Abstract
Metrics on rooted phylogenetic trees are integral to a number of areas of phylogenetic analysis. Cluster-similarity metrics have recently been introduced in order to limit skew in the distribution of distances, and to ensure that trees in the neighbourhood of each other have similar hierarchies. In the present paper we introduce a new cluster-similarity metric on rooted phylogenetic tree space that has an associated local operation, allowing for easy calculation of neighbourhoods, a trait that is desirable for MCMC calculations. The metric is defined by the distance on the Hasse diagram induced by a partial order on the set of rooted phylogenetic trees, itself based on the notion of a hierarchy-preserving map between trees. The partial order we introduce is a refinement of the well-known refinement order on hierarchies. Both the partial order and the hierarchy-preserving maps may also be of independent interest.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alberich R, Cardona G, Rosselló F, Valiente G (2009) An algebraic metric for phylogenetic trees. Appl Math Lett 22(9):1320–1324. https://doi.org/10.1016/j.aml.2009.03.003
Bogdanowicz D, Giaro K (2013) On a matching distance between rooted phylogenetic trees. Int J Appl Math Comput Sci 23(3):669–684. https://doi.org/10.2478/amcs-2013-0050
Cardona G, Llabrés M, Rosselló F, Valiente G (2009) Nodal distances for rooted phylogenetic trees. J Math Biol 61(2):253–276. https://doi.org/10.1007/s00285-009-0295-2
Cole SR, Wright DF, Ausich WI (2019) Phylogenetic community paleoecology of one of the earliest complex crinoid faunas (Brechin Lagerstätte, Ordovician). Palaeogeogr Palaeoclimatol Palaeoecol 521:82–98. https://doi.org/10.1016/j.palaeo.2019.02.006
Guo M-Z, Li J-F, Liu Y (2008) A topological transformation in evolutionary tree search methods based on maximum likelihood combining p-ECR and neighbor joining. BMC Bioinform 9(Suppl 6):S4. https://doi.org/10.1186/1471-2105-9-s6-s4
Hein J (1990) Reconstructing evolution of sequences subject to recombination using parsimony. Math Biosci 98(2):185–200. https://doi.org/10.1016/0025-5564(90)90123-g
Hendriksen M (2019) Clustermetric. https://github.com/mahendriksen/ClusterMetric. GitHub repository
Kuhner MK, Yamato J (2014) Practical performance of tree comparison metrics. Syst Biol 64(2):205–214. https://doi.org/10.1093/sysbio/syu085
Moore GW, Goodman M, Barnabas J (1973) An iterative approach from the standpoint of the additive hypothesis to the dendrogram problem posed by molecular data sets. J Theor Biol 38(3):423–457. https://doi.org/10.1016/0022-5193(73)90251-8
Moulton V, Taoyang W (2015) A parsimony-based metric for phylogenetic trees. Adv Appl Math 66:22–45. https://doi.org/10.1016/j.aam.2015.02.002
Okumura K, Shimomura Y, Murayama S, Yagi J, Ubukata K, Kirikae T, Miyoshi-Akiyama T (2012) Evolutionary paths of streptococcal and staphylococcal superantigens. BMC Genom 13(1):404. https://doi.org/10.1186/1471-2164-13-404
Robinson DF, Foulds LR (1981) Comparison of phylogenetic trees. Math Biosci 53(1–2):131–147. https://doi.org/10.1016/0025-5564(81)90043-2
Sevillya G, Snir S (2019) Synteny footprints provide clearer phylogenetic signal than sequence data for prokaryotic classification. Mol Phylogenet Evol 136:128–137. https://doi.org/10.1016/j.ympev.2019.03.010
Shuguang L, Zhihui L (2015) Algorithms for computing cluster dissimilarity between rooted phylogenetic trees. Open Cybern Syst J 9(1):2218–2223. https://doi.org/10.2174/1874110x01509012218
Steel MA (1988) Distribution of the symmetric difference metric on phylogenetic trees. SIAM J Discrete Math 1(4):541–551. https://doi.org/10.1137/0401050
Steel M (2016) Phylogeny: discrete and random processes in evolution. Society for Industrial and Applied Mathematics, Philadelphia
Zhang L-N, Ma P-F, Zhang Y-X, Zeng C-X, Zhao L, Li D-Z (2019) Using nuclear loci and allelic variation to disentangle the phylogeny of Phyllostachys (Poaceae, Bambusoideae). Mol Phylogenet Evol 137:222–235. https://doi.org/10.1016/j.ympev.2019.05.011
Acknowledgements
The authors thank the reviewers of the manuscript for many valuable suggestions, and Alexei Drummond and Bill Martin for helpful discussions while this manuscript was in preparation, at the New Zealand Phylogenetics meeting in February 2019. The first author thanks Western Sydney University for its support in the form of an Australian Postgraduate Award during this research.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Hendriksen, M., Francis, A. A partial order and cluster-similarity metric on rooted phylogenetic trees. J. Math. Biol. 80, 1265–1290 (2020). https://doi.org/10.1007/s00285-019-01461-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00285-019-01461-1