Oscillatory behavior of two nonlinear microbial models of soil carbon decomposition

Abstract

Abstract. A number of nonlinear models have recently been proposed for simulating soil carbon decomposition. Their predictions of soil carbon responses to fresh litter input and warming differ significantly from conventional linear models. Using both stability analysis and numerical simulations, we showed that two of those nonlinear models (a two-pool model and a three-pool model) exhibit damped oscillatory responses to small perturbations. Stability analysis showed the frequency of oscillation is proportional to √ (ϵ −1−1)Ks/Vs in the two-pool model, and to √ (ϵ −1−1)Kl/Vl in the three-pool model, where ϵ is microbial growth efficiency, Ks and Kl are the half saturation constants of soil and litter carbon, respectively, and Vs and Vl are the maximal rates of carbon decomposition per unit of microbial biomass for soil and litter carbon, respectively. For both models, the oscillation has a period between 5 and 15 yr depending on other parameter values, and has smaller amplitude at soil temperatures between 0 °C to 15 °C. In addition, the equilibrium pool sizes of litter or soil carbon are insensitive to carbon inputs in the nonlinear model, but are proportional to carbon input in the conventional linear model. Under warming, the microbial biomass and litter carbon pools simulated by the nonlinear models can increase or decrease, depending whether ϵ varies with temperature. In contrast, the conventional linear models always simulate a decrease in both microbial and litter carbon pools with warming. Based on the evidence available, we concluded that the oscillatory behavior and insensitivity of soil carbon to carbon input in the nonlinear models are unrealistic. We recommend that a better model for capturing the soil carbon dynamics over decadal to centennial timescales would combine the sensitivity of the conventional models to carbon influx with the flexible response to warming of the nonlinear model.

Nitrogen limitation on land: how can it occur in Earth system models?

“…While a thorough review of SOM models in ESMs is beyond the scope of this review (Todd-Brown et al, 2013, 2014, ESMs differ in the turnover times of different pools and how environmental conditions modify the turnover times. Models are beginning to include additional controls on decomposition through the addition of explicit microbial pools with dynamic carbon use efficiencies (Todd-Brown et al, 2012;Wieder et al, 2013;Wang et al, 2014;Xenakis & Williams, 2014), multilayer soil models where decomposition at depth is slowed because of cooler temperatures and physical protection of SOM (Koven et al, 2013), and feedbacks where soil organic stabilization increases with N availability (Gerber et al, 2010). The current generation of ESMs does not include mechanisms whereby plants alter N mineralization through root exudation or mycorrhizal associations (Brzostek et al, 2014)in ESMs, plants only alter N mineralization through changes in quality (i.e.…”

Microbial models with data‐driven parameters predict stronger soil carbon responses to climate change

“…Once, we ran the forward simulations, it became evident that we needed to test the microbial models for their intrinsic propensity to generate oscillations in carbon pool sizes, given that soil carbon pool sizes at local to global scales occasionally exhibited multiyear oscillations. We investigated the intrinsic propensity of the carbon pools to oscillate following the techniques described in Svirezhev (2002) and Wang et al (2013):…”

“…However, better representation of SOC distribution may not indicate that microbial models are better than conventional models at predicting SOC dynamics. For example, microbial models have been criticized for producing unrealistic SOC dynamics, such as oscillations in SOC pools (Wang et al, 2013). While there are reports of oscillations in microbial biomass and respiration observed in the incubation studies (Lloyd et al, 1982;Cenciani et al, 2008), the phenomenon needs to be investigated further prior to being considered true for natural ecosystems.…”

“…Moreover, replacing a conventional model with a microbial model in the Community Land Model improved its predictive accuracy for the global SOC distribution . However, microbial models may also produce responses not observed in nature: A recent analysis illustrated that microbial models produce unrealistic oscillatory responses to small perturbations (Wang et al, 2013). Such unrealistic dynamical properties emphasize the importance of investigating whether and why more realistic biological assumptions lead to more realistic biological predictions at the spatial and temporal scales they are intended to be applied.…”

Microbial stoichiometry overrides biomass as a regulator of soil carbon and nitrogen cycling

“…The central importance of decomposer microorganisms as the agents that degrade organic matter is generally acknowledged, but the most parsimonious characterization of microbes in biogeochemical models is a matter of debate (Wang et al 2014. Traditional models represent microbes implicitly using first-order reaction kinetics to approximate their activities (Parton et al 1987, 1998, Todd-Brown et al 2012).…”