Biodiversity accumulates hierarchically by means of ecological and evolutionary processes and feedbacks. Within ecological communities drift, dispersal, speciation, and selection operate simultaneously to shape patterns of biodiversity. Reconciling the relative importance of these is hindered by current models and inference methods, which tend to focus on a subset of processes and their resulting predictions. Here we introduce massive ecoevolutionary synthesis simulations (MESS), a unified mechanistic model of community assembly, rooted in classic island biogeography theory, which makes temporally explicit joint predictions across three biodiversity data axes: (i) species richness and abundances, (ii) population genetic diversities, and (iii) trait variation in a phylogenetic context. Using simulations we demonstrate that each data axis captures information at different timescales, and that integrating these axes enables discriminating among previously unidentifiable community assembly models. MESS is unique in generating predictions of community-scale genetic diversity, and in characterizing joint patterns of genetic diversity, abundance, and trait values. MESS unlocks the full potential for investigation of biodiversity processes using multidimensional community data including a genetic component, such as might be produced by contemporary eDNA or metabarcoding studies. We combine MESS with supervised machine learning to fit the parameters of the model to real data and infer processes underlying how biodiversity accumulates, using communities of tropical trees, arthropods, and gastropods as case studies that span a range of data availability scenarios, and spatial and taxonomic scales.