Circular Networks from Distorted Metrics
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Trees have long been used as a graphical representation of species relationships. However complex evolutionary events, such as genetic reassortments or hybrid speciations which occur commonly in viruses, bacteria and plants, do not fit into this elementary framework. Alternatively, various network representations have been developed. Circular networks are a natural generalization of leaf-labeled trees interpreted as split systems, that is, collections of bipartitions over leaf labels corresponding to current species. Although such networks do not explicitly model specific evolutionary events of interest, their straightforward visualization and fast reconstruction have made them a popular exploratory tool to detect network-like evolution in genetic datasets. Standard reconstruction methods for circular networks, such as Neighbor-Net, rely on an associated metric on the species set. Such a metric is first estimated from DNA sequences, which leads to a key difficulty: distantly related sequences produce statistically unreliable estimates. This is problematic for Neighbor-Net as it is based on the popular tree reconstruction method Neighbor-Joining, whose sensitivity to distance estimation errors is well established theoretically. In the tree case, more robust reconstruction methods have been developed using the notion of a distorted metric, which captures the dependence of the error in the distance through a radius of accuracy. Here we design the first circular network reconstruction method based on distorted metrics. Our method is computationally efficient. Moreover, the analysis of its radius of accuracy highlights the important role played by the maximum incompatibility, a measure of the extent to which the network differs from a tree.
KeywordsPhylogenetic networks Circular networks Finite metrics Split decomposition Distance-based reconstruction Distorted metrics
Work supported by NSF grants DMS-1007144, DMS-1149312 (CAREER), DMS-1614242 and CCF-1740707 (TRIPODS).
- 1.Felsenstein, J.: Inferring Phylogenies. Sinauer, Sunderland (2004)Google Scholar
- 13.King, V., Zhang, L., Zhou, Y.: On the complexity of distance-based evolutionary tree reconstruction. In: 2003 Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 444–453. SIAM, Philadelphia (2003)Google Scholar
- 20.Roshan, U.W., Moret, B.M.E., Warnow, T., Williams, T.L.: Rec-I-DCM3: a fast algorithmic technique for reconstructing large phylogenetic trees. In: International Computational Systems Bioinformatics Conference, pp. 98–109. IEEE Computer Society (2004)Google Scholar
- 21.Buneman, P.: The recovery of trees from measures of dissimilarity. In: Kendall, D.G., Tautu, P. (eds.) Mathematics in the Archaeological and Historical Sciences, pp. 387–395 (1971)Google Scholar
- 22.Jukes, T.H., Cantor, C.R.: Evolution of protein molecules. In: Mammalian Protein Metabolism, pp. 21–132. Academic Press, New York (1969)Google Scholar
- 24.Bryant, D.: Extending tree models to split networks. In: Pachter, L., Sturmfels, B. (eds.) Algebraic Statistics for Computational Biology, pp. 297–310. Cambridge University Press, Cambridge (2005)Google Scholar
- 25.Roch, S., Wang, K.C.: Circular networks from distorted metrics. Preprint (2017). arXiv:1707.05722