Publications related to 'weakly compatible' : A split system is weakly compatible if does not induce all three possible splits on any subset of four taxa.

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Vincent Berry and
David Bryant. Faster reliable phylogenetic analysis. In RECOMB99, Pages 5968, 1999. Keywords: abstract network, from quartets, phylogenetic network, phylogeny, polynomial, Program SplitsTree, reconstruction, split network, weakly compatible. Note: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.95.9151.






HansJürgen Bandelt and
Andreas W. M. Dress. A relational approach to split decomposition. In
H.H. Bock,
W. Lenski and
M. M. Richter editors, Information Systems and Data Analysis, Proceedings of the 17th Annual Conference of the Gesellschaft Für Klassifikation (GFKL93), Vol. 42:123131 of Studies in Classification, Data Analysis, and Knowledge Organization, springer, 1994. Keywords: characterization, from quartets, phylogenetic network, weakly compatible.






HansJürgen Bandelt and
Andreas W. M. Dress. A canonical decomposition theory for metrics on a finite set. In Advances in Mathematics, Vol. 92(1):47105, 1992. Keywords: abstract network, circular split system, from distances, split, split decomposition, split network, weak hierarchy, weakly compatible.
Toggle abstract
"We consider specific additive decompositions d = d1 + ... + dn of metrics, defined on a finite set X (where a metric may give distance zero to pairs of distinct points). The simplest building stones are the slit metrics, associated to splits (i.e., bipartitions) of the given set X. While an additive decomposition of a Hamming metric into split metrics is in no way unique, we achieve uniqueness by restricting ourselves to coherent decompositions, that is, decompositions d = d1 + ... + dn such that for every map f:X → R with f(x) + f(y) ≥ d(x, y) for all x, y ε{lunate} X there exist maps f1, ..., fn: X → R with f = f1 + ... + fn and fi(x) + fi(y) ≥ di(x, y) for all i = 1,..., n and all x, y ε{lunate} X. These coherent decompositions are closely related to a geometric decomposition of the injective hull of the given metric. A metric with a coherent decomposition into a (weighted) sum of split metrics will be called totally splitdecomposable. Tree metrics (and more generally, the sum of two tree metrics) are particular instances of totally splitdecomposable metrics. Our main result confirms that every metric admits a coherent decomposition into a totally splitdecomposable metric and a splitprime residue, where all the split summands and hence the decomposition can be determined in polynomial time, and that a family of splits can occur this way if and only if it does not induce on any fourpoint subset all three splits with block size two. © 1992."



