Comparing models of microbial–substrate interactions and their response to warming

Abstract. Recent developments in modelling soil organic carbon decomposition include the explicit incorporation of enzyme and microbial dynamics. A characteristic of these models is a positive feedback between substrate and consumers, which is absent in traditional first-order decay models. With sufficiently large substrate, this feedback allows an unconstrained growth of microbial biomass. We explore mechanisms that curb unrestricted microbial growth by including finite potential sites where enzymes can bind and by allowing microbial scavenging for enzymes. We further developed a model where enzyme synthesis is not scaled to microbial biomass but associated with a respiratory cost and microbial population adjusts enzyme production in order to optimise their growth. We then tested short- and long-term responses of these models to a step increase in temperature and find that these models differ in the long-term when short-term responses are harmonised. We show that several mechanisms, including substrate limitation, variable production of microbial enzymes, and microbes feeding on extracellular enzymes eliminate oscillations arising from a positive feedback between microbial biomass and depolymerisation. The model where enzyme production is optimised to yield maximum microbial growth shows the strongest reduction in soil organic carbon in response to warming, and the trajectory of soil carbon largely follows that of a first-order decomposition model. Modifications to separate growth and maintenance respiration generally yield short-term differences, but results converge over time because microbial biomass approaches a quasi-equilibrium with the new conditions of carbon supply and temperature.