Biology & Philosophy

, Volume 23, Issue 4, pp 455–473 | Cite as

The prior probabilities of phylogenetic trees

  • Joel D. Velasco


Bayesian methods have become among the most popular methods in phylogenetics, but theoretical opposition to this methodology remains. After providing an introduction to Bayesian theory in this context, I attempt to tackle the problem mentioned most often in the literature: the “problem of the priors”—how to assign prior probabilities to tree hypotheses. I first argue that a recent objection—that an appropriate assignment of priors is impossible—is based on a misunderstanding of what ignorance and bias are. I then consider different methods of assigning prior probabilities to trees. I argue that priors need to be derived from an understanding of how distinct taxa have evolved and that the appropriate evolutionary model is captured by the Yule birth–death process. This process leads to a well-known statistical distribution over trees. Though further modifications may be necessary to model more complex aspects of the branching process, they must be modifications to parameters in an underlying Yule model. Ignoring these Yule priors commits a fallacy leading to mistaken inferences both about the trees themselves and about macroevolutionary processes more generally.


Base rate fallacy Bayesianism Phylogenetic trees Phylogenetics Prior probabilities Systematics Tree shape Yule process 



I am grateful to David Baum, Matt Haber, James Justus, Bret Larget, Greg Novack, and especially Elliott Sober for their support and many helpful comments on earlier drafts of this paper. Thanks also to an anonymous reviewer who made several helpful comments which improved the presentation of this paper.


