Journal of Molecular Evolution

, Volume 37, Issue 1, pp 77–85 | Cite as

Network models for sequence evolution

  • Arndt von Haeseler
  • Gary A. Churchill


We introduce a general class of models for sequence evolution that includes network phylogenies. Networks, a generalization of strictly tree-like phylogenies, are proposed to model situations where multiple lineages contribute to the observed sequences. An algorithm to compute the probability distribution of binary character-state configurations is presented and statistical inference for this model is developed in a likelihood framework. A stepwise procedure based on likelihood ratios is used to explore the space of models. Starting with a star phylogeny, new splits (nontrivial bipartitions of the sequence set) are successively added to the model until no significant change in the likelihood is observed. A novel feature of our approach is that the new splits are not necessarily constrained to be consistent with a treelike mode of evolution. The fraction of invariable sites is estimated by maximum likelihood simultaneously with other model parameters and is essential to obtain a good fit to the data. The effect of finite sequence length on the inference methods is discussed. Finally, we provide an illustrative example using aligned VPl genes from the foot and mouth disease viruses (FMDV). The different serotypes of the FMDV exhibit a range of treelike and network evolutionary relationships.

Key words

Convergent evolution Gene conversion Maximum likelihood Phylogeny Quasi-species Recombination Substitution rate Virus evolution 


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  1. Bandelt HJ, Dress AWM (1990) A canonical decomposition theory for metrics on a finite set. Preprint 90-032, SFB 343, Universität BielefeldGoogle Scholar
  2. Barry D, Hartigan JA (1987) Statistical analysis of hominoid molecular evolution. Stat Sci 2:191–210Google Scholar
  3. Beck E, Strohmaier K (1987) Subtyping of european FMDV outbreak strains by nucleotide sequence determination. J Virol 61:1621–1629Google Scholar
  4. Brown WM, Prager EM, Wang A, Wilson AC (1982) Mitochondrial DNA sequences of primates: tempo and mode of evolution. J Mol Evol 18:225–239Google Scholar
  5. Buneman P (1971) The recovery of trees from measures of dissimilarity. In: Hodson FR, Kendall DG, Tantu P (eds) Mathematics in the archaeological and historical science. Proc of the Anglo-Romanian-Conference 1970, University Press Edinburgh, pp 387–395Google Scholar
  6. Cavender J (1978) Taxonomy with confidence. Math Biosc 40: 271–280Google Scholar
  7. Churchill GA, von Haeseler A, Navidi WC (1992) Sample size for a phylogenetic inference. Mol Biol Evol 9:753–769Google Scholar
  8. Dopazo J, Dress A, von Haeseler A (1990) Split decomposition: a new technique to analyze viral evolution. Preprint 90-037, Sonderforschungsbereich 343 Diskrete Strukturen in der Mathematik. Universität BielefeldGoogle Scholar
  9. Domingo E, Holland JJ (1988) High error rates, population equilibrium and evolution of RNA replication systems. In: Domingo E, Holland JJ, Ahlquist P (eds) RNA genetics, vol III. CRC Press, Boca Raton, FL, pp 3–36Google Scholar
  10. Draper NR, Smith H (1981) Applied regression analysis, 2nd ed. John Wiley, New YorkGoogle Scholar
  11. Felsenstein J (1981) Evolutionary trees from DNA sequences: a maximum likelihood approach. J Mol Evol 17:368–376PubMedGoogle Scholar
  12. Felsenstein J (1988) Phylogenies from molecular sequences: Inference and reliability. Annu Rev Genet 22:521–565Google Scholar
  13. Felsenstein J (1989) Phylip manual, version 3.2, University Herbarium of the University of California at BerkeleyGoogle Scholar
  14. Fitch WM (1986a) The estimate of total nucleotide substitutions from pairwise difference is biased. Philos Trans R Soc Lond [B] 312:317–324Google Scholar
  15. Fitch WM (1986b) An estimation of the number of invariable sites is necessary for the accurate estimation of nucleotide substitutions since a common ancestor. In: Gershowitz H (ed) Evolutionary perspectives and the new genetics. Alan R Liss, New York, pp 149–159Google Scholar
  16. Fitch WM, Margoliash E (1967) A method for estimating the number of invariant amino acid coding positions in a gene using cytochrome c as a model case. Biochem Genet 1:65–71Google Scholar
  17. Hasegawa M, Kishino H (1989) Confidence limits on the maximum likelihood estimate of the hominoid tree from mitochondrial DNA sequences. Evolution 43:672–677Google Scholar
  18. Hasegawa M, Kishino H, Yano K (1985) Dating of the human-ape splitting by a molecular clock of mitochondrial DNA. J Mol Evol 22:160–174PubMedGoogle Scholar
  19. Hendy MD (1989) The relationship between simple evolutionary tree models and observable sequence data. Syst Zool 38:310–321Google Scholar
  20. Hendy MD, Penny D (1991) Spectral analysis of phylogenetic data. (preprint)Google Scholar
  21. Hendy MD, Penny D (1989) A framework for the quantitative study of evolutionary trees. Syst Zool 38:297–309Google Scholar
  22. Navidi WC, Churchill GA, von Haeseler A (1991) Methods for inferring phylogenies from nucleic acid sequence data by using maximum likelihood and linear invariants. Mol Biol Evol 8:128–143Google Scholar
  23. Piccone ME, Kaplan G, Giavedoni L, Domingo E, Palma EL (1988) VP1 of serotype C foot-and-mouth disease virus: long-term conservation of sequences. J Virol 62:1469–1473Google Scholar
  24. Saitou N (1988) Property and efficiency of the maximum likelihood method for molecular phylogeny. J Mol Evol 27:261–273Google Scholar
  25. Sawyer S (1989) Statistical test for detecting gene conversion. Mol Biol Evol 6:526–538Google Scholar
  26. Shoemaker JS, Fitch WM (1989) Evidence from nuclear sequences that invariable sites should be considered when sequence divergence is calculated. Mol Biol Evol 6:270–289Google Scholar
  27. Sobrino F, Palma EL, Beck E, Davila M, de la Torre JC, Negro P, Villaneuva N, Ortin J, Domingo E (1986) Fixation of mutations in the viral genome during an outbreak of foot-and-mouth disease: heterogeneity and rate variations. Gene 50: 149–159Google Scholar
  28. Steinhauer DA, Holland JJ (1987) Rapid evolution of RNA viruses. Ann Rev Microbiol 41:409–433Google Scholar
  29. Swofford DL, Olsen GJ (1990) Phylogeny reconstruction. In: Hillis DM and Moritz C (eds) Molecular systematics. Sinauer Associates, Sunderland MA, pp 411–501Google Scholar
  30. Swofford DL (1991) PAUP 3.0 user's manual (Draft 2.9.91). Illinois Natural History Survey, Champaign, 1991Google Scholar
  31. Ward RH, Frazer BS, Dew K, Pääbo S (1991) A single north-american tribal group contains extensive mitochondrial diversity. Proc Natl Acad Sci USA 88:8720–8724Google Scholar

Copyright information

© Springer-Verlag New York Inc 1993

Authors and Affiliations

  • Arndt von Haeseler
    • 1
  • Gary A. Churchill
    • 2
  1. 1.Department of ZoologyUniversity of MunichMunich 2Federal Republic of Germany
  2. 2.Biometrics UnitCornell UniversityIthacaUSA

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