Partitioning of biodiversity effects
The net biodiversity effect (BE) of a polyculture mesocosm was measured by the difference between the observed yield and its expected yield, which was generated by a species proportional abundance multiplied by biomass estimated in monoculture. CE was the average performance of species above or below their expected performance. SE was measured by the covariance between the monoculture yield of species and their change in relative yield in the mixture. These various effects can be related by an additive partition (Loreau & Hector 2001):
\begin{equation} BE=CE+SE=N\ \overset{\overline{}}{{RY}_{i}}\ \overset{\overline{}}{M_{i}}+N\ cov({RY}_{i},M_{i})\nonumber \\ \end{equation}
where i was the component species in the mixture, N was the number of component species, ΔRYi was the deviation from expected relative abundance of species i in the mixture, and Mi was the yield of species iin its monoculture. Positive CE indicates that species yields in a mixture are on average higher than expected values of the component species (the weighted average monoculture yields), and positive SE indicates that species with higher-than-average monoculture yields dominate the mixture.