By assuming steady state, we calculated τ _e,C,τ _e,N or τ _e,P as the ratio of total pool size and input flux for C, N or P. NPP and seven model parameters for each site were estimated by applying optimization (see Supplementary Methods) to the framework based on mass balance (see Wanget al. (2018b) and Methods). Agreement is good between the simulated pool sizes by the optimized models and the observed values for biomass pools (r² = 0.926-0.981), litter C pool (r² = 0.932), and soil N (r² = 0.822) and P pools (r² = 0.827) (see Figure S2).

Among different forest types, ecosystem inputs of C (NPP, 669 g C m^-2 yr^-1) and N (6.0 g N m^-2 yr^-1) of EBF were the greatest, while external input of P (0.13 g P m^-2yr^-1) of DBF was the greatest. Biomass C (9964 g C m^-2), plant N uptake (12 g N m^-2yr^-1) and biomass N (96 g N m^-2) in EBF were the greatest. Plant P uptake (0.47 g P m^-2yr^-1) and biomass P pool (5.8 g P m^-2) of SMF were the smallest. Soil C (17480 g C m^-2) and N (1949 g N m^-2) pools were greatest in TENF, while soil P pool (324 g P m^-2) was greatest in TMF (see Table 1).

Across the latitudes, τ _e,C significantly increased with latitude quadratically (see Fig. 2a), andτ _e,N and τ _e,Psignificantly increased with latitude linearly (see Fig. 2b-c). Among the different forest types, SMF had the shortestτ _e,C, EBF had the shortestτ _e,N and τ _e,P, and TMF or TENF had the longest τ _e,C,τ _e,N and τ _e,P (see Fig. 2, Table 1). Variations of τ _e,C andτ _e,P were greatest in DBF around 35^oN, and in TMF around 45^oN.