Abstract
AbstractWe consider the problem of the minimum number of phylogenetic trees it would take to display all splits in a given set, a problem related to k-compatibility. A set of trees that displays every single possible split is termed a universal tree set. In this note, we find the universal incompatibility U(n), the minimal size of a universal tree set for n taxa. By normalising incompatibility using U(n), one can then compare incompatibility of split systems across different numbers of taxa. We demonstrate this application by comparing two SplitsTree networks derived from archaeal genomes, with different numbers of taxa.
Funder
Volkswagen Foundation
European Research Council
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,General Agricultural and Biological Sciences,Pharmacology,General Environmental Science,General Biochemistry, Genetics and Molecular Biology,General Mathematics,Immunology,General Neuroscience
Reference19 articles.
1. Ban N, Beckmann R, Cate JHD, Dinman JD, Dragon F, Ellis SR, Lafontaine DLJ, Lindahl L, Liljas A, Lipton JM et al (2014) A new system for naming ribosomal proteins. Curr Opin Struct Biol 24:165–169
2. Bandelt H, Forster P, Röhl A (1999) Median-joining networks for inferring intraspecific phylogenies. Mol Biol Evolut 16(1):37–48
3. Buneman P (1971) The recovery of trees from measures of dissimilarity. Mathematics in the Archaeological and Historical Sciences
4. Dilworth RP (1950) A decomposition theorem for partially ordered sets. Math 50:161–166
5. Dress A, Klucznik M, Koolen J, and Moulton V (2001) $$2kn - {2k+1 \atopwithdelims ()2}$$: a note on extremal combinatorics of cyclic split systems. Séminaire Lotharingien de Combinatoire, 47: 17