Daniel L. Rabosky introduced a method to automatically detect key innovations, rate shifts, and diversity dependence on phylogenetic trees. The method uses reversible-jump Markov Chain Monte Carlo (rjMCMC) to explore different models of diversification processes, allowing for an arbitrary number of time-varying processes without prior specification. The model assumes that changes in evolutionary regimes occur under a compound Poisson process, accounting for both time and lineage variation in speciation and extinction rates. Using simulated datasets, the method was shown to accurately quantify complex mixtures of diversification processes. It was compared to the MEDUSA model, and applied to the cetacean radiation, revealing significant rate shifts and diversity-dependent diversification. The method enables the exploration of macroevolutionary dynamics across large phylogenetic trees, accounting for heterogeneous evolutionary processes. The approach is Bayesian, allowing for a greater number of candidate models and automatic model selection based on posterior probabilities. The method provides marginal distributions of speciation and extinction rates for each branch in a phylogenetic tree. The results show that the method is robust to prior choices and accurately estimates speciation and extinction rates across various simulation scenarios. The analysis of the cetacean radiation revealed a significant increase in speciation rates during the Delphinidae radiation, with a strong posterior probability of rate shifts. The method is effective in detecting complex diversification patterns and is applicable to a wide range of phylogenetic trees.Daniel L. Rabosky introduced a method to automatically detect key innovations, rate shifts, and diversity dependence on phylogenetic trees. The method uses reversible-jump Markov Chain Monte Carlo (rjMCMC) to explore different models of diversification processes, allowing for an arbitrary number of time-varying processes without prior specification. The model assumes that changes in evolutionary regimes occur under a compound Poisson process, accounting for both time and lineage variation in speciation and extinction rates. Using simulated datasets, the method was shown to accurately quantify complex mixtures of diversification processes. It was compared to the MEDUSA model, and applied to the cetacean radiation, revealing significant rate shifts and diversity-dependent diversification. The method enables the exploration of macroevolutionary dynamics across large phylogenetic trees, accounting for heterogeneous evolutionary processes. The approach is Bayesian, allowing for a greater number of candidate models and automatic model selection based on posterior probabilities. The method provides marginal distributions of speciation and extinction rates for each branch in a phylogenetic tree. The results show that the method is robust to prior choices and accurately estimates speciation and extinction rates across various simulation scenarios. The analysis of the cetacean radiation revealed a significant increase in speciation rates during the Delphinidae radiation, with a strong posterior probability of rate shifts. The method is effective in detecting complex diversification patterns and is applicable to a wide range of phylogenetic trees.