Making quantitative predictions of the effects of human activities on ecological communities is crucial for their management. In the case of plant–pollinator mutualistic networks, despite the great progress in describing the interactions between plants and their pollinators, the capability of making quantitative predictions is still lacking. Here, in order to estimate pollinator species abundances and their niche distribution, I propose a general method to transform a plant–pollinator network into a competition model between pollinator species. Competition matrices were obtained from ‘first principles’ calculations, using qualitative interaction matrices compiled for a set of 38 plant–pollinator networks. This method is able to make accurate quantitative predictions for mutualistic networks spanning a broad geographic range. Specifically, the predicted biodiversity metrics for pollinators – species relative abundances, Shannon equitability and Gini–Simpson indices – agree quite well with those inferred from empirical counts of visits of pollinators to plants. Furthermore, this method allows building a one‐dimensional niche axis for pollinators in which clusters of generalists are separated by specialists thus rendering support to the theory of emergent neutrality. The importance of interspecific competition between pollinator species is a controversial and unresolved issue, considerable circumstantial evidence has accrued that competition between insects does occur, but a clear measure of its impact on their species abundances is still lacking. I contributed to fill this gap by quantifying the effect of competition between pollinators. Particular applications of our analysis could be to estimate the quantitative effects of removing a species from a community or to address the fate of populations of native organisms when foreign species are introduced to ecosystems far beyond their home range.