Nonequilibrium dynamics and non-neutral processes, such as trait-dependent dispersal, are often missing from quantitative island biogeography models despite their potential explanatory value. One of the most influential nonequilibrium models is the taxon cycle, but it has been difficult to test its validity as a general biogeographical framework. Here, we test predictions of the taxon cycle model using six expected phylogenetic patterns and a time-calibrated phylogeny of Indo-Pacific Odontomachus (Hymenoptera: Formicidae: Ponerinae), one of the ant genera that E.O. Wilson used when first proposing the hypothesis. We used model-based inference and a newly developed trait-dependent dispersal model to jointly estimate ancestral biogeography, ecology (habitat preferences for forest interiors, vs. "marginal" habitats, such as savannahs, shorelines, disturbed areas) and the linkage between ecology and dispersal rates. We found strong evidence that habitat shifts from forest interior to open and disturbed habitats increased macroevolutionary dispersal rate. In addition, lineages occupying open and disturbed habitats can give rise to both island endemics re-occupying only forest interiors and taxa that re-expand geographical ranges. The phylogenetic predictions outlined in this study can be used in future work to evaluate the relative weights of neutral (e.g., geographical distance and area) and non-neutral (e.g., trait-dependent dispersal) processes in historical biogeography and community ecology.