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New analytical results for the speciation times in neutral models

Tuesday 4th September 2007 - 15:50 to 16:10
INI Seminar Room 1

Did a reconstructed phylogeny evolve under a neutral model? We provide an analytical way – opposed to the common simulation approach – for comparing the speciation times of a reconstructed tree with the dates proposed by the neutral models, e.g. via lineages-through-time plots. Further, if dates are missing in a reconstructed tree which evolved under a neutral model, we provide the time of the speciation events. These methods, which make use of the rank function on a phylogenetic tree, can also be applied for calculating analytically the loss in biodiversity when some species become extinct. The neutral models considered in this work are the Yule model and a generalization which includes extinction as well, the critical branching process (CBP) model, recently introduced by D. Aldous and L. Popovic. Trees under these neutral models are conditioned on having $n$ extant species today which is crucial for data analysis.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons