Abstract
In this chapter, we develop a Bayesian approach to supertree construction. Bayesian inference requires that prior knowledge be specified in terms of a probability distribution and incorporates this evidence in new analyses. This provides a natural framework for the accumulation of phylogenetic evidence, but it requires that phylogenetic results be expressed as probability distributions on trees. Because there are so many possible trees, it is usually not feasible to estimate the probability of each individual tree. Therefore, Bayesians summarize the distribution typically in terms of taxon-bipartition frequencies instead. However, bipartition frequencies are related only indirectly to tree probabilities. We discuss two ways in which taxon-bipartition frequencies can be translated into sets of multiplicative factors that function as keys to the probability distribution on trees. The Weighted Independent Binary (WIB) method associates factors to the presence or absence of taxon bipartitions, whereas the Weighted Additive Binary (WAB) method has factors with graded responses dependent on the degree of conflict between the tree and the partition. Although the methods are similar, we found that WAB is superior to WIB. We discuss several ways of estimating WAB factors from partition frequencies or directly from the data. One of these methods suggests a similarity between WAB factors and the decay index; indeed, the WAB factors represent a more natural measure of clade support than the bipartition frequencies themselves or the decay index and its probabilistic analog. WAB factors provide an efficient and convenient way of retrieving prior tree probabilities and WAB supermatrices accurately describe fully statistically specified supertree spaces that can be sampled using MCMC algorithms with the computational efficiency of parsimony. This should allow construction of Bayesian supertrees with thousands of taxa.
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References
Baum, B. R. 1992. Combining trees as a way of combining data sets for phylogenetic inference, and the desirability of combining gene trees. Taxon 41:1–10.
Baum, B. R. and Ragan, M. A. 2004. The MRP method. In O. R. P. Bininda-Emonds (ed). Phylogenetic Supertrees: Combining Information to Reveal the Tree of Life, pp. 17–34. Kluwer Academic, Dordrecht, the Netherlands.
Bininda-Emonds, O. R. P. and Bryant, H. N. 1998. Properties of matrix representation with parsimony analyses. Systematic Biology 47:497–508.
Bininda-Emonds, O. R. P. and Sanderson, M. J. 2001. Assessment of the accuracy of matrix representation with parsimony analysis supertree construction. Systematic Biology 50:565–579.
Brooks, D. R. 1981. Hennig ’s parasitological method: a proposed solution. Systematic Zoology 30:229–249.
Farris, J. S., Kluge, A. G., and Eckhardt, M. J. 1970. A numerical approach to phylogenetic systematics. Systematic Zoology 19:172–191.
Felsenstein, J. 1978. The number of evolutionary trees. Systematic Zoology 27:27–33.
Gamerman, D. 1997. Markov Chain Monte Carlo. Chapman and Hall, Boca Raton, Florida.
Gatesy, J. and Springer, M. S. 2004. A critique of matrix representation with parsimony supertrees. In O. R. P. Bininda-Emonds (ed.), Phylogenetic Supertrees: Combining Information to Reveal the Tree of Life, pp. 369–388. Kluwer Academic, Dordrecht, the Netherlands.
Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. 1995. Bayesian Data Analysis. Chapman and Hall, Boca Raton, Florida.
Goloboff, P. A. 1996. Methods for faster parsimony analysis. Cladistics 12:199–220.
Huelsenbeck, J. P., Ronquist, F., Nielsen, R., and Bollback, J. P. 2001. Bayesian inference of phylogeny and its impact on evolutionary biology. Science 294:2310–2314.
Huelsenbeck, J. P., Larget, B., Miller, R. E., and Ronquist, F. 2002. Potential applications and pitfalls of Bayesian inference of phylogeny. Systematic Biology 51:673–688.
Lewis, P. O. 2000. Phylogenetic systematics turns over a new leaf. Trends in Ecology and Evolution 16:30–37.
Newton, M. A., Raftery, A. E., Davison, A. C., Bacha, M., Celeux, G., Carlin, B. P., Clifford, P., Lu, C., Sherman, M., Tanner, M. A., Gelfand, A. E., Mallick, B. K., Gelman, A., Grieve, A. P., Kunsch, H. R., Leonard, T., Hsu, J. S. J., Liu, J. S., Rubin, D. B.Lo, A. Y., Louis, T. A., Neal, R. M., Owen, A. B., Tu, D. S., Gilks, W. R., Roberts, G., Sweeting, T., Bates, D., Ritter, G., Worton, B. J., Barnard, G. A., Gibbens, R., and Silverman, B. 1994. Approximate Bayesian inference by the weighted bootstrap (with discussion). Journal of the Royal Statistical Society, Series B 56:3–48.
Page, R. D. M. 2002. Modified mincut supertrees. In R. Guigó and D. Gusfield (eds), Algorithms in Bioinformatics, Second International Workshop, Wabi 2002, Rome, Italy, September 17–21, 2002, Proceedings, pp. 537–552. Springer, Berlin.
Page, R. D. M. 2004. Taxonomy, supertrees, and the Tree of Life. In O. R. P. Bininda-Emonds (ed). Phylogenetic Supertrees: Combining Information to Reveal the Tree of Life, pp. 247–265. Kluwer Academic, Dordrecht, the Netherlands.
Purvis, A. 1995. A modification to Baum and Ragan ’s method for combining phylogenetic trees. Systematic Biology 44:251–255.
Ragan, M. A. 1992. Phylogenetic inference based on matrix representation of trees. Molecular Phylogenetics and Evolution1:53–58.
Robinson, D. F. and Foulds, L. R. 1981. Comparison of phylogenetic trees. Mathematical Biosciences 53:131–148.
Ronquist, F. 1996. Matrix representation of trees, redundancy, and weighting. Systematic Biology 45:247–253.
Ronquist, F. 1998. Fast Fitch-parsimony algorithms for large data sets. Cladistics 14:387–400.
Ronquist, F. and Huelsenbeck, J. P. 2003. MrBayes 3: Bayesian phylogenetic inference under mixed models. Bioinformatics 19:1572–1574.
Russo, C. A. M., Takezaki, N., and Nei, M. 1995. Molecular phylogeny and divergence times of drosophilid species. Molecular Biology and Evolution 12:391–404.
Sanderson, M. J., Purvis, A., and Henze, C. 1998. Phylogenetic supertrees: assembling the trees of life. Trends in Ecology and Evolution 13:105–109.
Semple, C. and Steel, M. 2000. A supertree method for rooted trees. Discrete Applied Mathematics 105:147–158
Steel, M., Dress, A., and Böcker, S. 2000. Simple but fundamental limitations on supertree and consensus tree methods. Systematic Biology 49:363–368.
Swofford, D. L. 2002. Paup*. Phylogenetic Analysis Using Parsimony (* and Other Methods). Version 4. Sinauer, Sunderland, Massachusetts.
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Ronquist, F., Huelsenbeck, J.P., Britton, T. (2004). Bayesian Supertrees. In: Bininda-Emonds, O.R.P. (eds) Phylogenetic Supertrees. Computational Biology, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-2330-9_10
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DOI: https://doi.org/10.1007/978-1-4020-2330-9_10
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