Who is Who in Phylogenetic Networks

Publications of Year 1992

Article (Journal)

1 Hans-Jürgen Bandelt and Andreas W. M. Dress. A canonical decomposition theory for metrics on a finite set. In Advances in Mathematics, Vol. 92(1):47-105, 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 split-decomposable. Tree metrics (and more generally, the sum of two tree metrics) are particular instances of totally split-decomposable metrics. Our main result confirms that every metric admits a coherent decomposition into a totally split-decomposable metric and a split-prime 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 four-point subset all three splits with block size two. © 1992." 2 Lucinda A. McDade. Hybrids and phylogenetic systematics II. The impact of hybrids on cladistic analysis. In Evolution, Vol. 46(5):1329-1346, 1992. Keywords: explicit network, from rooted trees, from species tree, hybridization, parsimony, phylogeny. Note: http://www.jstor.org/stable/2409940.         3 Hans-Jürgen Bandelt and Andreas W. M. Dress. Split Decomposition: A new and useful approach to phylogenetic analysis of distance data. In MPE, Vol. 1(3):242-252, 1992. Keywords: abstract network, from distances, phylogenetic network, phylogeny, reconstruction, split, split decomposition, split network. Note: http://dx.doi.org/10.1016/1055-7903(92)90021-8.         Toggle abstract "In order to analyze the structure inherent to a matrix of dissimilarities (such as evolutionary distances) we propose to use a new technique called split decomposition. This method accurately dissects the given dissimilarity measure as a sum of elementary "split" metrics plus a (small) residue. The split summands identify related groups which are susceptible to further interpretation when casted against the available biological information. Reanalysis of previously published ribosomal RNA data sets using split decomposition illustrate the potential of this approach. © 1992."

Misc

4 Hans-Jürgen Bandelt. Four-point characterization of the dissimilarity functions obtained from indexed closed weak hierarchies. 1992. Keywords: characterization, clustering, from distances, pyramid, weak hierarchy. Note: Mathematisches Seminar, Universität Hamburg.