The trophic theory of island biogeography (TTIB) posits that species at higher trophic levels should be most strongly limited by island size in the classical species-area relationship. This has rarely been tested, and it is still unclear whether the diversity scaling of different biodiversity dimensions - e.g. phylogenetic or functional diversity - are similarly affected by trophic position. We test predictions of the TTIB by examining the diversity-area scaling relationships of taxonomic, phylogenetic and functional diversity of avian trophic guilds across the Ryūkyū archipelago, Japan. We find a positive diversity-area relationship for all dimensions of biodiversity but uncover differences in scaling relationships among dimensions. We also find that diversity-area relationships are significantly related to trophic rank, as suggested by the TTIB, but that functional diversity of granivores was most strongly influenced by island area. Our results suggest that niche space scales asymmetrically with island area among trophic guilds of birds; a result that fits the TTIB. Scaling relationships differed between diversity dimensions - larger islands appeared to accommodate highest richness of intermediate predators, but highest functional diversity among consumers and granivores. Our findings suggest that niche-based processes operate across the Ryūkyū archipelago to disproportionately influence the diversity of species over their traits.