  In this paper we present a new way to understand the timing of branching
events in phylogenetic trees. Our method explicitly considers the relative
timing of diversification events between sister clades; as such it is
complimentary to existing methods using lineages-through-time plots which
consider diversification in aggregate. The method looks for evidence of
diversification happening in lineage-specific ``bursts'', or the opposite,
where diversification between two clades happens in an unusually regular
fashion. In order to be able to distinguish interesting events from
stochasticity, we propose two classes of neutral models on trees with timing
information and develop a statistical framework for testing these models. Our
models substantially generalize both the coalescent with ancestral population
size variation and the global-rate speciation-extinction models. We end the
paper with several example applications: first, we show that the evolution of
the Hepatitis C virus appears to proceed in a lineage-specific bursting
fashion. Second, we analyze a large tree of ants, demonstrating that a period
of elevated diversification rates does not appear to occurred in a bursting
manner.
