Ecosystem model and temperature dependencies
We use Allison et al.’s (2010) microbe-enzyme model of litter decomposition to describe the ecosystem dynamics of C , D ,M , and Z , given litter input, leaching rates, and soil temperature (equations (1a-d) in Box 1, Fig. 1a and Supplementary Fig. 1). DOC uptaken by individual cells is allocated to exoenzyme production (fraction φ ) or microbial biomass, with enzyme production efficiency denoted by γ Z and microbial growth efficiency (MGE) denoted by γ M.
At the molecular and cellular level, the effect of warming on microbial decomposition is mediated by the temperature sensitivity of intra- and extra-cellular enzymatic activity (Wallensteinet al. 2009; German et al. 2012; Burns et al.2013). In the baseline ‘kinetics-only’ scenario of temperature-dependent decomposition, microbial uptake parameters (maximum uptake rate, half-saturation constant) and exoenzyme kinetics parameters (maximum decomposition rate, half-saturation constant) increase with temperature (Hochachka & Somero 2002; Davidson & Janssens 2006) in a logistic manner (equations (2a-d) in Box 1). Two other scenarios have been proposed for the influence of temperature on decomposition. In the microbial mortality scenario, the microbial death rate also increases with temperature (equation (3) in Box 1). This could be due to a higher risk of predation or pathogenic infection at higher temperatures, or faster microbial senescence due to higher protein turnover (Hagerty et al.2014). In the microbial growth efficiency (MGE) scenario, MGE (the fraction of carbon allocated to growth that actually contributes to microbial biomass, as opposed to being released as CO2via growth respiration) decreases with warming (Allison et al.2010; Wieder et al. 2013) (equation (4) in Box 1), which could be due to higher maintenance costs at higher temperature (Sinsabaugh et al.2013).
The model parameters (microbial life history parameters, thermal dependencies, enzyme parameters, carbon inputs) were constrained by experimental and observational data (Allisonet al. 2010; Allison 2012; German et al. 2012) (see Abs and Ferriere 20 for a review, Supporting Notes 2 for details and Supplementary Table 1). Within these parameter ranges, the ecosystem model outputs are consistent with target empirical values (targetC of the order of 100 mg cm-3, M about 2% of C , Z about 1% of M , and limiting Dclose to zero). (Zhanget al. 2014) (2014) provided some more direct validation by successfully fitting a CDMZ model to time series of field measurements of soil respiration from a specific ecosystem (semiarid savannah subject to episodic rainfall pulses). How scenarios of temperature-dependence and parameter values influence the response of equilibrium C to temperature is shown in Supplementary Fig. 4 and commented on in the Supplementary Note 3.