A hierarchical branching model of evolutionary radiations

A hierarchical branching model is presented that tracks diversity of lineages and paraclades simultaneously. It is based on three parameters: (1) lineage origination within a paraclade, (2) lineage origination that founds new paraclades, and (3) lineage extinction. The model assumes stochastic constancy of evolutionary rates and, therefore, exponential growth of diversity is the null expectation. The probabilistic model can be used to generate confidence intervals for exponential growth through Monte Carlo simulation. These confidence intervals can be compared to empirical curves to test the null hypothesis of exponential growth. The analytic solution for paraclade diversity gives the statistical expectation for the probabilistic model. It can be applied to empirical diversity curves of supraspecific taxa to estimate total speciation rate, the intrinsic rate of increase, and the proportion of speciation events that found new paraclades. Two factors were identified with the model that may cause diversity curves for higher taxa (e.g., genera, families) to deviate from simple exponential growth during initial phases of diversification: (1) stochastic fluctuation at low diversity, and (2) taxonomic structure (i.e., species/genus ratio). These sources of variability should be evaluated before macroevolutionary explanations for specific diversity trends are invoked. Two kinds of evolutionary radiations were investigated with this model: (1) prolonged periods of low diversity (macroevolutionary lag) in cheilostome bryozoans and mammals prior to their main phases of diversification, and (2) rapid bursts in diversity of bivalves following the late Permian and end-Cretaceous mass extinctions. In all cases these patterns were found to deviate significantly from the null expectation of exponential growth lending support to previous macroevolutionary explanations. Finally, rates of speciation during radiations were compared to rates of speciation during background times for articulate brachiopods, cheilostome bryozoans, bivalves, and mammals. Speciation events that found new paraclades tend to make up a larger proportion of total speciation events during radiations compared to background times indicating that the opportunity for new adaptive zones to be filled at higher taxonomic levels is proportionately higher during these periods of increased evolutionary activity, and is not simply a result of an increased frequency of speciation.