Biodiversity is multifaceted and represents numerous dimensions expressing variation in richness and abundances of species, ecosystem functions, phylogenetic relationships, morphology, traits and interactions. Such dimensions are correlated to varying degrees and recent research has attempted to better understand behavior of such correlations. We define dimensionality of biodiversity as degree of redundancy in variation among multiple dimensions of biodiversity. One fundamental question regarding biodiversity is whether its dimensionality is spatially structured, also exhibiting geographic gradients. We examine if redundancy among dimensions of biodiversity changes latitudinally thereby contributing to increased tropical complexity. Geographic range maps of bats were overlaid on a 100 × 100 km grid of the New World to determine species composition of each cell. Species richness and three measures each of phylogenetic, functional and phenetic diversity were calculated. Dimensionality was estimated as evenness of eigenvalues generated from a principal components analysis (PCA) of multiple measures of biodiversity. High dimensionality is characterized by low correlations among biodiversity measures and high evenness of eigenvalues from PCA, whereas low dimensionality is characterized by high correlations and low evenness of eigenvalues. Latitudinal gradients of dimensionality were determined by regression analysis. Slope of the empirical relationship was compared to slopes generated from two null models that randomized the distribution of species. Dimensionality of biodiversity does indeed exhibit a latitudinal gradient, decreasing with increasing latitude. This empirical gradient was stronger than expected by the random distribution of species. Additionally, spatial variation in dimensionality of biodiversity could not be explained by a similar underlying pattern in variation of environmental conditions. Correlations among different dimensions of biodiversity vary spatially, and interpretations of such correlations should be geographically explicit. Mechanisms proposed to explain latitudinal gradients need not only account for gradients of biodiversity, but gradients in dimensionality as well. A gradient in dimensionality suggests that conservation strategies that rely on maximization of a single metric, such as species richness, might be of varying utility in different geographic contexts.