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Calculation of Q10 values
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Temperature sensitivity of SOM decomposition governed by aggregate protection and microbial communities

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We adopted three methods to calculate Q10 values for bulk soil and various SOM components. First, Q10 for bulk soil was calculated according to the decomposition rate at two incubation temperatures$Q10=(Rw/Rc)[10/(Tw−Tc)]$(1)where Rw and Rc denote the average rate of SOM decomposition at the warmer and colder temperature (mg CO2-C g−1 SOC day−1), respectively. Tw and Tc represent the warmer and colder temperature (°C). Q10 obtained by this method was referred to as bulk soil Q10.

Second, the Q10-q method, which is based on the measured cumulative percentage of soil C respired during incubation, was applied to calculate the Q10 values of different SOM fractions (22)$Q10−q=(tc/tw)[10/(Tw−Tc)]$(2)where tc and tw are the time needed to decompose a given soil C fraction at the colder and warmer temperature (day), respectively. Tw and Tc 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 Q10 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 Q10 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)$R(t)=∑i=12kifiCtote−kit$(3)$Q10i=(ki(Tw)ki(Tc))10Tw−Tc$(4)$f1+f2=1$(5)where R(t) is the measured decomposition rate at time t (mg CO2-C g−1 SOC day−1). Ctot denotes the initial SOC content (i.e., 1000 mg C g−1 SOC), k1 and k2 are the decay rates of active and slow pool (day−1), and f1 and f2 denote the fractions of the active pool and slow pool. $Q101$ and $Q102$ represent Q10 in the active pool and slow pool. ki(Tw) and ki(Tc) are the decay rates at the warmer (Tw) and colder (Tc) temperature, respectively. Before modeling, the prior range of the five parameters (k1 and k2 at 10°C, $Q101$, $Q102$, and f1; table S4) was set on the basis of previous studies (17, 50) and then determined by a Markov chain Monte Carlo (MCMC) approach as follows (26): Probabilistic inversion approach based on Bayes’ theorem (Eq. 6) was applied to optimize parameters (θ) in the model. In this approach, the posterior probability density function (PDF) P(θ|Z) was acquired from the prior knowledge of parameters and the information of incubation data, represented by a prior PDF P(θ) and a likelihood function P(Z|θ), respectively$P(θ∣Z)∝P(Z∣θ)P(θ)$(6)

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$P(Z∣θ)∝exp{−∑i=12∑tϵobs(Zi)[Zi(t)−Xi(t)]22σi2(t)}$(7)where Zi(t) and Xi(t) denote the measured and modeled data, and σi(t) represents the SD of the measurements. Metropolis-Hastings (M-H) algorithm, an MCMC technique, was used to complete the construction of P(θ|Z) of parameters (51, 52).

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