Table 1.

List of different functions to simulate the decomposition in models following the discussion of Parton et al. (2015). The publications listed refer to the example models. The abbreviations describe the carbon (C) at the start (C₀) and at a certain time (t) step (C_t), the decomposition rate (k), the Michaelis–Menten constant (K _m) and the maximum reaction velocity for the process (V _m), the carbon demand by the microbes (X ₀), the Monod constant (K _t) and the maximum growth rate (µ _max). The graphs show C_t in a time series for one set of arbitrary parameters

Approach	Equation	Graphical relation (C(t))	Example model	Publications
Zero‐order kinetics	${\mathrm{C}}_t={\mathrm{C}}_0-kt$
First‐order kinetics	${\mathrm{C}}_t={\mathrm{C}}_0{\mathrm{e}}^{-kt}$		RothC, ICBM	Jenkinson and Rayner (1977), Andrén and Kätterer (1997)
Enzyme kinetics	$\frac{\text{dC}}{\mathrm{d}t}=V_{\mathrm{m}}\frac{\mathrm{C}}{K_{\mathrm{m}}+\mathrm{C}}$		CLM, SEAM	Wieder et al. (2013), Wutzler et al. (2017)
Microbial growth	$-\frac{\text{dC}}{\mathrm{d}t}={\mu }_{max}\left(\frac{\mathrm{C}}{K_t+\mathrm{C}}\right)\left({\mathrm{C}}_0+X_0-\mathrm{C}\right)$		NICA	Blagodatsky and Richter (1998)