Abstract
Phylogenetic networks are rooted acyclic directed graphs in which the leaves are identified with members of a set X of species. The cluster of a vertex is the set of leaves that are descendants of the vertex. A network is “distinct-cluster” if distinct vertices have distinct clusters. This paper focuses on the set DC(X) of distinct-cluster networks whose leaves are identified with the members of X. For a fixed X, a metric on DC(X) is defined. There is a “cluster-preserving” simplification process by which vertices or certain arcs may be removed without changing the clusters of any remaining vertices. Many of the resulting networks may be uniquely determined without regard to the order of the simplifying operations.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Allen B., Steel M.: Subtree transfer operations and their induced metrics on evolutionary trees. Ann. Combin. 5(1), 1–15 (2001)
Baroni M., Semple C., Steel M.: A framework for representing reticulate evolution. Ann. Combin. 8(4), 391–408 (2004)
Boucher Y., Douady C.J., Papke R.T., Walsh D.A., Boudreau M.E.R., Nesbo C.L., Case R.J., Doolittle W.F.: Lateral gene transfer and the origins of prokaryotic groups. Ann. Rev. Genet. 37, 283–328 (2003)
Cardona G., Labrés M., Rossalló F., Valiente G.: A distance metric for a class of treesibling phylogenetic networks. Bioinform. 24(13), 1481–1488 (2008)
Cardona G., Labrés M., Rossalló F., Valiente G.: On Nakhleh’s metric for reduced phylogenetic networks. IEEE/ACM Trans. Comput. Biol. Bioinform. 6(4), 629–638 (2009)
Cardona G., Labrés M., Rossalló F., Valiente G.: Metrics for phylogenetic networks I: generalizations of the Robinson-Foulds metric. IEEE/ACM Trans. Comput. Biol. Bioinform. 6(1), 46–61 (2009)
Cardona G., Rossalló F., Valiente G.: Comparison of tree-child phylogenetic networks. IEEE/ACM Trans. Comput. Biol. Bioinform. 6(4), 552–569 (2009)
Critchlow D., Pearl D., Qian C.: The triples distance for rooted bifurcating phylogenetic trees. Syst. Biol. 45(3), 323–334 (1996)
Doolittle W.F., Bapteste E.: Pattern pluralism and the tree of life hypothesis. Proc. Natl. Acad. Sci. USA 104(7), 2043–2049 (2007)
Gusfield D., Eddhu S., Langley C.: The fine structure of galls in phylogenetic networks. INFORMS J. Comput. 16(4), 459–469 (2004)
Harary, F.: Graph Theory. Addison-Wesley, Reading, Mass. (1969)
Huson D., Rupp R., Scornavacca C.: Phylogenetic Networks: Concepts, Algorithms and Applications. Cambridge University Press, Cambridge (2010)
Lin Y., Rajan V., Moret B.: A metric for phylogenetic trees based on matching. IEEE/ACM Trans. Comput. Biol. Bioinform. 9(4), 1014–1022 (2012)
Mindell D.: The tree of life: metaphor, model, and heuristic Device. Syst. Biol. 62(3), 479–489 (2013)
Moret B., Nakhleh L., Warnow T., Linder C.R., Tholse A., Padolina A., Sun J., Timme R.: Phylogenetic networks: modeling, reconstructibility, and accuracy. IEEE Trans. Comput. Biol. Bioinform. 1(1), 13–23 (2004)
Morrison, D.: Introduction to Phylogenetic Networks. RJR Productions, Uppsala, Sweden (2011) http://www.rjr-productions.org/
Nakhleh L., Warnow T., Linder C.R., John K.: Reconstructing reticulate evolution in species — theory and practice. J. Comput. Biol. 12(5), 796–811 (2005)
Rhymer J., Symberloff D.: Extinction by hybridization and introgression. Ann. Rev. Ecol. Syst. 27, 83–109 (1996)
Robinson D.F.: Comparison of labeled trees with valency three. J. Combin. Theory Ser. B 11(2), 105–119 (1971)
Robinson D., Foulds I.: Comparison of phylogenetic trees. Math. Biosci. 53(1-2), 131–147 (1981)
Semple C., Steel M.: Phylogenetics. Oxford University Press, Oxford (2003)
van Iersel L., Keijsper J., Kelk S., Stouigie L., Hagen F., Boekhout T.: Constructing level-2 phylogenetic networks from triplets. IEEE/ACM Trans. Comput. Biol. Bioinform. 6(4), 667–681 (2009)
Waterman M., Smith T.: On the similarity of dendrograms. J. Theoret. Biol. 73(4), 789–800 (1978)
Willson S.: Properties of normal phylogenetic networks. Bull. Math. Biol. 72(2), 340–358 (2010)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Willson, S.J. Comparing and Simplifying Distinct-Cluster Phylogenetic Networks. Ann. Comb. 20, 917–938 (2016). https://doi.org/10.1007/s00026-016-0324-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00026-016-0324-y