A method for investigating relative timing information on phylogenetic trees.

In this paper, we present a new way to describe the timing of branching events in phylogenetic trees. Our description is in terms of the relative timing of diversification events between sister clades; as such it is complementary to existing methods using lineages-through-time plots which consider diversification in aggregate. The method can be applied to look for evidence of diversification happening in lineage-specific "bursts", or the opposite, where diversification between 2 clades happens in an unusually regular fashion. In order to be able to distinguish interesting events from stochasticity, we discuss 2 classes of neutral models on trees with relative timing information and develop a statistical framework for testing these models. These model classes include both the coalescent with ancestral population size variation and global rate speciation-extinction models. We end the paper with 2 example applications: first, we show that the evolution of the hepatitis C virus deviates from the coalescent with arbitrary population size. Second, we analyze a large tree of ants, demonstrating that a period of elevated diversification rates does not appear to have occurred in a bursting manner.