What if I don't have a tree? Split decomposition and related models.

Abstract excerpt

A set of aligned character sequences or a matrix of evolutionary distances often contains a number of different and sometimes conflicting phylogenetic signals, and thus does not always support a unique tree. The method of split decomposition addresses this problem. For ideal data, this method gives rise to a phylogenetic tree, whereas less ideal data are represented by a tree-like network that may indicate...

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