The relative importance of different modes of evolution in shaping phenotypic diversity remains a hotly debated question. Fossil data suggest that stasis may be a common mode of evolution, while modern data suggest very fast rates of evolution. One way to reconcile these observations is to imagine that evolution is punctuated, rather than gradual, on geological time scales. To test this hypothesis, we developed a novel maximum likelihood framework for fitting Lévy processes to comparative morphological data. This class of stochastic processes includes both a gradual and punctuated component. We found that a plurality of modern vertebrate clades examined are best fit by punctuated processes over models of gradual change, gradual stasis, and adaptive radiation. When we compare our results to theoretical expectations of the rate and speed of regime shifts for models that detail fitness landscape dynamics, we find that our quantitative results are broadly compatible with both microevolutionary models and with observations from the fossil record.A key debate in evolutionary biology centers around the seeming contradictions regarding the tempo and mode of evolution as seen in fossil data compared to ecological data. Fossil data often support models of stasis, in which little evolutionary change is seen within lineages over long timescales (Hunt 2007;Estes and Arnold 2007), while ecological data show that rapid bursts of evolution are not only possible, but potentially common (Reznick et al. 1997;Herrel et al. 2008;Brown and Brown 2013;Cresko et al. 2004). At face value, these observations seem to contradict one another, an observation known as the "paradox of stasis" (Hansen and Houle 2004). These observations are often reconciled through a descriptive model of punctuated evolution, entailing stasis interrupted by pulses of rapid change, as famously articulated by Simpson (Simpson 1944;1953).On macroevolutionary timescales, pulses of rapid change are expected to look roughly instantaneous. Only recently have statistical methods grown sophisticated enough to model punctuated evolution as a stochastic process, with advances showing that punctuation is detectable in some fossil time series (Hunt et al. 2015) and between pairs of living and extinct taxa (Uyeda et al. 2011).While these studies establish the existence of punctuated evolution, it is still unknown whether the evolutionary mode is common or rare. How many clades in the Tree of Life were shaped by abrupt pulses of rapid evolution? If these evolutionary pulses are common, then that should inform our expectations about how traits evolved for clades that left no fossils, and the potential for vulnerable species to adapt rapidly to climate change (Quintero and Wiens 2013). To this end, phylogenetic models-models of trait evolution that account for the shared ancestry of species-have played a vital role in measuring the relative support of competing Simpsonian modes of evolution.A pioneering meta-analysis (Harmon et al. 2010a) fitted a collection of phylogen...