The study of ancient biodiversity trends is confounded by biases of the paleontologic record, but standardizing sampling intensity among time intervals can ameliorate sample-size biases. We show that several existing standardization methods are intimately linked to the spatial components of diversity (alpha, the within-assemblage diversity; and beta, the between-assemblage diversity). The subsampling curves generated by these methods can also be generated by various manipulations of alpha and beta, so that one can predict the responses of the methods to specific changes in alpha or beta diversity. The responses of the subsampling methods to changes in total diversity depend on whether measured alpha or measured beta diversity changed. Like biodiversity, sampling consists of a within-sample component (the number of specimens collected per locality) and a between-sample component (the number of localities). Several subsampling methods (rarefaction, OW, O2W) attempt to standardize sampling effort at both levels, although they use no direct information on the former. Instead, they alter sampling intensity at the beta level to compensate for perceived biases at the alpha level. We show that alpha and beta diversity are not so easily interchangeable and that the accuracy of the subsampling methods depends critically on the spatial characteristics of diversity in a data set. Current methods are calibrated only to the abundance-richness characteristics of individual collections, but the amount of beta diversity and the degree to which the rareness/commonness of taxa correlates among samples also strongly affect the accuracy of the subsampling methods. We offer new calibrations based on empirical data sets that account for these factors. Our findings do not support Alroy et al.'s (2001) tentative claim that the taxonomic radiation in the Cenozoic marine realm is an artifact of biased sampling intensity. Their diversity curves that most strongly contradict Sepkoski's traditional Phanerozoic curve are based on a method that overcorrects for local sample-size biases, whereas the remaining curves are either consistent with the traditional curve or ambiguous because of the limited temporal and taxonomic coverage of the analysis. Other factors may bias Sepkoski's curve, but there is insufficient evidence to claim that variations in sampling intensity are the major determinant of its long-term trajectory.