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One of my favorite ideas in phylogenetics is that of a phylogenetic orange. The idea and the terminology come from a classic paper by  Junhyong KimSlicing hyperdimensional oranges: the geometry of phylogenetic estimation, Molecular Phylogenetics and Evolution, 17 (2000), p 58–75  (pdf available here). In the words of the author (from the abstract):

A new view of phylogenetic estimation is presented where data sets, tree evolution models, and estimation methods are placed in a common geometric framework.

Prior to Kim’s paper the term “space of phylogenetic trees” was used only metaphorically. Moreover, even though there were many papers proposing definitions for the “distance” between trees (the most popular being the Robinson-Foulds distance), the ideas were disconnected from the models used to analyze data, and therefore there was little hope of building a coherent theory of phylogenetics. The phylogenetic orange that Kim defined served to both define a “tree space” and at the same time provides a geometric framework for thinking about data and estimation in that space. Read the rest of this entry »

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