  1. Aldous DJ (2001) Stochastic models and descriptive statistics for phylogenetic trees, from yule to today. Stat Sci 16(1):23–34CrossRefGoogle Scholar
  2. Brown JKM (1994) Probabilities of evolutionary trees. Syst Biol 43(1):78–91CrossRefGoogle Scholar
  3. Centers for Disease Control and Prevention (2006) HIV/AIDS Surveillance Report, 2005, vol 17. U.S. Department of Health and Human Services, Centers for Disease Control and Prevention, Atlanta, pp 1–54. Also available at
  4. Edwards AWF (1970) Estimation of the branch points of a branching diffusion process. J R Stat Soc B (Methodological) 32(2):155–174Google Scholar
  5. Farris JS (1983) The logical basis of phylogenetic analysis. Adv Cladistics 2:7–36Google Scholar
  6. Felsenstein J (2004) Inferring phylogenies. Sinauer Associates, Sunderland, MassGoogle Scholar
  7. Goloboff PA, Pol D (2005) Parsimony and Bayesian phylogenetics. In: Victor AA (ed) Parsimony, phylogeny and genomics. Oxford University Press, Oxford, pp 148–159Google Scholar
  8. Haber MH (2005) On probability and systematics: possibility, probability, and phylogenetic inference. Syst Biol 54(5):831–841CrossRefGoogle Scholar
  9. Halliburton R (2004) Introduction to population genetics. Pearson/Prentice Hall, Upper Saddle RiverGoogle Scholar
  10. Harding EF (1971) The probabilities of rooted tree-shapes generated by random bifurcation. Adv Appl Probab 3(1):44–77CrossRefGoogle Scholar
  11. Hein J, Schierup M, Wiuf C (2005) Gene genealogies, variation and evolution: a primer in coalescent theory. Oxford University Press, OxfordGoogle Scholar
  12. Howson C, Urbach P (2005) Scientific reasoning: the Bayesian approach, 3rd edn. Open Court, La SalleGoogle Scholar
  13. Huelsenbeck JP, Kirkpatrick M (1996) Do phylogenetic methods produce trees with biased shapes? Evolution 50(4):1418–1424CrossRefGoogle Scholar
  14. Huelsenbeck JP, Ronquist F (2001) MR BAYES: Bayesian inference of phylogenetic trees. Bioinformatics (Oxford) 17(8):754–755CrossRefGoogle Scholar
  15. Huelsenbeck JP, Ronquist F (2005) Bayesian analysis of molecular evolution using Mr. Bayes. In: Nielson R (ed) Statistical methods in molecular evolution. Springer, New York, pp 183–232CrossRefGoogle Scholar
  16. Huelsenbeck JP, Ronquist F, Nielsen R, Bollback JP (2001) Bayesian inference of phylogeny and its impact on evolutionary biology. Science (Washington DC) 294(5550):2310–2314CrossRefGoogle Scholar
  17. Joyce J (2005) How probabilities reflect evidence. Philos Perspect 19:153CrossRefGoogle Scholar
  18. Kadane JB (2006) Is “objective Bayesian analysis” objective, Bayesian, or wise? (comment on articles by Berger and by Goldstein). Bayesian Anal 1(3):433–436Google Scholar
  19. Kingman JFC (1982) The coalescent. Stochastic Process Appl 13(3):235–248CrossRefGoogle Scholar
  20. Kluge AG (2005) What is the rationale for ‘Ockham’s razor’ (a.k.a. parsimony) in phylogenetic inference? In: Albert VA (ed) Parsimony, phylogeny and genomics. Oxford University Press, Oxford, pp 15–42Google Scholar
  21. Larget B (2005) Introduction to Markov Chain Monte Carlo methods in molecular evolution. In: Nielson R (ed) Statistical methods in molecular evolution. Springer, New York, pp 44–61Google Scholar
  22. Larget B, Simon DL (1999) Markov chain Monte Carlo algorithms for the Bayesian analysis of phylogenetic trees. Mol Biol Evol 16(6):750–759Google Scholar
  23. Metzker ML, Mindell DP, Liu XM, Ptak RG, Gibbs RA, Hillis DM (2002) Molecular evidence of HIV-1 transmission in a criminal case. Proc Nat Acad Sci 99(22):14292–14297CrossRefGoogle Scholar
  24. Mooers AO, Heard SB (1997) Inferring evolutionary process from phylogenetic tree shape. Q Rev Biol 72(1):31–54CrossRefGoogle Scholar
  25. Pickett KM, Randle CP (2005) Strange Bayes indeed: uniform topological priors imply non-uniform clade priors. Mol Phylogenet Evol 34(1):203–211CrossRefGoogle Scholar
  26. Pitnick S, Jones KE, Wilkinson GS (2006) Mating system and brain size in bats. Proc R Soc Biol Sci B 273(1587):719–724CrossRefGoogle Scholar
  27. Poux C, Madsen O, Marquard E, Vieites DR, de Jong WW, Vences M (2005) Asynchronous colonization of Madagascar by the four endemic clades of primates, tenrecs, carnivores, and rodents as inferred from nuclear genes. Syst Biol 54(5):719–730CrossRefGoogle Scholar
  28. Randle CP, Mort ME, Crawford DJ (2005) Bayesian inference of phylogenetics revisited: developments and concerns. Taxon 54(1):9–15CrossRefGoogle Scholar
  29. Rannala B, Yang Z (1996) Probability distribution of molecular evolutionary trees: a new method of phylogenetic inference. J Mol Evol 43(3):304–311CrossRefGoogle Scholar
  30. Semple C, Steel M (2003). Phylogenetics. Oxford University Press, OxfordGoogle Scholar
  31. Siddall ME, Kluge AG (1997). Probabilism and phylogenetic inference. Cladistics 13(4):313–336CrossRefGoogle Scholar
  32. Sober E (1988). Reconstructing the past. Parsimony, evolution, and inference. MIT Press, CambridgeGoogle Scholar
  33. Steel M, McKenzie A (2001). Properties of phylogenetic trees generated by yule-type speciation models. Math Biosci 170(1):91–112CrossRefGoogle Scholar
  34. Thompson EA (1975) Human evolutionary trees. Cambridge University Press, CambridgeGoogle Scholar
  35. Velasco JD (2007) Why non-uniform priors on clades are both unavoidable and unobjectionable. Mol Phylogenet Evol 45:748–749CrossRefGoogle Scholar
  36. Yang Z (2006) Computational molecular evolution. Oxford University Press, OxfordGoogle Scholar
  37. Yang Z, Rannala B (1997). Bayesian phylogenetic inference using DNA sequences: a Markov Chain Monte Carlo method. Mol Biol Evol 14(7):717–724Google Scholar
  38. Yule GU (1925) A mathematical theory of evolution, based on the conclusions of Dr. JC Willis, FRS. Philos Trans R Soc Lond B 213:21–87CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of WisconsinMadisonUSA

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