Comparing a single high-diversity mixture with all its component species in monocultures

It has been suggested that biodiversity experiments should be designed such that the productivity of a high-diversity mixture of N species can be compared with the productivities of all N monocultures. However, this leads to unequal replication of species richness levels (n = 1 for mixture and n = N for monocultures). Assuming a normal distribution of monoculture productivities, the expected value of the highest-yielding species is D = SD * ND(1-(1/N)/2). SD is the standard deviation of species yields in monoculture and ND is the standard normal deviate (in Excel: NORMINV). For example, if N = 10 and SD = 150 g/m² (a typical value for grassland species), then D = 150 g/m² * ND(0.95) = 150 g/m² * 1.64 = 246.7 g/m². It follows that by making the suggested comparison between many monocultures and a single high-diversity mixture, the mixture must yield much more than the AVERAGE monoculture to reach the BEST monoculture. A review of biodiversity experiments showed that the BEST monoculture species often yields about the same as the mixture. This implies that the so-called net biodiversity effect (NE) is similar in size to D. Interestingly, in no case the similarity NE ≈ D could be explained by a conversion of the mixture into the best monoculture. Rather, the mixtures remain mixtures, with several species contributing to the positive NE in a complementary way. Caution is required with unequal replication in biodiversity experiments, in particular if the analysis is not restricted to one using only averages.