Neutral biodiversity theory has the potential to contribute to our understanding of how macroevolutionary dynamics influence contemporary biodiversity, but there are issues regarding its dynamical predictions that must first be resolved. Here we address these issues by extending the theory in two ways using a novel analytical approach: (1) we set the absolute tempo of biodiversity dynamics by explicitly incorporating population-level stochasticity in abundance; (2) we allow new species to arise with more than one individual. Setting the absolute tempo yields quantitative predictions on biodiversity dynamics that can be tested using contemporary and fossil data. Allowing incipient-species abundances greater than one individual yields predictions on how these dynamics, and the form of the species-abundance distribution, are affected by multiple speciation modes. We apply this new model to contemporary and fossil data that encompass 30 Myr of macroevolution for planktonic foraminifera. By synthesizing the model with these empirical data, we present evidence that dynamical issues with neutral biodiversity theory may be resolved by incorporating the effects of environmental stochasticity and incipient-species abundance on biodiversity dynamics.