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. Wedemonstrate the frameworkby developing efficient algorithms for likelihood calculation and ancestral state reconstruction under Wright's thresholdmodel, applying ourmethods to a data set of trait data for extrafloral nectaries across a phylogeny of 839 Fabales species.