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We believe that punctuational change dominates the history of life: evolution is concentrated in very rapid events of speciation (geologically instantaneous, even if tolerably continuous in ecological time). Most species, during their geological history, either do not change in any appreciable way, or else they fluctuate mildly in morphology, with no apparent direction. Phyletic gradualism is very rare and too slow, in any case, to produce the major events of evolution. Evolutionary trends are not the product of slow, directional transformation within lineages; they represent the differential success of certain species within a clade—speciation may be random with respect to the direction of a trend (Wright's rule). As an a priori bias, phyletic gradualism has precluded any fair assessment of evolutionary tempos and modes. It could not be refuted by empirical catalogues constructed in its light because it excluded contrary information as the artificial result of an imperfect fossil record. With the model of punctuated equilibria, an unbiased distribution of evolutionary tempos can be established by treating stasis as data and by recording the pattern of change for all species in an assemblage. This distribution of tempos can lead to strong inferences about modes. If, as we predict, the punctuational tempo is prevalent, then speciation—not phyletic evolution—must be the dominant mode of evolution. We argue that virtually none of the examples brought forward to refute our model can stand as support for phyletic gradualism; many are so weak and ambiguous that they only reflect the persistent bias for gradualism still deeply embedded in paleontological thought. Of the few stronger cases, we concentrate on Gingerich's data for Hyopsodus and argue that it provides an excellent example of species selection under our model. We then review the data of several studies that have supported our model since we published it five years ago. The record of human evolution seems to provide a particularly good example: no gradualism has been detected within any hominid taxon, and many are long-ranging; the trend to larger brains arises from differential success of essentially static taxa. The data of molecular genetics support our assumption that large genetic changes often accompany the process of speciation. Phyletic gradualism was an a priori assertion from the start—it was never “seen” in the rocks; it expressed the cultural and political biases of 19th century liberalism. Huxley advised Darwin to eschew it as an “unnecessary difficulty.” We think that it has now become an empirical fallacy. A punctuational view of change may have wide validity at all levels of evolutionary processes. At the very least, it deserves consideration as an alternate way of interpreting the history of life.