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Time-calibrated molecular phylogenies provide a valuable window into the tempo and mode of species diversification, especially for the large number of groups that lack adequate fossil records. Molecular phylogenetic data frequently suggest an initial “explosive speciation” phase, leading to widespread speculation that ecological niche-filling processes might govern the dynamics of species diversification during evolutionary radiations. However, these patterns are difficult to reconcile with the fossil record. The fossil record strongly suggests that extinction rates have been high relative to speciation rates, but such elevated background extinction should erase the signal of early, rapid speciation from molecular phylogenies. For this reason, extinction rates in molecular phylogenies are frequently estimated as zero under the widely used birth–death model. Here, I construct a simple model that combines phylogenetically patterned extinction with pulsed turnover dynamics and constant diversity through time. Using approximate Bayesian methods, I show that heritable extinction can easily explain the phenomenon of explosive early diversification, even when net diversification rates are equal to zero. Several assumptions of the model are more consistent with both the fossil record and neontological data than the standard birth–death model and it may thus represent a viable alternative interpretation of phylogenetic diversification patterns. These results suggest that variation in the absolute rate of lineage turnover through time, in conjunction with phylogenetically nonrandom extinction, may underlie the apparent diversity-dependent speciation observed in molecular phylogenies. [ABSTRACT FROM PUBLISHER]