Partitioning of net diversity effects
By calculating net diversity effects ΔY as defined above, we were able to apply an additive partitioning approach (Loreau & Hector 2001) that separates complementarity effects (CE) from selection effects (SE) as
\(Y=Y_{O}-Y_{E}=N\ \overline{{RY}_{i}}\ \overline{M_{i}}+\text{N\ cov}\left({RY}_{i},M_{i}\right)=CE+SE\),
with N being the species richness of the mixture, ΔRYibeing the deviation of the observed relative productivity from the expected relative productivity of species i, and Mibeing the absolute monoculture productivity of species i. Complementarity effects quantify the average difference in productivity of the considered producer species mixture as compared to its monocultures, whereas selection effects quantify a possible bias towards better or worse than average performing monoculture species. To successfully calculate complementarity and selection effects for a given mixture, it was necessary to know the productivity of all its monocultures. Thus, we could not calculate them for mixtures that contained producer species with unviable monocultures that lead to global extinctions when simulated.