Dominant theories in island biogeography, such as the Equilibrium Theory of Island Biogeography (ETIB) and the General Dynamic Model (GDM), provide conceptual frameworks to quantitatively examine diversity patterns across islands. However, little is known about community assembly processes on islands or the mechanisms shaping it. The composition of island biotas likely reflects the net effect of multiple ecological processes on islands, such as dispersal and environmental filtering, which suggest that island communities assemble non-randomly and not neutrally, as assumed by the ETIB and GDM. Functional traits capture variation in ecological strategies among species and therefore can directly be linked to mechanisms associated with community assembly. However, trait-based frameworks were predominantly developed for mainland communities, and their application to islands remains limited. We developed and tested a trait-based framework to examine community assembly on islands. We used a novel dataset of woody plants on 40 small islands in the Raja Ampat Archipelago in Indonesia and collected functional traits (related to leaf, stem, seed, and whole-plant) that represent major dimensions of variation in plant form and function. When grouping traits into life history dimensions related to species dispersal and environmental adaptations, we found evidence that island communities were jointly shaped by dispersal and environmental filtering and that the relative importance of these processes was affected by island area. Small islands were generally more functionally underdispersed than larger islands, indicating that the filtering strength decreased non-linearly with increasing island area. Small island communities were more strongly shaped by dispersal constraints and limited niche space, whereas greater niche differentiation enhanced functional diversity of communities on larger islands. Our trait-based framework indicated that island communities are shaped by non-random assembly processes that vary with island area independent of species richness, thereby questioning whether neutral based models adequately describe dispersal and establishment dynamics of island floras.