Nutrient Constrained Allocation

Published

June 6, 2025

In APSIM Next Generation (APSIM NG), plant biomass growth is computed based on potential dry matter (DM) production from photosynthesis, reallocation, and retranslacation. However, this potential growth must be adjusted according to nutrient constraints, primarily nitrogen (N), which depends on nitrogen supply.

The NutrientConstrainedAllocationMethod model is responsible for scaling biomass allocations to organs based on the amount of nitrogen allocated to those organs. This ensures that growth is biologically feasible given available N and minimum nitrogen concentration.

Role in APSIM Simulation Pipeline

The NutrientConstrainedAllocationMethod is invoked after biomass has been distributed to organs (e.g., by RelativeAllocation) but before final biomass commitment. Its purpose is to:

  • Check whether each organ has received enough nitrogen to support its allocated biomass (i.e. satisfy the minimum concentration).
  • Scale biomass down proportionally if nitrogen is insufficient.
  • Track how much biomass was reduced due to nitrogen limitations (i.e. the difference between allocated and actual biomass). The reporting variable DM.NutrientLimitation captures this reduction, which is crucial for understanding crop performance under nutrient stress (e.g. [Wheat].Arbitrator.DM.NutrientLimitation).

Inputs and Assumptions

  • Organs (IArbitration[]): A list of organs participating in allocation (e.g., leaf, stem, root, grain).
  • BiomassArbitrationType (DM): Contains the dry matter allocations (structural, metabolic, storage) from the prior allocation step.
  • NutrientArbitrationType (N): Contains nitrogen demand and allocation for each organ.

Key Assumptions:

  • Each organ has a defined minimum nitrogen concentration (MinNConc), below which it cannot support biomass.
  • Nitrogen allocated to an organ must meet this minimum to validate the associated DM allocation.

Step-by-Step Process

  1. Calculate Total N Allocation per Organ

For each organ i, sum all nitrogen allocations:

\[ N_{\text{TotalAllocation},i} = N_{\text{StructuralAllocation},i} + N_{\text{MetabolicAllocation},i} + N_{\text{StorageAllocation},i} \]

This value represents the nitrogen available to support DM growth.

  1. Calculate N-Constrained Growth Capacity

Determine the maximum biomass (N.ConstrainedGrowth[i]) that each organ can support based on its nitrogen allocation:

This logic checks:

  • If total nitrogen allocation meets or exceeds demand, growth is unconstrained.
  • If no nitrogen is allocated or the organ has no minimum N concentration, growth is zero.
  • Otherwise, it computes the maximum biomass based on the minimum nitrogen concentration required by the organ. The constrained growth for each organ is calculated as:

\[ N_\text{ConstrainedGrowth}[i] = \frac{N_\text{TotalAllocation}[i]}{\text{Organs}[i]_\text{MinNConc}} \]

where:

  • \(N_\text{TotalAllocation}[i]\) is the total nitrogen allocated to organ \(i\)
  • \(\text{Organs}[i]_\text{MinNConc}\) is the minimum nitrogen concentration required for organ \(i\)

This yields a per-organ limit on biomass, ensuring growth is feasible under nitrogen constraints. This is the most common case where nitrogen limits growth.

  1. Scale Biomass Allocation Proportionally

The total biomass previously allocated (structural + metabolic + storage) is compared to ConstrainedGrowth[i].

If total allocation exceeds the constrained limit, all organs are scaled proportionally:

Let:

Let \(DM_{total}[i]\) be the total biomass allocated to organ \(i\):

\[ DM_{total}[i] = DM_{structural}[i] + DM_{metabolic}[i] + DM_{storage}[i] \]

Calculate the proportion of each component:

\[ P_{structural}[i] = \frac{DM_{structural}[i]}{DM_{total}[i]} \]

\[ P_{metabolic}[i] = \frac{DM_{metabolic}[i]}{DM_{total}[i]} \]

\[ P_{storage}[i] = \frac{DM_{storage}[i]}{DM_{total}[i]} \]

Scale each component by the N-constrained growth:

\[ DM_{structural}[i] = \min\left(DM_{structural}[i], N_{constrained}[i] \times P_{structural}[i]\right) \]

\[ DM_{metabolic}[i] = \min\left(DM_{metabolic}[i], N_{constrained}[i] \times P_{metabolic}[i]\right) \]

\[ DM_{storage}[i] = \min\left(DM_{storage}[i], N_{constrained}[i] \times P_{storage}[i]\right) \]

This ensures:

  • No component exceeds the N-limited capacity.
  • Ratios between structural, metabolic, and storage biomass are preserved.
  1. Update Final Biomass and Stress Report

After applying constraints, updating the final biomass allocation and calculating the nutrient limitation is done as follows:

\[ DM_\text{Allocated} = \sum_{i=1}^{n} \left( DM_{structural}[i] + DM_{metabolic}[i] + DM_{storage}[i] \right) \]

\[ DM_\text{NutrientLimitation} = DM_\text{PreNStressAllocation} - DM_\text{Allocated} \]

Where:

  • \(DM_\text{Allocated}\) is the total biomass realized after N constraints.
  • \(DM_\text{PreNStressAllocation}\) is the total biomass allocated before applying N constraints.
  • \(DM_\text{NutrientLimitation}\) is the biomass lost due to insufficient nitrogen.

Practical Example

A leaf organ receives:

  • Nitrogen allocated: 0.3 g
  • Minimum N concentration: 0.03 g/g DM
  • Maximum supportable biomass: 0.3 / 0.03 = 10 g
  • If initial biomass allocated was 12 g:
  • Final biomass is scaled to 10 g
  • All sub-pools (structural, metabolic, storage) are reduced by 10 / 12 = 0.833

Scientific Rationale

  • Nitrogen is a key building block for proteins, nucleic acids, and enzymes.
  • Without sufficient N, plants cannot construct tissue even if photosynthate is available.
  • This constraint ensures simulations realistically capture nutrient stress.

Extensibility

While this method currently constrains biomass based only on nitrogen:

  • It is designed to be extended for other nutrients (e.g., phosphorus, potassium).
  • Additional constraints could be implemented by combining multiple nutrient-limited growth values.

Outputs and Implications

  • DM.Allocated: Actual biomass realized under nutrient constraints.
  • DM.NutrientLimitation: Biomass lost due to insufficient nitrogen.

Potential bugs and Limitations

The current implementation assumes all organs have a defined minimum N concentration. The biomass is dropped if nitrogen uptake cannot meet the minimum concentration. This assumption is reasonable for photosynthesis, but may not be reasonable for reallocation and retranslocation. These unallocated biomass should return to original organs.

References