1. The classical MacArthur-Wilson theory of island biogeography (TIB) emphasizes the role of island area and isolation in determining island biotas, but is neutral with respect to species differences that could affect community assembly and persistence. Recent extensions of island biogeography theory address how functional differences among species may lead to non-random community assembly processes and different diversity-area scaling patterns. First, the trophic TIB considers how diversity scaling varies across trophic position in a community, with species at higher trophic levels being most strongly influenced by island area. Second, further extensions have predicted how trait distributions, and hence functional diversity, should scale with area. Trait-based theory predicts richness-corrected functional diversity should be low on small islands but converge to null on larger islands. Conversely, competitive assembly predicts high diversity on small islands converging to null with increasing size. 2. However, despite mounting interest in diversity-area relationships across different dimensions of diversity, these predictions derived from theory have not been extensively tested across taxa and island systems. 3. Here, we develop and test predictions of the trophic TIB and extensions to functional traits, by examining the diversity-area relationship across multiple trophic ranks and dimensions of avian biodiversity in the Ryūkyū archipelago of Japan. 4. We find evidence for a positive species- and phylogenetic diversity-area relationship, but functional diversity was not strongly affected by island area. Counter to the Trophic TIB, we found no differences in the slopes of species-area relationships among trophic ranks, although slopes varied among trophic guilds at the same rank. We revealed differential assembly of trophic ranks, with evidence of trait-based assembly of intermediate predators but otherwise neutral community assembly. 5. Our results suggest that niche space differs among trophic guilds of birds, but that differences are mostly not predicted by current extensions of island biogeography theory. Whilst predicted patterns do not fit the empirical data well in this case, the development of such theory provides a useful framework to analyse island patterns from new perspectives. The application of empirical datasets such as ours should help provide a basis for developing further iterations of island biogeography theory.