In this paper we present a new way to understand the timing of branchingevents in phylogenetic trees. Our method explicitly considers the relativetiming of diversification events between sister clades; as such it iscomplimentary to existing methods using lineages-through-time plots whichconsider diversification in aggregate. The method looks for evidence ofdiversification happening in lineage-specific ``bursts'', or the opposite,where diversification between two clades happens in an unusually regularfashion. In order to be able to distinguish interesting events fromstochasticity, we propose two classes of neutral models on trees with timinginformation and develop a statistical framework for testing these models. Ourmodels substantially generalize both the coalescent with ancestral populationsize variation and the global-rate speciation-extinction models. We end thepaper with several example applications: first, we show that the evolution ofthe Hepatitis C virus appears to proceed in a lineage-specific burstingfashion. Second, we analyze a large tree of ants, demonstrating that a periodof elevated diversification rates does not appear to occurred in a burstingmanner.
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