One of the oldest and richest questions in biology is that of how species diversity is related to the availability of resources that limit the productivity of ecosystems. Researchers from a variety of disciplines have pursued this question from at least three different theoretical perspectives. Species energy theory has argued that the summed quantities of all resources influence species richness by controlling population sizes and the probability of stochastic extinction. Resource ratio theory has argued that the imbalance in the supply of two or more resources, relative to the stoichiometric needs of the competitors, can dictate the strength of competition and, in turn, the diversity of coexisting species. In contrast to these, the field of Biodiversity and Ecosystem Functioning has argued that species diversity acts as an independent variable that controls how efficiently limited resources are utilized and converted into new tissue. Here we propose that all three of these fields give necessary, but not sufficient, conditions to explain productivity-diversity relationships (PDR) in nature. However, when taken collectively, these three paradigms suggest that PDR can be explained by interactions among four distinct, non-interchangeable variables: (i) the overall quantity of limiting resources, (ii) the stoichiometric ratios of different limiting resources, (iii) the summed biomass produced by a group of potential competitors and (iv) the richness of co-occurring species in a local competitive community. We detail a new multivariate hypothesis that outlines one way in which these four variables are directly and indirectly related to one another. We show how the predictions of this model can be fit to patterns of covariation relating the richness and biomass of lake phytoplankton to three biologically essential resources (N, P and light) in a large number of Norwegian lakes.