Jay T. Lennon and Kathryn L. Cottingham. 2008. Microbial productivity in variable resource environments. Ecology 89:1001–1014.

Appendix F. Labile carbon concentrations are the key to understanding the effects of variable BGE on Pulse/Press differences.

If we solve for bacterial growth efficiency BGE by substituting the equation for BC (text Eq. 4) into the equation for BGE (text Eq. 5), we can express BGE in terms of the labile carbon concentration L:

(F.1)

This indicates that BGE is a saturating function of L whose shape depends on the Michaelis-Menten parameters for both carbon uptake and BGE. If K_BGE = 0, the labile carbon concentration does not affect BGE because BGE = M_BGE.

For non-zero K_BGE, we expect BGE to increase with increased M_BGE and decrease with increased K_BGE or K_C. As M_C increases, the maximum BGE increases (the function becomes “taller”) but so does the rate of increase (the function becomes “steeper”), making it difficult to predict the effects of this parameter alone.

Based on the equation for dL/dt (text Eq. 2), we expect that Press-Pulse differences will be exacerabated by factors that create differences in the labile C concentration such that bacteria in the Pulse treatment are able to realize their maximum BGE, whereas bacteria in the Press treatment are not.

Specifically, we would expect that BP_Pulse:Press will be larger when L is much larger in the Pulse treatment; this can happen with decreased r or increased I_e (L increases with (1-r) × I_e). However, as seen in Fig. F1, the exact relationship with r and I_edepends on the values of r, I_e, I_i, and K_BGE.

Moreover, we expect smaller BP_Pulse:Press ratios when there is a larger background mineralization of refractory carbon (m) or drip of labile C (I_i), since these would be identical in the two scenarios.