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).