ESS enzyme allocation fraction at given temperature
The exoenzyme allocation fraction ESS, φ *, corresponds to a maximum of microbial fitness relative to other trait values, and therefore depends on the parameters defining microbial net growth rate, i.e. MGE (γ M), maximum uptake rate (\(v_{\max}^{U}\)), mortality (d M), and local competitive advantage to exoenzyme producers, or ‘competition asymmetry’ (c 0):
(8)\(\varphi^{*}(T)=1-\frac{d_{M}}{\gamma_{\text{M\ }}v_{\max}^{U}}-\frac{1}{c_{0}}\)
Note that c 0, the degree of competition asymmetry, measures the differential availability of enzymatically produced dissolved organic carbon (DOC) to different microbial strains. Competition asymmetry is shaped by diffusion of exoenzymes and DOC, and by microbial mobility, and is thus likely influenced by soil physical properties, such as texture or moisture. For simplicity, we assume that competition asymmetry is independent of temperature.
At a fixed temperature, the model predicts that microbes invest less in exoenzymes when exposed to hostile conditions causing high mortality (d M), low MGE (γ M), low maximal uptake rate (\(v_{\max}^{U}\)), and/or low competitive advantage to producers (c 0). Conversely, microbes are selected to allocate more resource into exoenzyme production when more favourable growth conditions yield a better ‘return on investment’ (Schimel & Weintraub 2003).