Variation in both inter- and intraspecific traits affects community dynamics, yet we know little regarding the relative importance of external environmental filters versus internal biotic interactions that shape the functional space of communities along broad-scale environmental gradients, such as latitude, elevation, or depth. We examined changes in several key aspects of functional alpha diversity for marine fishes along depth and latitude gradients by quantifying intra- and interspecific richness, dispersion, and regularity in functional trait space. We derived eight functional traits related to food acquisition and locomotion and calculated seven complementary indices of functional diversity for 144 species of marine ray-finned fishes along large-scale depth (50–1200 m) and latitudinal gradients (29°–51° S) in New Zealand waters. Traits were derived from morphological measurements taken directly from footage obtained using Baited Remote Underwater Stereo-Video systems and museum specimens. We partitioned functional variation into intra- and interspecific components for the first time using a PERMANOVA approach. We also implemented two tree-based diversity metrics in a functional distance-based context for the first time: namely, the variance in pairwise functional distance and the variance in nearest neighbor distance. Functional alpha diversity increased with increasing depth and decreased with increasing latitude. More specifically, the dispersion and mean nearest neighbor distances among species in trait space and intraspecific trait variability all increased with depth, whereas functional hypervolume (richness) was stable across depth. In contrast, functional hypervolume, dispersion, and regularity indices all decreased with increasing latitude; however, intraspecific trait variation increased with latitude, suggesting that intraspecific trait variability becomes increasingly important at higher latitudes. These results suggest that competition within and among species are key processes shaping functional multidimensional space for fishes in the deep sea. Increasing morphological dissimilarity with increasing depth may facilitate niche partitioning to promote coexistence, whereas abiotic filtering may be the dominant process structuring communities with increasing latitude.