Research on island species–area relationships (ISAR) has expanded to incorporate functional (IFDAR) and phylogenetic (IPDAR) diversity. However, relative to the ISAR, we know little about IFDARs and IPDARs, and lack synthetic global analyses of variation in form of these three categories of island diversity–area relationship (IDAR). Here, we undertake the first comparative evaluation of IDARs at the global scale using 51 avian archipelagic data sets representing true and habitat islands. Using null models, we explore how richness-corrected functional and phylogenetic diversity scale with island area. We also provide the largest global assessment of the impacts of species introductions and extinctions on the IDAR. Results show that increasing richness with area is the primary driver of the (non-richness corrected) IPDAR and IFDAR for many data sets. However, for several archipelagos, richness-corrected functional and phylogenetic diversity changes linearly with island area, suggesting that the dominant community assembly processes shift along the island area gradient. We also find that archipelagos with the steepest ISARs exhibit the biggest differences in slope between IDARs, indicating increased functional and phylogenetic redundancy on larger islands in these archipelagos. In several cases introduced species seem to have ‘re-calibrated’ the IDARs such that they resemble the historic period prior to recent extinctions.