*Ecological Archives*
E092-116-A3

**John Connolly, Marc W. Cadotte, Caroline Brophy, Áine Dooley, John Finn, Laura Kirwan, Christiane Roscher, and Alexandra Weigelt**. 2011. **Phylogenetically diverse grasslands are associated with pairwise interspecific processes that increase biomass**. *Ecology* 92:1385–1392.

Appendix C. Calculation of the standard deviation of the variable C_{D} across all communities at a given level of richness.

At a given level of richness (t) the value of C_{D} will vary depending on the identity and relative abundances of the species in the community and its effect for a community can be estimated from the sown relative abundance of species in the community using equation [4]. The following allows us to estimate the broad effect of community phylogenetic diversity on differences between communities at the same level of richness. For a design in which all component species in a community have the same relative abundance, the average and standard deviation of C_{D} across all possible communities of richness t are 0 and respectively, where SD(D_{ij}) is the standard deviation of all D_{ij} distances and (s-t)/(s-1) is a finite sampling correction.

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