1 Global climate models have not yet considered the effects of nutrient cycles and limitation when forecasting carbon uptake by the terrestrial biosphere into the future. Using the principle of resource optimization, we here develop a new theory by which C, N, and P cycles interact. Our model is able to replicate the observed responses of net primary production to nutrient additions in N‐limited, N‐ and P‐colimited, and P‐limited terrestrial environments. Our framework identifies a new pathway by which N 2 fixers can alter P availability: By investing in N‐rich, phosphorus liberation enzymes (phosphatases), fixers can greatly accelerate soil P availability and P cycling rates. This interaction is critical for the successful invasion and establishment of N 2 fixers in an N‐limited environment. We conclude that our model can be used to examine nutrient limitation broadly, and thus offers promise for coupling the biogeochemical system of C, N, and P to broader climate‐system models. Introduction 2 Considerable uncertainty surrounds the prediction of carbon (C) uptake and storage by the terrestrial biosphere, with the potential for major constraints imposed by nutrient limitation.

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For instance, in their examination of the third IPCC assessment, found that nitrogen (N) inputs estimated for the next 100 years fell well short of those required to sustain the amount of C storage projected by four of six model scenarios. In fact, the only two models that yielded sustainable estimates for C storage included a simplified version of the N cycle. More recently, this theoretical expectation for a nutritional constraint on C storage has been shown to hold across a variety of terrestrial ecosystems exposed to elevated CO 2. It therefore appears as if global models must consider the effects of soil nutrients in the prediction of ecosystem responses to elevated CO 2 and climate change. 3 Nitrogen (N) and phosphorus (P) are the nutrients that most often limit the productivity and functioning of terrestrial ecosystems ; hence, it is essential to include both of these element cycles in ecosystem models. Two key concepts have driven our understanding of how N and P cycles interact in shaping the productivity and C cycle of terrestrial ecosystems over long versus short timescales. Over the long term (100,000 years) course of ecosystem development, posited that ecosystems ought to proceed from a state of N limitation to P limitation.

N is often absent from most geologic materials; thus fixation and deposition provide N fertility as ecosystems develop. However, as N pools accumulate past the point at which this nutrient is no longer limiting, symbiotic N 2 fixers should lose their competitive advantage and be excluded from plant communities. On the contrary, P‐bearing minerals are abundant in young rock substrates but are progressively leached or locked up in unavailable pools as ecosystems age, thereby causing ecosystems to progress toward a terminal state of P limitation. While this model has received considerable support empirically ; , it has remained difficult to understand why terrestrial N and P cycles do not appear to equilibrate with respect to biological demands see. 4 On shorter timescales (. Model Description 6 Two groups of plants are considered: one fixes N 2 symbiotically (N 2 fixers) and other does not (nonfixers). Each type of plants is divided into leaves, wood and coarse roots, and fine roots.

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We consider one litter pool, one soil organic matter (SOM) pool, one inorganic nitrogen pool and four inorganic phosphorus pools (labile P, sorbed P, strongly sorbed P and occluded P); a total of 29 pools are represented (see ). In presenting our model, we use C, N and P to present the pool size, and F for flux from or into and out of a pool. The units are in g element m −2 for pool sizes and g element m −2 year −1 for fluxes. Symbols and their definition are also listed in the notation section. A schematic diagram of the model. The grey square box represents the spatial domain of a terrestrial ecosystem, within which plant pools (in light grey) and litter and soil pools (in dark grey) are included. Exchanges with the atmosphere, hydrosphere, and geosphere are indicated by arrows.

Biochemical phosphorus mineralization rate (FPtase) represents the flow of organic P from litter or soil organic matter pool to the labile P pool. 7 In our model, fixers and nonfixers engage in aboveground (for light) and belowground (for N and P) competition. The competition between fixers and nonfixers depends on their respective leaf area indices for light and root length densities for nutrient uptake (see ). Uptake of C, N and P by plants is allocated to leaf, woody tissue and roots using constant allocation coefficients that can differ between C, N and P. During senescence, all plant C enters the litter pool, a fraction of N or P in the plant tissue is resorbed into live tissue, and the remaining N or P enters the litter pool. When litter decomposes in the soil, a fraction of the C becomes incorporated into the soil organic pool, and the remaining is respired as CO 2.

Litter decomposition is reduced when N immobilization exceeds the total mineral N available from gross mineralization. We do not distinguish different forms for mineral N in the soil. Four pools, labile, sorbed, strongly sorbed and occluded, are used to partition the inorganic soil P into different classes of availability for plant and microbial uptake. In addition to P mineralization during decomposition (biological P mineralization), we also consider phosphatase enzymes produced by plant roots which cleave organically bound P into inorganic labile P (biochemical P mineralization). In this way, plants can accelerate the mineralization of P directly.

8 Carbon enters the ecosystem by net primary production (NPP), and returns to the atmosphere via heterotrophic respiration. N can enter the ecosystem via atmospheric deposition and N 2 fixation, and can leave via denitrification and leaching. Our model assumes that the rate of inorganic N loss is proportional to the amount of soil mineral N, and does not take account of the effects of soil moisture on N losses explicitly see. Loss of organic N or P from soil, by leaching or erosion, is not considered in our model. Rate of P loss is assumed to be proportional to the amount of labile P in soil.

Input of P to the ecosystem includes atmospheric deposition and rock weathering. 9 We modeled the dynamics of C, N and P in the plant pools using first‐order reaction kinetics.

Where the subscript i represents N 2‐fixer ( i = fix) or nonfixer ( i = nf), j for leaf ( j = l), wood and coarse roots ( j = w) or fine roots ( j = r). Here η C,i,j, η N,i,j and η P,i,j represent the fraction of C, N or P uptake by plant i that is allocated to pool j, F c,i, F N,i and F P,i represent the uptake of C, N and P by plant i, and their formulation is described in. Τ i,j is the turnover rate of a pool and n i,j and p i,j are the resorption coefficients for N and P in the plant tissue before senescence. 10 Litter C dynamics ( C d) in the soil is modeled as. 12 The first term on the right‐hand side of represents the input of organic N to the litter pool via litter fall, and the second term represent mineralization of litter N in the soil. When potential litter N immobilization exceeds the gross mineralization rate of both litter and soil and the total amount of soil mineral N available, litter decomposition is reduced by x d (see ). Therefore x d depends on the N:C ratios and decomposition rates of both litter and SOM pools.

Proposed Biogeochemical Model For Machine Learning

We do not consider N immobilization directly into the litter pool. 13 Dynamics of soil organic C ( C s) and nitrogen ( N s) is modeled as. Where ɛ is microbial efficiency, τ s is the turnover rate of SOM, α s is the N:C ratio of SOM and α d is the N:C ratio of plant litter pool. The first term on the right‐hand side of represents the direct transfer of organic N from litter to soil, the second represents the rate of N immobilization by SOM (or the soil microbial community), and the third term is the mineralization of soil organic N. We assume that the C:N:P ratios of the SOM are constant at each site, and decomposition of SOM does not vary on its C:N:P ratios, and can be limited by available soil mineral N if N immobilization is greater than the gross N mineralization and the amount of soil mineral N. 14 Dynamics of soil mineral N pool ( N min) is modeled as.