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Assume that total ecosystem productivity is determined by dominance of the most productive species, and all species responses are independent of each other and obey the same stochastic process. Further assume that the mean of the response is 1/2, as in the β-distribution (Fig. ​(Fig.33A), in which case the variance of the species response may be viewed as a measure of a species’ contribution to maximum ecosystem productivity (in this case, 1). This is because a greater variance means a greater probability of a species taking on the maximum productivity at each time. The results are summarized in Fig. ​Fig.33B. For a given species richness, as the variance of the species response increases, the temporal mean of ecosystem productivity is elevated, that is, the effect of species richness is enhanced. But as a result, the species richness beyond which the ecosystem is redundant also decreases.