Soil nutrient cycles as a nonlinear dynamical system

Manzoni, Stefano; Porporato, Amilcare; D’Odorico, Paolo; Laio, Francesco; Rodrı́guez-Iturbe, Ignacio

doi:10.5194/npg-11-589-2004

Cited by 46 publications

(38 citation statements)

References 29 publications

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“…Some studies have explored the mathematical properties of these nonlinear models in detail (for example, Manzoni et al, 2004;Manzoni and Porporato, 2007;Raupach, 2007;Wang et al, 2014). However, to date these have been predominantly restricted to obtaining insights for individual models and with a specific parameterization.…”

Section: Y-p Wang Et Al: Responses Of Two Nonlinear Microbial Modementioning

confidence: 99%

Responses of two nonlinear microbial models to warming and increased carbon input

et al. 2016

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Abstract.A number of nonlinear microbial models of soil carbon decomposition have been developed. Some of them have been applied globally but have yet to be shown to realistically represent soil carbon dynamics in the field. A thorough analysis of their key differences is needed to inform future model developments. Here we compare two nonlinear microbial models of soil carbon decomposition: one based on reverse Michaelis-Menten kinetics (model A) and the other on regular Michaelis-Menten kinetics (model B). Using analytic approximations and numerical solutions, we find that the oscillatory responses of carbon pools to a small perturbation in their initial pool sizes dampen faster in model A than in model B. Soil warming always decreases carbon storage in model A, but in model B it predominantly decreases carbon storage in cool regions and increases carbon storage in warm regions. For both models, the CO 2 efflux from soil carbon decomposition reaches a maximum value some time after increased carbon input (as in priming experiments). This maximum CO 2 efflux (F max ) decreases with an increase in soil temperature in both models. However, the sensitivity of F max to the increased amount of carbon input increases with soil temperature in model A but decreases monotonically with an increase in soil temperature in model B. These differences in the responses to soil warming and carbon input between the two nonlinear models can be used to discern which model is more realistic when compared to results from field or laboratory experiments. These insights will contribute to an improved understanding of the significance of soil microbial processes in soil carbon responses to future climate change.

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Section: Y-p Wang Et Al: Responses Of Two Nonlinear Microbial Modementioning

confidence: 99%

Responses of two nonlinear microbial models to warming and increased carbon input

et al. 2016

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“…We therefore conducted linear stability analyses to evaluate the stability of the two models more generally. This technique has been used in many studies of ecological models, biogeochemical models and human-carbon cycle interactions (see Manzoni et al, 2004;Raupach, 2007). The linear stability of a system dy/dt = f (y, t), where y is a state vector, and f is a function -to small perturbations can be determined by the Jacobian matrix (J = df /dy) of the system.…”

Section: Mathematical Analysismentioning

confidence: 99%

Oscillatory behavior of two nonlinear microbial models of soil carbon decomposition

et al. 2014

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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 K s /V s in the two-pool model, and to ε −1 − 1 K l /V l in the threepool model, where ε is microbial growth efficiency, K s and K l are the half saturation constants of soil and litter carbon, respectively, and V s and V l 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 of between 5 and 15 years depending on other parameter values, and has smaller amplitude at soil temperatures between 0 and 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 are notable features in these nonlinear models that are somewhat 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.

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“…In this regard, simplified analytical models provide a useful alternative, especially when cast in the form of systems of ordinary differential equations (Manzoni et al, 2004;Lasaga, 1980;DeLonge et al, 2008), for which the apparatus of dynamical system theory becomes readily available (e.g., Strogatz, 1994). With this intent, here we propose a simple analytical P-cycle model, valid at long temporal (decades and higher) and large spatial (regional to continental) scales, with the aim of clarifying how tectonic uplift, climate, vegetation, and exogenous inputs interact to maintain the active P-cycle in terrestrial ecosystems under different hydroclimatic conditions.…”

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The role of tectonic uplift, climate, and vegetation in the long-term terrestrial phosphorous cycle

2010

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Abstract. Phosphorus (P) is a crucial element for life and therefore for maintaining ecosystem productivity. Its local availability to the terrestrial biosphere results from the interaction between climate, tectonic uplift, atmospheric transport, and biotic cycling. Here we present a mathematical model that describes the terrestrial P-cycle in a simple but comprehensive way. The resulting dynamical system can be solved analytically for steady-state conditions, allowing us to test the sensitivity of the P-availability to the key parameters and processes. Given constant inputs, we find that humid ecosystems exhibit lower P availability due to higher runoff and losses, and that tectonic uplift is a fundamental constraint. In particular, we find that in humid ecosystems the biotic cycling seem essential to maintain long-term Pavailability. The time-dependent P dynamics for the Franz Josef and Hawaii chronosequences show how tectonic uplift is an important constraint on ecosystem productivity, while hydroclimatic conditions control the P-losses and speed towards steady-state. The model also helps describe how, with limited uplift and atmospheric input, as in the case of the Amazon Basin, ecosystems must rely on mechanisms that enhance P-availability and retention. Our novel model has a limited number of parameters and can be easily integrated into global climate models to provide a representation of the response of the terrestrial biosphere to global change.

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Soil nutrient cycles as a nonlinear dynamical system

Cited by 46 publications

References 29 publications

Responses of two nonlinear microbial models to warming and increased carbon input

Responses of two nonlinear microbial models to warming and increased carbon input

Oscillatory behavior of two nonlinear microbial models of soil carbon decomposition

The role of tectonic uplift, climate, and vegetation in the long-term terrestrial phosphorous cycle

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