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Theor Popul Biol. 2004 May;65(3):249-61.

Brownian models and coalescent structures.

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Laboratoire Ecologie, Systematique et Evolution, Université Paris Sud, Bâtiment 360, F91405 Orsay, France.


Brownian motions on coalescent structures have a biological relevance, either as an approximation of the stepwise mutation model for microsatellites, or as a model of spatial evolution considering the locations of individuals at successive generations. We discuss estimation procedures for the dispersal parameter of a Brownian motion defined on coalescent trees. First, we consider the mean square distance unbiased estimator and compute its variance. In a second approach, we introduce a phylogenetic estimator. Given the UPGMA topology, the likelihood of the parameter is computed thanks to a new dynamical programming method. By a proper correction, an unbiased estimator is derived from the pseudomaximum of the likelihood. The last approach consists of computing the likelihood by a Markov chain Monte Carlo sampling method. In the one-dimensional Brownian motion, this method seems less reliable than pseudomaximum-likelihood.

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