NutrientConstrainedAllocationMethod

The NutrientConstrainedAllocationMethod 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 requirements.

Overview

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

The NutrientConstrainedAllocationMethod model determines nutrient limitations to dry matter allocations by checking whether each organ has received enough nitrogen to support its allocated biomass and scales biomass down proportionally if nitrogen is insufficient.

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).

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.

Model Structure

This section describes how this model is positioned within the APSIM framework. It outlines the broader structural and computational components that define its role and interactions in the simulation system.

This model inherits structural and functional behaviour from the following core APSIM components:

Model
IAllocationMethod

Connections to Other Components

This section describes how the model interacts with other components in the APSIM Next Generation framework.
These connections allow the model to exchange information—such as environmental conditions, developmental stage, or physiological responses—with other parts of the simulation system. For a general overview of how model components are connected in APSIM, see the Connections Overview.

Component	Model	Connection Type	Description
Arbitrator	IArbitrator	Link, Ancestor By Name	Provides nitrogen allocation information for organs.

Processes and Algorithms

This section describes the scientific processes and algorithms represented by this component. Each process corresponds to a biological, physical, or chemical mechanism simulated during a model time step. Where appropriate, equations or conceptual summaries are provided to explain how the process operates within the APSIM Next Generation framework.

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 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.

Step 2: Calculate N-Constrained Growth Capacity

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

If total nitrogen allocation meets or exceeds demand, growth is unconstrained (assigned a very high value: 100,000,000).
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:

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

where:

\(N_\text{TotalAllocation}[i]\) is the total nitrogen allocated to organ \(i\)
\(\text{MinNConc}[i]\) 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.

Step 3: 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 biomass components are scaled proportionally:

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.

Step 4: Update Final Biomass and Nutrient Limitation

After applying constraints, the final biomass allocation and the nutrient limitation are calculated 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.

User Interface

NutrientConstrainedAllocationMethod can be added as a child of a BiomassTypeArbitrator node in the model tree. Right-click the parent node, select “Add Model…”, and search for NutrientConstrainedAllocationMethod in the Filter Box.

Practical Example

Example Calculation

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 \(10 / 12 = 0.833\)

Extensibility and Limitations

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.

Current 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.