The quasi-equilibrium framework revisited: Analyzing long-term CO2 enrichment responses in plant-soil models

Mingkai Jiang*, Sönke Zaehle, Martin G. De Kauwe, Anthony P. Walker, Silvia Caldararu, David S. Ellsworth, Belinda E. Medlyn

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

4 Citations (Scopus)


Elevated carbon dioxide (CO2) can increase plant growth, but the magnitude of this CO2 fertilization effect is modified by soil nutrient availability. Predicting how nutrient availability affects plant responses to elevated CO2 is a key consideration for ecosystem models, and many modeling groups have moved to, or are moving towards, incorporating nutrient limitation in their models. The choice of assumptions to represent nutrient cycling processes has a major impact on model predictions, but it can be difficult to attribute outcomes to specific assumptions in complex ecosystem simulation models. Here we revisit the quasi-equilibrium analytical framework introduced by Comins and McMurtrie (1993) and explore the consequences of specific model assumptions for ecosystem net primary productivity (NPP). We review the literature applying this framework to plant-soil models and then analyze the effect of several new assumptions on predicted plant responses to elevated CO2. Examination of alternative assumptions for plant nitrogen uptake showed that a linear function of the mineral nitrogen pool or a linear function of the mineral nitrogen pool with an additional saturating function of root biomass yield similar CO2 responses at longer timescales (>5 years), suggesting that the added complexity may not be needed when these are the timescales of interest. In contrast, a saturating function of the mineral nitrogen pool with linear dependency on root biomass yields no soil nutrient feedback on the very-long-term (>500 years), near-equilibrium timescale, meaning that one should expect the model to predict a full CO2 fertilization effect on production. Secondly, we show that incorporating a priming effect on slow soil organic matter decomposition attenuates the nutrient feedback effect on production, leading to a strong medium-term (5-50 years) CO2 response. Models incorporating this priming effect should thus predict a strong and persistent CO2 fertilization effect over time. Thirdly, we demonstrate that using a "potential NPP" approach to represent nutrient limitation of growth yields a relatively small CO2 fertilization effect across all timescales. Overall, our results highlight the fact that the quasi-equilibrium analytical framework is effective for evaluating both the consequences and mechanisms through which different model assumptions affect predictions. To help constrain predictions of the future terrestrial carbon sink, we recommend the use of this framework to analyze likely outcomes of new model assumptions before introducing them to complex model structures.

Original languageEnglish
Pages (from-to)2069-2089
Number of pages21
JournalGeoscientific Model Development
Issue number5
Publication statusPublished - 28 May 2019

Bibliographical note

Funding Information:
ported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (QUINCY; grant no. 647204) and the German Academic Exchange Service (DAAD; project ID 57318796). David S. Ellsworth and Mingkai Jiang were also supported by the DAAD.

Publisher Copyright:
© 2019 Author(s).


Dive into the research topics of 'The quasi-equilibrium framework revisited: Analyzing long-term CO2 enrichment responses in plant-soil models'. Together they form a unique fingerprint.

Cite this