Experiments on biodiversity have shown that productivity is often a deceleratingmonotonic function of biodiversity. A property of nonlinear functions, known asJensen’s inequality, predicts negative effects of the variance of predictor variables on themean of response variables. One implication of this relationship is that an increase inspatial variability of biodiversity can cause dramatic decreases in the mean productivityof the system. Here I quantify these effects by conducting a meta-analysis ofexperimental data on biodiversity-productivity relationships in grasslands and using theempirically derived estimates of parameters to simulate various scenarios of levels ofspatial variance and mean values of biodiversity. Jensen’s inequality was estimatedindependently using Monte Carlo simulations and quadratic approximations. The medianvalues of Jensen’s inequality estimated with the first method ranged from 3.2 to 26.7%,whilst values obtained with the second method ranged from 5.0 to 45.0%. Meta-analysesconducted separately for each combination of simulated values of mean and spatialvariance of biodiversity indicated that effect sizes were significantly larger than zero in allcases. Because patterns of biodiversity are becoming increasingly variable under intenseanthropogenic pressure, the impact of loss of biodiversity on productivity may be largerthan current estimates indicate.
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