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The properties of cladistic data sets from small monophyletic groups (6-1 2 species) are investigated using computer simulations of macroevolution. Two evolutionary models are simulated: gradualism and the punctuated-equilibrium hypothesis. Under the conditions of our simulations these two models of evolution make consistently different predictions about the distribution of autapomorphies among species. When strict stasis is enforced, the punctuated-equilibrium hypothesis predicts that the most expected number of autapomorphies per species will be zero, no matter how many characters are used in the analysis. As the number of characters used in the analysis increases, the distribution of the number of autapomorphies per species becomes bimodal. Under gradualism, the distribution of autapomorphies remains unimodal under all conditions, but the number of species without autapomorphies can fall to zero. A survey of real cladograms of extant monophyletic groups from a wide range of taxa indicates that the predictions of the punctuated- equilibrium hypothesis about autapomorphies do not hold. This constitutes strong evidence against the punctuated-equilibrium hypothesis.