Abstract
We establish a limit formula for the median of the distance between two leaves in a fully resolved unrooted phylogenetic tree with n leaves. More precisely, we prove that this median is equal, in the limit, to \(\sqrt{4{\rm ln}(2)n}\).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bluis, J., Shin, D.G.: Nodal distance algorithm: Calculating a phylogenetic tree comparison metric. In: Proc. 3rd IEEE Symp. BioInformatics and BioEngineering, p. 87 (2003)
Chang, H., Fuchs, M.: Limit theorems for patterns in phylogenetic trees. Journal of Mathematical Biology 60, 481–512 (2010)
Farris, J.: A successive approximations approach to character weighting. Syst. Zool. 18, 374–385 (1969)
Farris, J.: On comparing the shapes of taxonomic trees. Syst. Zool. 22, 50–54 (1973)
Felsenstein, J.: Inferring Phylogenies. Sinauer Associates Inc., (2004)
Mir, A., Rosselló, F.: The mean value of the squared path-difference distance for rooted phylogenetic trees. Submitted to J. Math. Biol (2009), http://es.arxiv.org/abs/0906.2470
Penny, D., Hendy, M.D.: The use of tree comparison metrics. Syst. Zool. 34(1), 75–82 (1985)
Petkovsek, M., Wilf, H., Zeilberger, D.: A = B. AK Peters Ltd., Wellesley (1996), http://www.math.upenn.edu/~wilf/AeqB.html
Phipps, J.B.: Dendrogram topology. Syst. Zool. 20, 306–308 (1971)
Steel, M.A., Penny, D.: Distributions of tree comparison metrics—some new results. Syst. Biol. 41, 126–141 (1993)
Williams, W.T., Clifford, H.T.: On the comparison of two classifications of the same set of elements. Taxon 20(4), 519–522 (1971)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mir, A., Rosselló, F. (2010). The Median of the Distance between Two Leaves in a Phylogenetic Tree. In: Rocha, M.P., Riverola, F.F., Shatkay, H., Corchado, J.M. (eds) Advances in Bioinformatics. Advances in Intelligent and Soft Computing, vol 74. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13214-8_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-13214-8_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13213-1
Online ISBN: 978-3-642-13214-8
eBook Packages: EngineeringEngineering (R0)