Ecosystem response (ECOS) and ecosystem evolutionary response (EVOL) to warming
As temperature rises from T 0 to T , the direction and magnitude of the microbial adaptive response is measured by\(\varphi=\varphi^{*}\left(T\right)-\varphi^{*}\left(T_{0}\right)\), which depends on the scenario of temperature dependence. The ecosystem-evolutionary response (EVOL response) of SOC is given by
(9) EVOL response = ΔC EVOL(T0 , T ) = C (T ,φ *(T )) – C (T0 ,φ *(T0 ))
where C (T , φ ) denotes ecosystem equilibriumC at temperature T , given enzyme allocation fractionφ . The EVOL response is to be compared with the response in the absence of evolution (ECOS response):
(10) ECOS response = ΔC ECOS(T 0, T ) = C (T ,φ *(T 0)) –C (T 0,φ *(T 0))
in which the enzyme allocation fraction is fixed at itsT 0 -adapted value,φ *(T 0) (Fig. 1c).
We measure the magnitude of the evolutionary effect (EVO effect) as the difference between the EVOL response averaged over the temperature range (T 0, T ) and the ECOS response averaged over the same temperature range, normalized by the ECOS response:
(11) EVO effect =\(\frac{\left|\int_{T_{0}}^{T}{}C_{\text{EVOL}}(T_{0},T)-\int_{T_{0}}^{T}{}C_{\text{ECOS}}(T_{0},T)\right|}{\left|\int_{T_{0}}^{T}{}C_{\text{ECOS}}(T_{0},T)\right|}\)
This evaluation allows us to compare EVO effects across systems that differ in the magnitude of their ECOS response. In all simulations we use \(T=T_{0}+\Delta T\) where ΔT = 5 °C. In general, the ECOS and EVOL responses are monotonic, close-to-linear functions ofT over the considered temperature ranges\((T_{0},\ T_{0}+\Delta T)\), which makes all our comparative analyses almost insensitive to our choice of ΔT .