams and reduced cladistic consensus trees and profiles, Systematic Biology, 43, 343–368.Google Scholar
  190. Wilkinson, M. (1996): Majority-rule reduced consensus trees and their use in boostrapping Molecular Biology and Evolution13, 437–444.Google Scholar
  191. Williams, D. M. (1994): Combining trees and combining data Taxon43, 449–453.Google Scholar
  192. Williams, W. T. and Clifford, FL T. (1971): On the comparison of two classifications ou the same set of elements Taxon20, 519–522.Google Scholar
  193. Zaretskii, K. (1965): Constructing a tree on the basis of a set of distances between the hanging vertices Uspekhi Mathematika Nauk20, 90–92. (in Russian).Google Scholar
  194. Zharkikh, A. and Li, W.-H. (1992a): Statistical properties of bootstrap estimation of phylogenetic variability from nucleotide sequences. I. Four taxa with a molecular clock, Molecular Biology and Evolution, 9, 1119–1147.Google Scholar
  195. Zharkikh, A. and Li, W.-H. (1992b): Statistical properties of bootstrap estimation of phylogenetic variability from nucleotide sequences. I1. Four taxa without a molecular clock. Journal of Molecular Evolution, 35, 356–366.CrossRefGoogle Scholar
  196. Zharkikh, A. and Li, W.-H. (1995): Estimation of confidence in phylogeny: The full-and-partial bootstrap technique, Molecular Phylogenetics and Evolution, 4, 44–63.CrossRefGoogle Scholar

Copyright information

© Springer Japan 1998

Authors and Affiliations

  • François-Joseph Lapointe
    • 1
  1. 1.Département de sciences biologiquesUniversité de MontréalMontréalCanada

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