To quantify the influences of different factors onτ _e,C, τ _e,N andτ _e,P, we grouped those factors into four groups: climate, vegetation, soil and terrain (see Table S3), and estimated the contributions by each group to the total variance in the estimatedτ _e,C, τ _e,N andτ _e,P among the 127 forest sites, respectively. Those four groups together explained 57%, 79% and 45% of the variances of the estimated τ _e,C,τ _e,N and τ _e,P (see Fig. 3a-c). For individual effects, the greatest contributor was climate forτ _e,C (21%) and τ _e,N(14%), but was soil for τ _e,P (16%). Soil was the second largest contributor to the variance ofτ _e,C through its individual effect and interaction with climate, and terrain had the smallest influence on the variance of the τ _e,C. Vegetation, soil and terrain contributed equally to the variance ofτ _e,N through their direct effects and interactions with others. For τ _e,P, vegetation was the smallest contributor, and soil and terrain had similar influences, and interactive effect of climate and terrain was strongest.

Given the importance of climate to all three mean ecosystem residence times, we further analysed the correlations betweenτ _e,C,τ _e,N or τ _e,P and different climate variables (see Fig. 5), and found that correlation coefficients were highest with T _min. Correlations were also significant with MAT and MAP for τ _e,C,τ _e,N and τ _e,P because of the significant correlations between T _min and MAT or MAP (see Figure S1).

For ecosystem C, C input increased linearly withT _min with no significant difference in its response to T _min betweenT _min < 1.5 ℃ andT _min > 1.5 ℃ (see Fig. 4a), whereas responses of both ecosystem C pool size and τ _e,Cto T _min decreased linearly with an increase inT _min when T _min was below their respective breakpoint (-0.9 ℃ for τ _e,C, 1 ℃ for ecosystem C pool), but increased with T _minwhen T _min was above their respective breakpoint (see Fig. 4d and 4g), and those changes in the responses below and above the breakpoints were statistically significant. The change in the direction of τ _e,C largely resulted from the change of the sensitivity of ecosystem C pool size rather than NPP, as the breaking point for NPP was insignificant (see Fig. 4a).

For ecosystem N, only the sensitivity of N input (deposition and biological N fixation) to T _min had a breaking point at T _min of -6.9 ℃ (see Fig. 4b), the sensitivities of both ecosystem N and τ _e,Ndecreased with an increase in T _min without a significant breaking point (see Fig. 4e and 4h).

For ecosystem P, the sensitivity of external P input (deposition and weathering) increased with T _min whenT _min < -2.5 ℃, but decreased with an increase in T _min when T _min> -2.5 ℃ (see Fig. 4c), and the sensitivity of ecosystem P pool size varied with T _min with two breaking points at T _min = -12.9 ℃ and -2.1 ℃, see Fig. 4f), and both breaking points were statistically significant (p< 0.05). τ _e,P decreased with an increase in T _min when T _min< 0.2 ℃, and increased with T _min whenT _min > 0.2 ℃ (see Fig. 4i).