Abstract
Phylogenetic trees are fundamental to biology and are benefitting several other research areas. Various methods have been developed for inferring such trees, and comparing them is an important problem in computational phylogenetics. Addressing this problem requires tree measures, but all of them suffer from problems that can severely limit their applicability in practice. This also holds true for one of the oldest and most widely used tree measures, the Robinson-Foulds distance. While this measure is satisfying the properties of a metric and is efficiently computable, it has a negatively skewed distribution, a poor range of discrimination and diameter, and may not be robust when comparing erroneous trees. The cluster distance is a measure for comparing rooted trees that can be interpreted as a weighted version of the Robinson-Foulds distance. We show that when compared with the Robinson-Foulds distance, the cluster distance is much more robust towards small errors in the compared trees, and has a significantly improved distribution and range.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Allen, B.L., Steel, M.: Subtree transfer operations and their induced metrics on evolutionary trees. Ann. Comb. 5(1), 1–15 (2001)
Arvestad, L., et al.: Gene tree reconstruction and orthology analysis based on an integrated model for duplications and sequence evolution. In: RECOMB, pp. 326–335. ACM (2004)
Betkier, A., Szczęsny, P., Górecki, P.: Fast algorithms for inferring gene-species associations. In: Harrison, R., Li, Y., Măndoiu, I. (eds.) ISBRA 2015. LNCS, vol. 9096, pp. 36–47. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-19048-8_4
Bogdanowicz, D., Giaro, K.: On a matching distance between rooted phylogenetic trees. Int. J. Appl. Math. Comput. Sci. 23(3), 669–684 (2013)
Bordewich, M., Semple, C.: On the computational complexity of the rooted subtree prune and regraft distance. Ann. Comb. 8(4), 409–423 (2005)
Bourque, M.: Arbres de Steiner et réseaux dont varie l’emplagement de certains sommets. Ph.D. thesis, University of Montréal Montréal, Canada (1978)
Bryant, D.: Hunting for trees, building trees and comparing trees: theory and method in phylogenetic analysis. Ph.D. thesis, University of Canterbury, New Zealand (1997)
Bryant, D., Steel, M.: Computing the distribution of a tree metric. IEEE/ACM Trans. Comput. Biol. Bioinf. 6(3), 420–426 (2009)
Das Gupta, B., et al.: On distances between phylogenetic trees. In: SODA 1997, pp. 427–436 (1997)
Day, W.H.E.: Optimal algorithms for comparing trees with labeled leaves. J. Classif. 2(1), 7–28 (1985)
Felenstein, J.: Inferring Phylogenies. Sinauer, Sunderland (2003)
Forster, P., Renfrew, C.: Phylogenetic Methods and the Prehistory of Languages. McDonald Institute of Archeological, Cambridge (2006)
Harding, E.F.: The probabilities of rooted tree-shapes generated by random bifurcation. Adv. Appl. Probab. 3(1), 44–77 (1971)
Harris, S.R., et al.: Whole-genome sequencing for analysis of an outbreak of meticillin-resistant staphylococcus aureus: a descriptive study. Lancet. Infect. Dis. 13(2), 130–136 (2013)
Hein, J., et al.: On the complexity of comparing evolutionary trees. Discret. Appl. Math. 71(1–3), 153–169 (1996)
Hickey, G., et al.: SPR distance computation for unrooted trees. Evol. Bioinform. Online 4, 17–27 (2008)
Huber, K.T., Spillner, A., Suchecki, R., Moulton, V.: Metrics on multilabeled trees: interrelationships and diameter bounds. IEEE/ACM Trans. Comput. Biol. Bioinf. 8(4), 1029–1040 (2011)
Hufbauer, R.A., et al.: Population structure, ploidy levels and allelopathy of Centaurea maculosa (spotted knapweed) and C. diffusa (diffuse knapweed) in North America and Eurasia. In: ISBCW, pp. 121–126. USDA Forest Service (2003)
Katherine, S.J.: Review paper: the shape of phylogenetic treespace. Syst. Biol. 66(1), e83–e94 (2017)
Kuhner, M.K., Yamato, J.: Practical performance of tree comparison metrics. Syst. Biol. 64(2), 205–214 (2015)
Li, M., Tromp, J., Zhang, L.: On the nearest neighbour interchange distance between evolutionary trees. J. Theor. Biol. 182(4), 463–467 (1996)
Li, M., Zhang, L.: Twist-rotation transformations of binary trees and arithmetic expressions. J. Algorithms 32(2), 155–166 (1999)
Lin, Y., Rajan, V., Moret, B.M.E.: A metric for phylogenetic trees based on matching. IEEE/ACM Trans. Comput. Biol. Bioinf. 9(4), 1014–1022 (2012)
Ma, B., Li, M., Zhang, L.: From gene trees to species trees. SIAM J. Comput. 30(3), 729–752 (2000)
Makarenkov, V., Leclerc, B.: Comparison of additive trees using circular orders. J. Comput. Biol. 7(5), 731–744 (2000)
Nik-Zainal, S., et al.: The life history of 21 breast cancers. Cell 149(5), 994–1007 (2012)
Robinson, D.F., Foulds, L.R.: Comparison of weighted labelled trees. In: Horadam, A.F., Wallis, W.D. (eds.) Combinatorial Mathematics VI. LNM, vol. 748, pp. 119–126. Springer, Heidelberg (1979). https://doi.org/10.1007/BFb0102690
Robinson, D.F.: Comparison of labeled trees with valency three. J. Comb. Theory Ser. B 11(2), 105–119 (1971)
Robinson, D.F., Foulds, L.R.: Comparison of phylogenetic trees. Math. Biosci. 53(1–2), 131–147 (1981)
Semple, C., Steel, M.A.: Phylogenetics. Oxford (2003)
Steel, M.A., Penny, D.: Distributions of tree comparison metrics. Syst. Biol. 42(2), 126–141 (1993)
Sukumaran, J., Holder, M.T.: DendroPy: a python library for phylogenetic computing. Bioinformatics 26(12), 1569–1571 (2010)
Than, C.V., Rosenberg, N.A.: Mathematical properties of the deep coalescence cost. IEEE/ACM Trans. Comput. Biol. Bioinf. 10(1), 61–72 (2013)
Wilkinson, M., et al.: The shape of supertrees to come: tree shape related properties of fourteen supertree methods. Syst. Biol. 54(3), 419–431 (2005)
Wu, Y.-C., et al.: TreeFix: statistically informed gene tree error correction using species trees. Syst. Biol. 62(1), 110–120 (2013)
Acknowledgments
This material is based upon work supported by the National Science Foundation under Grant No. 1617626.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Moon, J., Eulenstein, O. (2018). Cluster Matching Distance for Rooted Phylogenetic Trees. In: Zhang, F., Cai, Z., Skums, P., Zhang, S. (eds) Bioinformatics Research and Applications. ISBRA 2018. Lecture Notes in Computer Science(), vol 10847. Springer, Cham. https://doi.org/10.1007/978-3-319-94968-0_31
Download citation
DOI: https://doi.org/10.1007/978-3-319-94968-0_31
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-94967-3
Online ISBN: 978-3-319-94968-0
eBook Packages: Computer ScienceComputer Science (R0)