Machine Learning Biogeographic Processes from Biotic Patterns: A New Trait-Dependent Dispersal and Diversification Model with Model Choice By Simulation-Trained Discriminant Analysis

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 macroevolutionary biogeographical theories that relate geographical and species histories through lineage-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. 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 selection by classification of empirical data with respect to data generated under training models is shown to be efficient, robust, and performs well 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, that is testing for habitat and trophic level constraints in the dispersal regimes of the Wallacean avifaunal radiation.