title: Efficient Recycled Algorithms for Quantitative Trait Models on Phylogenies.
abstract: We present an efficient and flexible method for computing likelihoods for phenotypic traits on a phylogeny. The method does not resort to Monte Carlo computation but instead blends Felsenstein's discrete character pruning algorithm with methods for numerical quadrature. It is not limited to Gaussian models and adapts readily to model uncertainty in the observed trait values. We demonstrate the framework by developing efficient algorithms for likelihood calculation and ancestral state reconstruction under Wright's threshold model, applying our methods to a data set of trait data for extrafloral nectaries across a phylogeny of 839 Fabales species.
authors.affiliation: Department of Mathematics and Statistics, University of Otago, Dunedin, New Zealand.
authors.forename: Gordon
authors.initials: G
authors.lastname: Hiscott
authors.affiliation: Department of Physics, University of Otago, Dunedin, New Zealand.
authors.forename: Colin
authors.initials: C
authors.lastname: Fox
authors.affiliation: Department of Mathematics and Statistics, University of Otago, Dunedin, New Zealand.
authors.forename: Matthew
authors.initials: M
authors.lastname: Parry
authors.affiliation: Department of Mathematics and Statistics, University of Otago, Dunedin, New Zealand david.bryant@otago.ac.nz.
authors.forename: David
authors.initials: D
authors.lastname: Bryant
mesh_terms: D000465:Algorithms; D007887:Fabaceae / Q000235:genetics*; D009010:Monte Carlo Method; D010641:Phenotype; D010802:Phylogeny; D040641:Quantitative Trait Loci / Q000235:genetics*
keywords: comparative method; continuous traits; likelihood algorithm; numerical integration; numerical quadrature; quantitative traits