### Study site and soil sampling

This study has been carried out in the Taiyueshan Long-Term Forest Ecology Research Station, which is located at the National Forest Park of Lingkongshan (36°33′–36°42′ N, 111°59′–112°07′ E; elevation ranging from 1100 to 1950 m a.s.l.). This forest park is located about 200 km southwest of Taiyuan in the Shanxi Province of northern China. The geographic and meteorological conditions and species composition of the forest communities for this study area had already been introduced in detail by (Zhou et al. 2013). The tree species extensively distributed across this forest park are *Pinus tabulaeformis* Carrière, *Quercus wutaishanica* Mayr, *Betula dahurica* Pall, *Betula platyphylla* Suk, *Juglans mandshurica* Maxim, *Tilia mongolica* Maxim, *Populus davidiana* Dode, *Malus baccata* Borkh. The major shrub species are *Corylus mandshurica* Maxim, *Corylus heterophylla* Fisch, *Acer ginnala* Maxim, *Lespedeza bicolor* Turcz, *Philadelphus incanus* Koehne, *Rosa bella* Rehd. The herbaceous community mainly consists of *Carex lanceolata* Boott, *Spodiopogon sibiricus* Trin, *Rubia chinensis* Regel et Maack, *Thalictrum petaloideum* Linn, *Melica pappiana* Hempel.

Five forest plots of 20 m × 20 m were established in 2013, for each of three forest types: a *Pinus tabulaeformis* forest, a *Quercus wutaishanica* forest, and a mixed forest of *P. tabulaeformis* and *Q. wutaishanica.* The plots were laid out along the topography of the Xiaoshegou catchment area, at a distance of 3 km west of the research station. Five soil samples at 20 cm depth were taken using a 4-cm diameter soil auger to assess the soil condition of each forest plot in late August; these samples were then mixed and combined into a single sample after passing through a 2 cm sieve screen to separate rocks and debris. Each composite soil sample was separated into two sub-samples. One sub-sampled was transported in an ice-cooled container to the Key Laboratory for Forest Resources & Ecosystem Processes of the Beijing Forestry University. Soil physicochemical properties were analyzed with air-dried soil of 20 g being ground and passed through a 0.18-mm sieve screen. SOC content was analyzed via the standard Mebius method (Nelson and Sommers 1982). TN content was analyzed following the Kjeldahl digestion procedure and ammonium nitrogen (NH_{4} - N) was colorimetrically measured by the alkali method with a Tector KJeltec 1025 Distilling system (Gallaher et al. 1976). The soil pH was measured in deionized H_{2}O with a water to soil ratio of 2.5:1 using the Sartorius AG method (PB-10, Sartorius, Germany). The water holding capacity (WHC) was determined by saturating 20 g fresh soil above a filter paper in a 10-cm glass funnel, and then permitting the water to drain for 4–6 h before being weighed (*n* = 5). The saturated soils were then oven-dried at 105 °C to a constant mass, until the WHC was equal to the percentage of water retained after several hours’ drainage (for 100% WHC). Soil microbial biomass carbon and nitrogen contents were measured using the chloroform-fumigation method with a mean calibration factor *k*_{C} of 0.38 (Vance et al. 1987a, 1987b). Concurrently with soil sampling, soil bulk density was measured by dividing the mass of oven-dried soil (at 105 °C) by the cylinder volume (100 cm^{3}) after subtracting the detritus volume for each forest plot.

### Incubation and measurement of SOC mineralization rate

The second sub-sampled soil was immediately (< 2 d) delivered in a cooler with blue ice to the Key Laboratory of Ecosystem Network Observation and Modeling, Chinese Academy of Sciences. The sub-sampled soil of each forest plot was divided into eighteen 40 g equivalent aliquots; the soil moisture content (SMC) of every six aliquots was individually adjusted to 30, 60 and 90% WHC. The moisture-adjusted soil samples were placed in 200 cm^{3} plastic flasks with lids perforated to allow gas diffusion, and connected directly to the CO_{2} measurement system. After getting static and equilibrated for 5 days, six soil samples separately at 30, 60 and 90% of WHC for each forest plot were respectively incubated for 387 days in a microcosm with temperatures of 5 °C, 10 °C, 15 °C, 20 °C, 25 °C and 30 °C and a stable air moisture content (*n* = 5 per incubator). To prevent anaerobiosis, the perforated hole of the flask lid was not sealed until 24 h before the measurement of soil organic carbon mineralization rate. Throughout the whole incubation period, the flask was periodically weighed and the required proportion of deionized water was added to maintain soil moisture content at 30%, or 60%, or 90% of WHC.

