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.