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Appendix S1. Supporting text and information on monoculture variation.

Appendix S2. Supporting text and information on the methods and analyses.

Fig. S1. Ratio values of mixture/monoculture for total yield and yield of sown species.

Fig. S2. Relationship between the diversity effect and evenness for annual yield of sown species.

Table S1. Detailed information on sites and species.

Table S2. The relative abundances of communities used in the simplex design.

Table S3. Analysis of total annual yield: model selection.

Table S4. Analysis of total annual yield: parameter estimates.

Table S5. Analysis of annual yield of sown species: model selection.

Table S6. Analysis of annual yield of sown species: parameter estimates.

Table S7. Analysis of mean yield (averaged across 3 years) of sown species.

Table S8. Further information on switching of the identity of the best-performing monoculture.

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