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Testing for equality of rates of evolution

A new method of data analysis offers a potentially powerful tool for statistically evaluating hypotheses of rate in temporally-ordered evolutionary phenomena. We present a method for bootstrapping time-ordered data sets to test hypotheses of the equality of rate. This method is applicable to both nonrandom and random generative processes. The method is applied to the data of Malmgren et al. (1983) for the Globorotalia plesiotumida–G. tumida planktonic foraminiferan lineage and the data of Reyment (1982) for the benthonic foraminiferan Afrobolivina afar. G. plesiotumida is recognizable on the basis of independent data as a species distinct from G. tumida, its descendant. Evolutionary change rate during the evolution of G. tumida from G. plesiotumida is shown to be faster than rates within either species. The pattern of variation exhibited by A. afar includes a time interval of more rapid change; this more rapid change is observed post hoc. A bootstrapping model based on post hoc observations reveals the rate in this time interval to be not significantly faster than expected in such post hoc intervals.