Current statistical biogeographical analysis methods are limited in the ways ecology can be related to the processes of diversification and geographical range evolution, requiring conflation of geography and ecology, and/or assuming ecologies that are uniform across all lineages and invariant in time. This precludes the possibility of studying a broad class of macro-evolutionary biogeographical theories that relate geographical and species histories through iineage-specific ecological and evolutionary dynamics, such as taxon cycle theory. Here we present a new model that generates phylogenies under a complex of superpositioned geographical range evolution, trait evolution, and diversification processes that can communicate with each other.This means that, under our model, the diversification and transition of the states of a lineage through geographical space is separate from, yet is conditional on, the state of the lineage in trait space (or vice versa). We present a likelihood-free method of inference under our model using discriminant analysis of principal components of summary statistics calculated on phylogenies, with the discriminant functions trained on data generated by simulations under our model. This approach of model classification is shown to be efficient, robust, and performant over a broad range of parameter space defined by the relative rates of dispersal, trait evolution, and diversification processes. We apply our method to a case study of the taxon cycle, i.e. testing for habitat and trophic-level constraints in the dispersal regimes of the Wallacean avifaunal radiation.