title: Brownian models and coalescent structures.
abstract: 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.
authors.affiliation: Laboratoire Ecologie, Systematique et Evolution, Université Paris Sud, Bâtiment 360, F91405 Orsay, France. michael.blum@imag.fr
authors.forename: Michael G B
authors.initials: MG
authors.lastname: Blum
authors.forename: Christophe
authors.initials: C
authors.lastname: Damerval
authors.forename: Stephanie
authors.initials: S
authors.lastname: Manel
authors.forename: Olivier
authors.initials: O
authors.lastname: François
mesh_terms: D000465:Algorithms; D003710:Demography; D019143:Evolution, Molecular; D005828:Genetics, Population; D006801:Humans; D018895:Microsatellite Repeats / Q000235:genetics; D008957:Models, Genetic; D009154:Mutation / Q000235:genetics; D010375:Pedigree; D010802:Phylogeny; D016012:Poisson Distribution; D011110:Polymorphism, Genetic; D011995:Recombination, Genetic; D013269:Stochastic Processes