*2.3. Data Analysis*

The mean temperature and frequency of the freeze–thaw cycles of each forest gap were calculated in each decomposition stage using the every 2 h temperature data in situ. Freezing and thawing in the non-growing season are important physical processes that impact below-ground ecological functions in alpine forests. We calculated the freeze–thaw cycles per day during each decomposition period; one freeze–thaw cycle was defined as the temperature increasing above 0 ◦C or decreasing below 0 ◦C for 3 h or more, followed by a decrease below 0 ◦C or an increase above 0 ◦C for at least3h[42].

The litter mass loss (*ML*, %) and carbon release (*CR*, %) were calculated as follows:

$$ML\_t = (M\_0 - M\_t) / M\_0 \times 100\%$$

$$\mathbb{C}R\_l = (\mathbb{C}\_{l\text{-}1} \times M\_{l\text{-}1} - \mathbb{C}\_l \times M\_l) / (\mathbb{C}\_0 \times M\_0) \times 100\%$$

where *M*0 (g) and *Mt* (g) are the litter's remaining mass in the litterbags at the initial and sampling times, respectively; *C*0 (g·kg−1), *Ct* (g·kg−1) *Ct-*1 (g·kg−1) are the litter carbon content at the initial, sampling and previous sampling times, respectively. All analyses were conducted in triplicate.

The Olson exponential decay model [43] was used to fit the relationship of litter remaining mass and decomposition year:

$$M\_t = M\_0 \cdot e^{-kt}$$

where *M*0 is the litter initial dry mass; *e* is a natural constant; *k* is the litter decomposition constant; *t* is the decomposition year; *Mt* is the litter's remaining mass at *t*.

In this study, gap size (with three sizes and closed canopy) was a main-plot factor, elevation (with three elevations) was a sub-plot factor, and decomposition time (with sixteen stages) was a sub-subplot factor.

A two-way ANOVA (with the LSD post hoc test) was used to examine the differences of litter decomposition constant (*k*) generated from the Olson exponential decay model, mass loss, carbon content and release both among the gap sizes and elevations. Linear mixed models were conducted to analyze the effects of gap size, elevation, decomposition time and their interaction on litter mass loss, carbon content and release; the bags within gap sizes were set as random effects. All data were subjected to a normality test and homogeneity of variance test prior to the analysis of variance. Multiple non-linear regressions were conducted to evaluate the links of the litter's remaining mass and carbon content from the scales of gap size and elevation. Spearman correlation analysis was performed to describe the relationship between mean temperature, freeze–thaw cycles and litter mass loss, carbon release in the non-growing season, growing season and the whole four decomposition years. All statistical analyses were performed using SPSS 27.0 (SPSS Inc., Chicago, IL, USA) and Prism GraphPad 8.0 (GraphPad Software Inc. San Diego, CA, USA).
