Fig. 1: A conceptual representation of our decomposition quantifying the difference in biomass between two sites: a reference or reference site (B) and a comparison site (F).

Notation: S_c, S_uB, and S_uF refers to the number of species: in common, unique to B and unique to F, respectively; and Z_uB, Z_cB, Z_cF, and Z_uF to average ecological function (in this example, biomass) of species: unique to B, common to both sites when present at B, common to both sites when present at F, and unique to F, respectively. The first term, RICH-L, reflects loss of species from the reference site that are most like the average of the species that are retained. In Contrast I, the comparison site lacks some species present at the reference site (left column), so the species richness is lower at the comparison site (second column). In this case, the species in common between the two sites have the same average contribution to biomass (per species) as species unique to the reference (i.e., z_cB = z_uB, third column). Thus, the difference in biomass between the two sites in Contrast I is entirely captured by the RICH-L effect (last column). The second term, COMP-L, reflects the loss of biomass beyond what is expected given the number of species lost and average per species contribution of the reference species, i.e., the shared species. Unlike in Contrast I, in the case shown for Contrast II the species unique to the reference site are larger and therefore greater contributors (per species) to total biomass than the species that are shared between sites (\({\bar{{{{{{\boldsymbol{z}}}}}}}}_{{{{{{\boldsymbol{uB}}}}}}}{{{{{\boldsymbol{-}}}}}}{\bar{{{{{{\boldsymbol{z}}}}}}}}_{{{{{{\boldsymbol{cB}}}}}}}\) = δ_B > 0). The difference in total biomass between communities in Contrast II would be captured by the COMP-L term (last column) in addition to the RICH-L term (as shown for Contrast I). The RICH-G and COMP-G terms are analogous to RICH-L and COMP-L but arise from species that are present in the comparison site and absent from the reference (as illustrated in Contrasts III and IV). The final term, the “context-dependent effect” or CDE, considers only the species shared among both the reference and comparison sites. Differences in the contributions of shared species among the two sites reflect processes other than changes in richness and composition, such as changes in per species biomass, community size structure, resources, or the abiotic environment (e.g., temperature). In Contrasts I-IV, the shared species did not differ in their average per species contribution between the two sites (i.e., z_uF = z_cB) so there was no CDE. In Contrast V, the shared species differ in their average per species contribution to biomass, resulting in a nonzero CDE. In a real comparison, all five components can occur simultaneously. The five components sum to the observed difference in biomass between the reference and comparison communities.