Fitting diversification models on undated or partially dated trees

Abstract

Dating the tree of life is a task far more complicated than only determining the evolutionary relationships between species. It is therefore of interest to develop approaches apt to deal with undated phylogenetic trees. The main result of this work is a method to compute probabilities of undated phylogenetic trees under Markovian diversification models by constraining some of the divergence times to belong to given time intervals and by allowing diversification shifts on certain clades. If the diversification models considered are lineage-homogeneous, the time complexity of this computation is quadratic with the number of species of the phylogenetic tree and linear with the number of temporal constraints. The interest of this computation method is illustrated with three applications, namely, • to compute the distribution of the divergence times of a tree topology with temporal constraints, • to directly sample the divergence times of a tree topology, and • to test for a diversification shift at a given clade.