  Resolving the relationship between biodiversity and ecosystem functioning has
been one of the central goals of modern ecology. Early debates about the
relationship were finally resolved with the advent of a statistical
partitioning scheme that decomposed the biodiversity effect into a "selection"
effect and a "complementarity" effect. We prove that both the biodiversity
effect and its statistical decomposition into selection and complementarity are
fundamentally flawed because these methods use a na\"ive null expectation based
on neutrality, likely leading to an overestimate of the net biodiversity
effect, and they fail to account for the nonlinear abundance-ecosystem
functioning relationships observed in nature. Furthermore, under such
nonlinearity no statistical scheme can be devised to partition the biodiversity
effects. We also present an alternative metric providing a more reasonable
estimate of biodiversity effect. Our results suggest that all studies conducted
since the early 1990s likely overestimated the positive effects of biodiversity
on ecosystem functioning.
