The nature of evolutionary changes recorded by the fossil record has long been controversial, with particular disagreement concerning the relative frequency of gradual change versus stasis within lineages. Here, I present a large-scale, statistical survey of evolutionary mode in fossil lineages. Over 250 sequences of evolving traits were fit by using maximum likelihood to three evolutionary models: directional change, random walk, and stasis. Evolution in these traits was rarely directional; in only 5% of fossil sequences was directional evolution the most strongly supported of the three modes of change. The remaining 95% of sequences were divided nearly equally between random walks and stasis. Variables related to body size were significantly less likely than shape traits to experience stasis. This finding is in accord with previous suggestions that size may be more evolutionarily labile than shape and is consistent with some but not all of the mechanisms proposed to explain evolutionary stasis. In general, similar evolutionary patterns are observed across other variables, such as clade membership and temporal resolution, but there is some evidence that directional change in planktonic organisms is more frequent than in benthic organisms. The rarity with which directional evolution was observed in this study corroborates a key claim of punctuated equilibria and suggests that truly directional evolution is infrequent or, perhaps more importantly, of short enough duration so as to rarely register in paleontological sampling.gradualism ͉ modes of evolution ͉ punctuated equilibria

For almost 30 years, paleontologists have analyzed evolutionary sequences in terms of simple null models, most commonly random walks. Despite this long history, there has been little discussion of how model parameters may be estimated from real paleontological data. In this paper, I outline a likelihood-based framework for fitting and comparing models of phyletic evolution. Because of its usefulness and historical importance, I focus on a general form of the random walk model. The long-term dynamics of this model depend on just two parameters: the mean (μstep) and variance (σ2step) of the distribution of evolutionary transitions (or “steps”). The value of μstepdetermines the directionality of a sequence, and σ2stepgoverns its volatility. Simulations show that these two parameters can be inferred reliably from paleontological data regardless of how completely the evolving lineage is sampled.In addition to random walk models, suitable modification of the likelihood function permits consideration of a wide range of alternative evolutionary models. Candidate evolutionary models may be compared on equal footing using information statistics such as the Akaike Information Criterion (AIC). Two extensions to this method are developed: modeling stasis as an evolutionary mode, and assessing the homogeneity of dynamics across multiple evolutionary sequences. Within this framework, I reanalyze two well-known published data sets: tooth measurements from the Eocene mammalCantius, and shell shape in the planktonic foraminiferaContusotruncana. These analyses support previous interpretations about evolutionary mode in size and shape variables inCantius, and confirm the significantly directional nature of shell shape evolution inContusotruncana. In addition, this model-fitting approach leads to a further insight about the geographic structure of evolutionary change in this foraminiferan lineage.

The largest known dinosaurs weighed at least 20 million times as much as the smallest, indicating exceptional phenotypic divergence. Previous studies have focused on extreme giant sizes, tests of Cope's rule, and miniaturization on the line leading to birds. We use non-uniform macroevolutionary models based on Ornstein-Uhlenbeck and trend processes to unify these observations, asking: what patterns of evolutionary rates, directionality and constraint explain the diversification of dinosaur body mass? We find that dinosaur evolution is constrained by attraction to discrete body size optima that undergo rare, but abrupt, evolutionary shifts. This model explains both the rarity of multilineage directional trends, and the occurrence of abrupt directional excursions during the origins of groups such as tiny pygostylian birds and giant sauropods. Most expansion of trait space results from rare, constraint-breaking innovations in just a small number of lineages. These lineages shifted rapidly into novel regions of trait space, occasionally to small sizes, but most often to large or giant sizes. As with Cenozoic mammals, intermediate body sizes were typically attained only transiently by lineages on a trajectory from small to large size. This demonstrates that bimodality in the macroevolutionary adaptive landscape for land vertebrates has existed for more than 200 million years.