. 1998 May 12;95(10):5632–5636. doi: 10.1073/pnas.95.10.5632

Table 1.

Effects of abiotic nutrient flux parameters on soil nutrient concentration below the rooting zone (R^*), plant biomass (B^*), and primary productivity (Φ^*) at equilibrium

Effect of	Type of effect
Effect of	Indirect	Direct	Net
R₀ on R^*	−	+	+
R₀ on B^* or Φ^*	+	+	+
q on R^*	−	+	+
q on B^* or Φ^*	+	− (if k low)	− (if k low)
		+ (if k high)	+ (if k high)
k on R^*	+	−	−
k on B^* or Φ^*	−	+	+

Effects are given qualitatively by the sign of the partial derivative of the ecosystem stock or process with respect to the abiotic parameter considered. Direct effects are the effects obtained when the number of species is held fixed in Eqs. 6–8. Indirect effects are the effects mediated by changes in maximum species richness (Eq. 11 or 12), assuming that species richness acts to increase plant biomass, primary productivity, and nutrient retention, as in the “complementary species” case. Net effects are the effects obtained when the number of species is at its maximum, that is, when Eq. 11 or 12 is substituted into Eqs. 6–8. The signs of the effects are identical in the two cases of “redundant” and “complementary” species. Note that the net effect always has the sign of the direct effect; only the k values required for the transition from a negative to a positive effect of q on plant biomass and productivity differ.