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Diversity effects were quantified with two complementary metrics. First, for each experiment i, we calculated the proportional difference in the response variable y between the mean value of the most species-rich polyculture p- and the mean value of these same species grown in monoculture  m- as the log response ratio LRm- = ln (yip- /yim-). This unitless metric allows us to test whether there is a significant change in y with increasing richness when averaged across all species used in an experiment. We then calculated a complementary metric that quantifies the proportional difference between the mean value of the most species-rich polyculture and that of the taxon having the highest (lowest) mean value of y in monoculture m ¡¯ ,m, as LRm ¡¯ = ln (yip- /yim¡¯), where yim ¡¯is the highest (lowest) value when LRm->0(<0). Testing whether LRm ¡¯>0 is analogous to tests for ¡®transgressive¡¯ overyielding, which are widely used to assess whether diverse polycultures are any more productive than the single most productive species.
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