RelativeAllocation

The RelativeAllocation module implements a proportional allocation strategy to distribute available biomass or nutrient supply among plant organs based on each organ’s demand relative to total demand.

Overview

The RelativeAllocation method is a general-purpose mechanism that underpins how APSIM handles partitioning of dry matter (DM) and nutrients (e.g. nitrogen) among competing plant organs. This method is part of the broader plant allocation system and is invoked by arbitrator components such as BiomassTypeArbitrator.

Arbitration is performed in two passes for each of the supply sources. On the first pass, biomass or nutrient supply is allocated to structural and metabolic pools of each organ based on their demand relative to the demand from all organs. On the second pass, any remaining supply is allocated to non-structural (storage) pools based on the organ’s relative demand.

Biological Motivation

Plants must allocate available assimilates or nutrients among organs in a coordinated way. The RelativeAllocation method mimics this by:

Prioritizing structural and metabolic demands (essential growth),
Then allocating any residual supply to storage pools (non-essential, luxury uptake).

This reflects physiological prioritization in plant growth where essential structural and metabolic needs are met before luxury storage.

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
IArbitrationMethod

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.

The allocation occurs in two sequential passes:

First Pass – Structural and Metabolic Allocation
Second Pass – Storage (Luxury) Allocation

First Pass: Structural and Metabolic Allocation

Objective: Distribute available supply to fulfill structural and metabolic demands proportionally.

Definitions:

Let:

\(S_{\text{total}}\): Total supply available (e.g. dry biomass or nitrogen)
\(D_s^{(i)}\): Structural demand of organ \(i\)
\(D_m^{(i)}\): Metabolic demand of organ \(i\)
\(D_{s,\text{total}} = \sum_i D_s^{(i)}\): Total structural demand across all organs
\(D_{m,\text{total}} = \sum_i D_m^{(i)}\): Total metabolic demand across all organs

We define the structural fraction of supply as:

\[ f_s = \frac{D_{s,\text{total}}}{D_{s,\text{total}} + D_{m,\text{total}}} \]

Then, for each organ \(i\):

Structural allocation:

\[ A_s^{(i)} = \min\left(R_s^{(i)}, S_{\text{total}} \cdot f_s \cdot \frac{D_s^{(i)}}{D_{s,\text{total}}} \right) \]

Metabolic allocation:

\[ A_m^{(i)} = \min\left(R_m^{(i)}, S_{\text{total}} \cdot (1 - f_s) \cdot \frac{D_m^{(i)}}{D_{m,\text{total}}} \right) \]

where \(R_s^{(i)}\) and \(R_m^{(i)}\) are the remaining unmet demand for structural and metabolic pools, respectively.

Second Pass: Storage (Luxury) Allocation

Objective: Allocate any remaining supply to storage pools (non-essential or luxury growth) based on proportional demand.

Definitions:

Let:

\(S_{\text{rem}}\): Remaining supply after first pass
\(D_t^{(i)}\): Storage demand of organ \(i\)
\(D_{t,\text{total}} = \sum_i D_t^{(i)}\): Total storage demand across all organs

Then, for each organ \(i\):

\[ A_t^{(i)} = \min\left(R_t^{(i)}, S_{\text{rem}} \cdot \frac{D_t^{(i)}}{D_{t,\text{total}}} \right) \]

where \(R_t^{(i)}\) is the remaining unmet storage demand for organ \(i\).

Final Accounting

After both passes, the module tracks:

Total allocation: Sum of structural, metabolic, and storage allocations across all organs.
Not allocated: Any supply that remains unallocated due to demand being fully satisfied or due to zero total demand (e.g., at early stages).

\[ S_{\text{not\_allocated}} = S_{\text{total}} - \sum_i \left( A_s^{(i)} + A_m^{(i)} + A_t^{(i)} \right) \]

This is useful for diagnostics, such as reporting sink limitations.

Key Features

Prioritizes essential growth (structural and metabolic) over luxury (storage)
Proportional to each organ’s share of total demand
Applies generically to both biomass and nutrients
Uses a two-pass method to avoid allocating luxury growth when essential needs are unmet

User Interface

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

Practical Example

Assume:

Leaf has a structural demand of 50 units and a metabolic demand of 20 units.
Stem has a structural demand of 60 units and a metabolic demand of 60 units.
Total supply is 120 units.

Then:

Total structural demand = 50 (leaf) + 60 (stem) = 110 units
Total metabolic demand = 20 (leaf) + 60 (stem) = 80 units
Structural fraction:
\(f_s = \frac{110}{110 + 80} = 0.579\)
First pass allocates:
- Structural: \(120 \times 0.579 = 69.48\) units, distributed as:
  - Leaf: \(69.48 \times \frac{50}{110} = 31.58\) units
  - Stem: \(69.48 \times \frac{60}{110} = 37.90\) units
- Metabolic: \(120 \times 0.421 = 50.52\) units, distributed as:
  - Leaf: \(50.52 \times \frac{20}{80} = 12.63\) units
  - Stem: \(50.52 \times \frac{60}{80} = 37.89\) units
Second pass allocates any leftover proportionally to storage demands.

Applications

Biomass partitioning after photosynthesis, reallocation, and retranslocation
Nitrogen allocation after uptake, reallocation, and retranslocation
Any generic resource arbitration among competing sinks