The quasi-equilibrium framework revisited: analyzing long-term CO 2 enrichment responses in plant–soil models
Abstract. Elevated carbon dioxide ( CO 2 ) can increase plant growth, but themagnitude of this CO 2 fertilization effect is modified by soilnutrient availability. Predicting how nutrient availability affects plantresponses to elevated CO 2 is a key consideration for ecosystemmodels, and many modeling groups have moved to, or are moving towards,incorporating nutrient limitation in their models. The choice of assumptionsto represent nutrient cycling processes has a major impact on modelpredictions, but it can be difficult to attribute outcomes to specificassumptions in complex ecosystem simulation models. Here we revisit thequasi-equilibrium analytical framework introduced by Comins andMcMurtrie (1993) and explore the consequences of specific model assumptionsfor ecosystem net primary productivity (NPP). We review the literature applying this framework to plant–soilmodels and then analyze the effect of several new assumptions on predictedplant responses to elevated CO 2 . Examination of alternativeassumptions for plant nitrogen uptake showed that a linear function of themineral nitrogen pool or a linear function of the mineral nitrogen pool withan additional saturating function of root biomass yield similar CO 2 responses at longer timescales ( >5 years), suggesting that the addedcomplexity may not be needed when these are the timescales of interest. Incontrast, a saturating function of the mineral nitrogen pool with lineardependency on root biomass yields no soil nutrient feedback on thevery-long-term ( >500 years), near-equilibrium timescale, meaning that oneshould expect the model to predict a full CO 2 fertilization effecton production. Secondly, we show that incorporating a priming effect on slowsoil organic matter decomposition attenuates the nutrient feedback effect onproduction, leading to a strong medium-term (5–50 years) CO 2 response. Models incorporating this priming effect should thus predict astrong and persistent CO 2 fertilization effect over time. Thirdly,we demonstrate that using a “potential NPP” approach to represent nutrientlimitation of growth yields a relatively small CO 2 fertilizationeffect across all timescales. Overall, our results highlight thefact that the quasi-equilibriumanalytical framework is effective for evaluating both the consequences andmechanisms through which different model assumptions affect predictions. Tohelp constrain predictions of the future terrestrial carbon sink, werecommend the use of this framework to analyze likely outcomes of new modelassumptions before introducing them to complex model structures.