A new parsimonious approach to modelling soil microbial respiration

Soil microbes are essential to the turnover of the soil organic matter, being involved in the intricate processes of the global carbon and nutrient cycles, hence regulating climate and pedogenesis, which in turn affects plant growth and ecosystem dynamics. Assays of soil functioning such as substrate-induced respiration give access to microbial activity and substrate uptake levels and allows elucidating the biogeochemical pathways of organic matter decomposition and mineralisation. Here we investigate the effects on the soil respiration response of different land-use histories corresponding to long-term grass, arable or fallow by revisiting previous experimental work. We use high temporal-resolution respirometery datasets from the incubation of small soil samples (0.5 g, 4 replicates) collected on experimental plots from the Rothamsted Highfield long term experiment. For each land-use history, the soil respiration rate was measured using a conductimetric respirometer for about 90 hours at 6-minute intervals. Distinct respiration responses are observed depending on whether soils experienced continuous long-term land-use, or transitions from arable to grass or vice versa. Typically grassland soils show an initial exponential-looking decay of the respiration rate followed by a wide respiration pulse with bell-shape characteristics. Fallow soils usually do not exhibit this initial decay phase, while arable soils present oscillations, intermediate between grass and fallow.

Good fits of these data were obtained from developing a parsimonious mathematical model of microbial growth consisting of a set of coupled non-linear differential equations determining the time evolution of the amounts of substrate and microbial biomass in terms of carbon mass concentration, assuming that only an active fraction of the biomass can grow, while its inactive counterpart uses part of the substrate only for its maintenance needs. Our model reveals that the soil respiration rate is governed by three successive phases. For grassland especially, the initial decay originates from the maintenance respiration of the inactive biomass. This is followed by the growth of the active biomass. The last phase results from the microbial biomass degradation once most of the substrate has been consumed. Dimensional analysis of this nonlinear system shows that the dynamics are primarily determined by a single dimensionless parameter, say ρ, which is the ratio of the rate of catabolism to the rate of anabolism. Preliminary results show that the different land uses are clearly distinguished with the hierarchy ρ_grass > ρ_arable > ρ_fallow > 1. This suggests that grass soils promote a faster turnover of the microbial biomass, than arable and fallow soils.