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The long‐term diversification of life probably cannot be modelled as a simple equilibrial process: the time scales are too long, the potential for exploring new ecospace is too large and it is unlikely that ecological controls can act at global scales. The sum of many clade expansions and reductions, each of which happens according to its own dynamic, probably approximates more a damped exponential curve when translated into a global‐scale species diversification curve. Unfortunately, it is not possible to plot such a meaningful global‐scale species diversification curve through time, but curves at higher taxonomic levels have been produced. These curves are subject to the vagaries of the fossil record, but it is unlikely that the sources of error entirely overwhelm the biological signal. Clades radiate when the external and internal conditions are right: a new territory or ecospace becomes available, and the lineage …