Patterns of biodiversity provide insights into the processes that shape biological communities around the world. Variation in species diversity along biogeographical or ecological gradients, such as latitude or precipitation, can be attributed to variation in different components of biodiversity: changes in the total abundance (i.e., more-individual effects) and changes in the regional species abundance distribution (SAD). Rarefaction curves can provide a tool to partition these sources of variation on diversity, but first must be converted to a common unit of measurement. Here, we partition species diversity gradients into components of the SAD and abundance using the effective number of species (ENS) transformation of the individual-based rarefaction curve. Because the ENS curve is unconstrained by sample size, it can act as a standardized unit of measurement when comparing effect sizes among different components of biodiversity change. We illustrate the utility of the approach using two data sets spanning latitudinal diversity gradients in trees and marine reef fish and find contrasting results. Whereas the diversity gradient of fish was mostly associated with variation in abundance (86\%), the tree diversity gradient was mostly associated with variation in the SAD (59\%). These results suggest that local fish diversity may be limited by energy through the more-individuals effect, while species pool effects are the larger determinant of tree diversity. We suggest that the framework of the ENS-curve has the potential to quantify the underlying factors influencing most aspects of diversity change.