Understanding how biodiversity influences ecosystem functioning is one of the central goals of modern ecology. The early and often acrimonious debates about the relationship between biodiversity and ecosystem functioning were largely resolved following the advent of a statistical partitioning scheme that decomposed the net effect of biodiversity on ecosystem functioning into a “selection” effect and a “complementarity” effect. Here we show that both the biodiversity effect and its statistical decomposition into selection and complementarity are fundamentally flawed because these methods use a naïve null expectation based on neutrality, likely leading to an overestimate of the net biodiversity effect, and because they fail to account for the nonlinear abundance‐ecosystem‐functioning relationships widely observed in nature. Furthermore, under nonlinearity no such statistical scheme can be devised to partition the biodiversity effect. We also present an alternative approach that provides a more reasonable starting point for estimating biodiversity effects. Overall, our results suggest that all studies conducted since the early 1990s are likely to have overestimated the positive effects of biodiversity on ecosystem functioning.