The neutral theory of biodiversity and biogeography has stimulated much research in community ecology. Here, exact results are used to apply neutral model predictions to large regional samples. Three complementary neutral models are presented: the Ewens canonical neutral model, a model of subdivided ecological communities, and a “diversity begets diversity” neutral model. For all three models, an exact sampling formula is provided, and a new R package neutr , is presented. This package is used to fit species abundances from regional inventories of tropical forest trees in the Amazon, tropical Africa and Southeast Asia. It is shown that the neutral models fit well empirical data for all but the few most abundant species (from 6 to 40 depending on the continent). When the parameter θ is taken as an index or regional diversity, the Amazonia and Southeast Asia emerge with similar regional diversities ( θ = 654 for Amazonia, versus θ = 726 for Southeast Asia), with a less diverse tropical African tree flora ( θ = 219). The model infers 10,141 tree species with at least 50 individuals in Amazonia, 3477 in tropical Africa and 9915 in Southeast Asia. The spatially subdivided neutral model provides clear evidence for a spatial substructure in all three regional floras. These results show how neutral models are useful to explore regional patterns of species abundance and to provide insights about regional species pools.