## 2.21.6. N Competition between plant uptake and soil immobilization fluxes[¶](#n-competition-between-plant-uptake-and-soil-immobilization-fluxes "Permalink to this headline")
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Once \\({NF}\_{immob\\\_demand }\\) and \\({NF}\_{nit\\\_demand }\\) for each layer _j_ are known, the competition between plant and microbial nitrogen demand can be resolved. Mineral nitrogen in the soil pool (\\({NS}\_{sminn}\\), gN m\-2) at the beginning of the timestep is considered the available supply.

Here, the \\({NF}\_{plant\\\_demand}\\) is the theoretical maximum demand for nitrogen by plants to meet the entire carbon uptake given an N cost of zero (and therefore represents the upper bound on N requirements). N uptake costs that are \\(>\\) 0 imply that the plant will take up less N that it demands, ultimately. However, given the heuristic nature of the N competition algorithm, this discrepancy is not explicitly resolved here.

The hypothetical plant nitrogen demand from the soil mineral pool is distributed between layers in proportion to the profile of available mineral N:

(2.21.26)[¶](#equation-21-291 "Permalink to this equation")\\\[NF\_{plant\\\_ demand,j} = NF\_{plant\\\_ demand} NS\_{sminn\\\_ j} / \\sum \_{j=1}^{nj}NS\_{sminn,j}\\\]

Plants first compete for ammonia (NH4). For each soil layer (_j_), we calculate the total NH4 demand as:

(2.21.27)[¶](#equation-21-292 "Permalink to this equation")\\\[NF\_{total\\\_ demand\_nh4,j} = NF\_{immob\\\_ demand,j} + NF\_{immob\\\_ demand,j} + NF\_{nit\\\_ demand,j}\\\]

where If \\({NF}\_{total\\\_demand,j}\\)\\(\\Delta\\)_t_ \\(<\\) \\({NS}\_{sminn,j}\\), then the available pool is large enough to meet both the maximum plant and microbial demand, then immobilization proceeds at the maximum rate.

(2.21.28)[¶](#equation-21-29 "Permalink to this equation")\\\[f\_{immob\\\_demand,j} = 1.0\\\]

where \\({f}\_{immob\\\_demand,j}\\) is the fraction of potential immobilization demand that can be met given current supply of mineral nitrogen in this layer. We also set the actual nitrification flux to be the same as the potential flux (\\(NF\_{nit}\\) = \\(NF\_{nit\\\_ demand}\\)).

If \\({NF}\_{total\\\_demand,j} \\Delta t \\mathrm{\\ge} {NS}\_{sminn,j}\\), then there is not enough mineral nitrogen to meet the combined demands for plant growth and heterotrophic immobilization, immobilization is reduced proportional to the discrepancy, by \\(f\_{immob\\\_ demand,j}\\), where

(2.21.29)[¶](#equation-21-30 "Permalink to this equation")\\\[f\_{immob\\\_ demand,j} = \\frac{NS\_{sminn,j} }{\\Delta t\\, NF\_{total\\\_ demand,j} }\\\]

The N available to the FUN model for plant uptake (\\({NF}\_ {plant\\\_ avail\\\_ sminn}\\) (gN m\-2), which determines both the cost of N uptake, and the absolute limit on the N which is available for acquisition, is calculated as the total mineralized pool minus the actual immobilized flux:

(2.21.30)[¶](#equation-21-311 "Permalink to this equation")\\\[NF\_{plant\\\_ avail\\\_ sminn,j} = NS\_{sminn,j} - f\_{immob\\\_demand} NF\_{immob\\\_ demand,j}\\\]

This treatment of competition for nitrogen as a limiting resource is referred to a demand-based competition, where the fraction of the available resource that eventually flows to a particular process depends on the demand from that process in comparison to the total demand from all processes. Processes expressing a greater demand acquire a larger vfraction of the available resource.

