Much of our knowledge on biodiversity and ecosystem functioning comes from studies examining the effects of biodiversity on biomass production within a trophic group. A large number of these studies have found that increasing biodiversity tends to increase biomass production, leading many ecologists to believe that there exists a general positive relationship between biodiversity and ecosystem functioning. Here we argue that such a positive relationship may not be general, particularly for ecosystem functions other than biomass. Our argument centers on the potential importance of the negative selection effect, which operates where competitively dominant species do not contribute significantly to the function of interest. We suggest that negative selection effects may be potentially common for non-biomass functions, for which species competitive ability may often be a poor indictor of its functional impact. We conclude that diverse (positive, negative, and neutral) BEF relationships are possible for non-biomass functions and that for a particular function, the exact form of the BEF relationship may depend on how species functional impacts relate to their competitive abilities in the community.