2.2. Model description

This protocol is extracted from research article:

Determinism of nonadditive litter mixture effect on decomposition: Role of the moisture content of litters

**
Ecol Evol**,
Jun 21, 2021;
DOI:
10.1002/ece3.7771

Determinism of nonadditive litter mixture effect on decomposition: Role of the moisture content of litters

DOI:
10.1002/ece3.7771

Procedure

The time step of all the discrete equations is the day. The relationship between the different equations is illustrated in Figure 4. Equation 1 was used to model the decomposition of OM with time (discretization of the negative exponential decay model), with parameter *k* as the decomposition rate.

*M _{t}
*

Schematic diagram showing the model relating litter water content to evaporation rate, the reaction rate to the litter water content, and the remaining mass to the change of reaction rate with time, with LWC: litter water content, *k*: decomposition rate, *M*: remaining mass, *c*, *d*, *e*: empirical parameters, and *k*
_{max}: maximum decomposition rate

To account for the effect of the properties of litter related to water content (maximum water content, varying water content with time) on the decomposition rate, the relationship between *k* and litter water content (LWC) as well as the evaporation rate was modeled. In a first step, two models of OM decomposition, which incorporate sensitivity to water content in different ways, were compared. Both models used two Michaelis–Menten equations to account for the simultaneous dependence of the biological processes on water and oxygen. The more water available, the less oxygen, and vice versa. However, the two models differ by their representation of the relationship to oxygen. The first one was derived from Moyano et al. (2013, Equation 2), which models soil OM and not specifically litter. This model assumes no biological activity at water saturation and uses oxygen as a substrate. Conversely, the Bunnell et al. (1977) model allows biological activity at water saturation. It derives from a Michaelis–Menten equation and LWC a coefficient, which describes how the gas exchange is facilitated. This coefficient is maximal at low LWC, but is not necessarily equal to zero at saturation.

with *O _{a}
* represented as follows (Equation 4):

LWC_{max} is the maximum water content for a specific litter (water saturation) and *a*, *b*, *c*, and *d* are the Michaelis–Menten constants (the LWC when the reaction rates are equal to half of the *k*
_{max}). *O _{a}
* is a coefficient calculated to allow the decomposition rate to be equal to zero at maximum LWC (when LWC = LWC

At the start of each numerical experiment, the LWC of each litter was set at its maximum (LWC_{max}). At the beginning of each time step, LWC was allowed to change depending on the evaporation rate *e* (Equation5; Figure 4a), which was allowed to differ between species (Figure 1). The calculated LWC was then injected into Equation 3 (Figure 4b) and 4 to calculate *k*
_{Bunnell} and *O _{a}
*, respectively, and then

Values of the parameters used in the Model Comparison and Rate Combinations experiments (LWC_{max} = maximum litter water content in g of water g^{−1} of dry mass, *k*
_{max} and e in d^{−1}, *a*, *b*, *c,* and *d* in g of water g^{−1} of dry mass, and n.a. = not applicable)

HIGH and low in brackets refer to the relative intensity of the different rates.

This is an open access article under the terms of the http://creativecommons.org/licenses/by/4.0/ License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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