Evolution provides many cases of apparent shifts in diversification associated with particular anatomical traits. Three general models connect these patterns to anatomical evolution: (i) elevated net extinction of taxa bearing particular traits, (ii) elevated net speciation of taxa bearing particular traits, and (iii) elevated evolvability expanding the range of anatomies available to some species. Traitbased diversification shifts predict elevated hierarchical stratigraphic compatibility (i.e., primitive→derived→highly derived sequences) among pairs of anatomical characters. The three specific models further predict (i) early loss of diversity for taxa retaining primitive conditions (elevated net extinction), (ii) increased diversification among later members of a clade (elevated net speciation), and (iii) increased disparity among later members in a clade (elevated evolvability). Analyses of 319 anatomical and stratigraphic datasets for fossil species and genera show that hierarchical stratigraphic compatibility exceeds the expectations of trait-independent diversification in the vast majority of cases, which was expected if traitdependent diversification shifts are common. Excess hierarchical stratigraphic compatibility correlates with early loss of diversity for groups retaining primitive conditions rather than delayed bursts of diversity or disparity across entire clades. Cambrian clades (predominantly trilobites) alone fit null expectations well. However, it is not clear whether evolution was unusual among Cambrian taxa or only early trilobites. At least among post-Cambrian taxa, these results implicate models, such as competition and extinction selectivity/resistance, as major drivers of trait-based diversification shifts at the species and genus levels while contradicting the predictions of elevated net speciation and elevated evolvability models.A basic question in evolution is whether shifts in taxonomic and/or morphologic diversification are tied to particular anatomical traits. The fossil record includes many examples of taxa possessing one set of traits losing diversity over time, whereas other taxa with different sets of traits gain diversity (1-4). Similarly, phylogenies of extant taxa often suggest that speciose subclades possessing derived traits were once much less diverse than the remainder of the clade diagnosed by primitive traits (5-7). In a different vein, morphospace studies often indicate that particular subclades diversify in regions of morphospace seemingly off limits to the remainder of the clade (8-10). Three models of traitbased diversification shifts explain these patterns. Model 1 (elevated net extinction) posits elevated extinction rates and/or decreased origination rates among taxa with primitive traits (11, 12). Model 2 (elevated net speciation) posits elevated speciation rates and/or decreased extinction rates among some taxa with derived traits (11,13,14). Model 3 (elevated evolvability) posits that some characters vary only among some derived taxa and not among the remainder...