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.