The measurement of SOC mineralization started at different time intervals after the equilibrated soil samples had been incubated in microcosms. The instantaneous rate of SOC mineralization was measured as CO_{2} efflux from soil within flask on day 1, 3, 5, 8, 16, 23, 29, 36, 43, 57, 75, 118, 151, 180, 225, 252, 293, 361, 387 in sequence. Sixteen flasks of soil samples were placed in an electronic water bath at the same temperature as that at which the soil samples were incubated. These flasks were connected to a PRI-8800 Automatic Temperature Control Soil Flux System (PRI-8800; Pre-Eco, Beijing, China). This automated system was mainly composed of a Li-Cor CO_{2} analyzer (Li-7000), an air-flow controller, soda-lime equipment to manipulate the initial CO_{2} concentration, and a data collector. Comprehensive information and the schematic configuration of this automated system were introduced in detail by He et al. (2013). The SOC mineralization rate was estimated using the following equation:

$$ {R}_s=\left(L\times V\times \alpha \times \beta \right)/m $$

(1)

where *R*_{
s
} represents the instantaneous rate of SOC mineralization (μg C∙g^{− 1} soil∙h^{− 1}); *L* refers to the slope of the CO_{2} concentration; *V* is the volume of the incubation flask and gas tube (cm^{3}); *m* is the dry weight of the soil sample (g); *α* is the transformation parameter of the CO_{2} mass; *β* is the transformation coefficient of time.

Based on the SOC mineralization rate, the cumulative mineralized SOC for a specific period of time was also calculated following the empirical function below.

$$ {C}_{cum}=1/{SOC}_f\times \sum \left\{\left({R}_{si}+{R}_{s\left(i+1\right)}\right)\times \left({t}_{i+1}-{t}_i\right)/2\right\} $$

(2)

where C_{
cum
} *C*_{
cum
} is the cumulative mineralized SOC (mg C∙g^{− 1} SOC); *SOC*_{
f
} *SOC*_{
f
} refers to soil organic carbon content (g∙kg^{− 1}) for the corresponding forest plot; *R*_{
si
} and *R*_{s(i + 1)} are the instantaneous rates of SOC mineralization measured consecutively at time *i* and *i* + 1, as calculated by Eq. (1).

### Calculation of soil carbon fractions

Different soil carbon pools were estimated by the first-order kinetic one-compartment and two-compartment models based on the relationship of cumulative mineralized SOC and the time length of the incubation period. Firstly, the potentially mineralizable carbon pool in soil was calculated via fitting the mean cumulative mineralized carbon data at a different incubation temperature and moisture for each forest type to the following model (Sanford and Smith 1972; Rey and Jarvis 2006):

$$ {C}_{cum}(t)={C}_0\times \left(1-{e}^{-{k}_0t}\right) $$

(3)

where *C*_{
cum
}(*t*) is the mean cumulative mineralized SOC until time *t* (mg C∙g^{− 1} SOC), *C*_{0} is the ‘potential’ mineralizable C (mg C∙g^{− 1} SOC), *k*_{0} is the decomposition rate constant for mineralization carbon (day^{− 1}), and *t* is the incubation time (day).

Secondly, the first-order two-compartment model was applied to calculate labile carbon fraction and recalcitrant carbon fraction (Andrén and Paustian 1987; Rey and Jarvis 2006). This equation was displayed as below:

$$ {C}_{cum}(t)={C}_1\times \left(1-{e}^{-{k}_1t}\right)+{C}_2\times \left(1-{e}^{-{k}_2t}\right) $$

(4)

where *C*_{
cum
}(*t*) is the mean cumulative carbon mineralized during the incubation period time *t* (mg C∙g^{− 1} SOC), *C*_{1} is the labile carbon fraction (mg C∙g^{− 1} SOC), *C*_{2} is the recalcitrant carbon fraction (mg C∙g^{− 1} SOC), *k*_{1} and *k*_{2} are the first-order kinetic decomposition rate constants for the labile and recalcitrant carbon fractions (day^{− 1}) respectively. The cumulative mineralized SOC (the emitted CO_{2}) is expressed on a basis of SOC content (mg C∙g^{− 1} SOC) when fitting models (3) and (4) to the incubation data, and the modeled result essentially represents the SOC fraction that was mineralized. More detailed information about the law to employ these models may be found in Rasmussen et al. (2006) and Rey and Jarvis (2006).

In order to get the reasonable parameters from functions (3) and (4), several criteria were set up: that (i) *k*_{0} and *k*_{1} were larger than 0, and that (ii) *k*_{1} was larger than *k*_{2}, and that (iii) *C*_{0}, *C*_{1} and *C*_{2} were larger than zero. Additionally, one assumption was followed that (*C*_{1} + *C*_{2}) was equal to 1000 mg C∙g^{− 1} SOC (i.e. the two carbon fractions add up to the total amount of initial organic carbon in the sample). Based on the functions (2), (3) and (4) and the estimations of different carbon pools, the quantity of mineralized recalcitrant carbon was assumed to be the difference between the total amount of mineralized carbon and that of *C*_{0} (potential mineralizable C) or *C*_{1} (labile carbon fraction). In the present study, *C*_{0} was used to estimate the amount of mineralized recalcitrant carbon, as most *C*_{1} could not meet the criterion (iii) at a moisture content of 30% for all forest types (Additional file 1).

### Statistical analyses

The data presented in the tables and figures represent the mean value under different incubation conditions for each forest type. The differences of soil carbon pools for various incubation conditions and forest types were tested using one way ANOVA or multi-factor analysis of variance. Equations (3) and (4) were fitted using non-linear regression analysis (‘*nls*’ of R language). The starting value for each parameter was obtained from the published literature. Canonical correspondence analysis (CCA) was applied using the function ‘*cca*’ in the vegan package of R. All of the statistical analyses were done using the software R3.4.0. The figures in this paper were compiled using SigmaPlot 10.0 and R software.