Effect of warming on the enzyme allocation fraction ESS
According to equation (8), the adaptive response of exoenzyme allocation to warming depends on how the MGE, maximum uptake, and mortality vary with temperature. We investigate how parameters influence the direction and sensitivity of the exoenzyme allocation fraction ESS to temperature by calculating the derivative of φ * with respect to T , for each scenario of temperature dependence (Supplementary Note 4, Supplementary Fig. 5a-d). In the baseline ‘kinetics-only’ scenario (in which \(v_{\max}^{U}\) is the only parameter in equation (8) that depends on temperature), increasing temperature creates more favorable growth conditions through higher resource uptake capacity (higher\(v_{\max}^{U}\)), which selects for higher investment in exoenzyme production (Supplementary Fig. 5a), resulting in lower equilibrium SOC. This is an evolutionary amplification of the positive feedback to warming driven by the ECOS response. Because dφ */dT is proportional to both exp(1/T ) and 1/T 2, the sensitivity of φ * to temperature is strongest across low temperatures (Supplementary Note 4, Supplementary Fig. 5a). The adaptive response is generally greatest (and the amplification of the positive climate feedback strongest) when warming enhances microbial growth potential (by increasing \(v_{\max}^{U}\)) under initially hostile conditions (high \(d_{M}\), low \(\gamma_{M}\), low \(v_{\max}^{U}\) due to low intrinsic uptake rate \(v_{0}^{U}\)and/or high activation energy\(E_{v}^{U}\), low initial temperature T 0).
In the temperature-dependent mortality scenario, both mortality and uptake respond exponentially to temperature. Microbes evolve a higher investment in exoenzyme production in response to warming if the change in resource uptake capacity remains greater than the change in mortality rate; otherwise, microbes evolve a lower investment (Supplementary Note 4 and Supplementary Fig. 5b, c). In the MGE-temperature dependent scenario, the response of φ * to temperature is proportional to the inverse of an exponential function of temperature (through the uptake rate, \(v_{\max}^{U}\)) times a linear function of temperature (through MGE) (Hagertyet al. 2014). As a consequence, at low initial temperature, the adaptive response of the allocation strategy to warming is mainly driven by the thermal dependence of resource uptake, and microbes adapt by increasing their resource investment in exoenzyme production. For ecosystems that are initially warmer, the microbial evolutionary adaptation to warming (lower allocation to exoenzymes) is mainly driven by the reduction of MGE (Supplementary Note 4 and Supplementary Fig. 5d).
We therefore conclude that microbial evolutionary adaptation to warming generally leads to larger resource allocation to exoenzyme production and a stronger positive carbon feedback to warming, with a greater response in initially colder ecosystems. There are two cases where positive soil C feedbacks to warming (due to higher enzyme kinetic rates) could be attenuated or even reversed: temperature sensitive mortality, or temperature-dependent MGE in an initially warm ecosystem (Supplementary Fig. 5c, d). Next we examine the magnitude of the amplification, attenuation, or reversal of positive carbon feedbacks to warming.