Abstract
This paper presents a review of mathematical techniques capable of representing reticulate events in phylogenetics. Two families of methods are identified; they relax either the ultrametric inequality defining dendrograms or the four-point condition defining additive trees. Pyramids and weak hierarchies are techniques developed to fit dendrograms with overlapping clusters. Splitsgraphs and reticulograms are extensions of the additive tree model; they allow one to fit a dissimilarity matrix using a graph containing reticulations. The four methods are applied to a data set; the results are compared and discussed in a phylogenetic setting.
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