Calculation of Q10 values

SQ Shuqi Qin LC Leiyi Chen KF Kai Fang QZ Qiwen Zhang JW Jun Wang FL Futing Liu JY Jianchun Yu YY Yuanhe Yang

This protocol is extracted from research article:

Temperature sensitivity of SOM decomposition governed by aggregate protection and microbial communities

**
Sci Adv**,
Jul 10, 2019;
DOI:
10.1126/sciadv.aau1218

Temperature sensitivity of SOM decomposition governed by aggregate protection and microbial communities

Procedure

We adopted three methods to calculate *Q*_{10} values for bulk soil and various SOM components. First, *Q*_{10} for bulk soil was calculated according to the decomposition rate at two incubation temperatures$${Q}_{10}={({R}_{\mathrm{w}}/{R}_{\mathrm{c}})}^{[10/({T}_{\mathrm{w}}-{T}_{\mathrm{c}})]}$$(1)where *R*_{w} and *R*_{c} denote the average rate of SOM decomposition at the warmer and colder temperature (mg CO_{2}-C g^{−1} SOC day^{−1}), respectively. *T*_{w} and *T*_{c} represent the warmer and colder temperature (°C). *Q*_{10} obtained by this method was referred to as bulk soil *Q*_{10}.

Second, the *Q*_{10-q} method, which is based on the measured cumulative percentage of soil C respired during incubation, was applied to calculate the *Q*_{10} values of different SOM fractions (*22*)$${Q}_{10-q}={({t}_{\mathrm{c}}/{t}_{\mathrm{w}})}^{[10/({T}_{\mathrm{w}}-{T}_{\mathrm{c}})]}$$(2)where *t*_{c} and *t*_{w} are the time needed to decompose a given soil C fraction at the colder and warmer temperature (day), respectively. *T*_{w} and *T*_{c} denote the warmer and colder temperature (°C). In this study, we chose the upper limit of soil C fraction according to the lowest cumulative percentage of respired C at 10°C (3.9%; fig. S3), which was within the range of previous incubations (0.4 to 17.0%) based on the same temperature and the approximate duration (*48*, *49*). According to a previous study (*16*), we then set the size of the fractions as 0.5% of total soil C and estimated *Q*_{10} values for three fractions of soil C (i.e., 1 to 1.5%, 2 to 2.5%, and 3 to 3.5% of cumulative respired soil C), which represent a gradient of decreasing substrate lability.

Last, we used a two-pool (that is, active and slow pools with different turnover times) model to estimate *Q*_{10} for each C pool using data from our 330-day incubation experiment. The two-pool model performed well in simulating the soil C flux (fig. S4) and was applied to each sample at the two temperatures as follows (*26*)$${R}_{(t)}={\displaystyle \sum _{i=1}^{2}}{k}_{i}{f}_{i}{C}_{\text{tot}}{e}^{-{k}_{i}t}$$(3)$${Q}_{10}^{i}={\left(\frac{{k}_{i}({T}_{\mathrm{w}})}{{k}_{i}({T}_{\mathrm{c}})}\right)}^{\frac{10}{{T}_{\mathrm{w}}-{T}_{\mathrm{c}}}}$$(4)$${f}_{1}+{f}_{2}=1$$(5)where *R*_{(t)} is the measured decomposition rate at time *t* (mg CO_{2}-C g^{−1} SOC day^{−1}). *C*_{tot} denotes the initial SOC content (i.e., 1000 mg C g^{−1} SOC), *k*_{1} and *k*_{2} are the decay rates of active and slow pool (day^{−1}), and *f*_{1} and *f*_{2} denote the fractions of the active pool and slow pool. ${Q}_{10}^{1}$ and ${Q}_{10}^{2}$ represent *Q*_{10} in the active pool and slow pool. *k _{i}*(

To calculate the likelihood function *P*(*Z*|θ), we assumed that errors between modeled and observed values followed a multivariate Gaussian distribution with a zero mean$$P(Z\mid \mathrm{\theta})\propto \text{exp}\{-{\displaystyle \sum _{i=1}^{2}}{\displaystyle \sum _{t\mathrm{\u03f5obs}({Z}_{i})}}\frac{{[{Z}_{i}(t)-{X}_{i}(t)]}^{2}}{2{\mathrm{\sigma}}_{i}^{2}(t)}\}$$(7)where *Z _{i}*(

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