The Transport model extends the FlowerAging model by implementing a physiologically-based system for sugar transport from photosynthetically active leaves through the plant architecture to developing fruits. This creates a more realistic simulation of source-sink relationships in the virtual plant.

The model introduces a new parameter as (assimilate storage) to track sugar content in different organs: module Internode(super.length, int age, int rank, float as)

extends Cylinder(length, 0.1);

module Leaf(super.length, super.width, float al, int age, float as,

  int rank) extends Box(length, width, 0.01);

module Fruit(float size, int age, float as) =⇒ Sphere(size).(setShader(RED)); Note that we now track assimilates (as) in three types of modules: leaves (where they are produced), internodes (where they are transported), and fruits (where they accumulate). 2) Maintenance Respiration A maintenance respiration constant has been added to simulate the metabolic cost of keeping tissues alive (L. 78): const float MR = 0.01; maintenance respiration This is applied to internodes during growth to simulate sugar consumption: itn:Internode ::> { itn[age]++; if(itn[as]>0) {itn[as] *= (1-MR); } itn[length] += logistic(1, itn[age], 10, 0.1); } 3) Transport Mechanism The core innovation is the implementation of a diffusion-based transport system. The transport occurs with a diffusion constant that controls the rate (L. 75): const float DIFF_CONST = 0.001; The transport is invoked periodically in the grow() method - every 24 timesteps to simulate hourly transport (L. 138-143): if(time % 24 == 0) { for(int hour = 0; hour < 24; hour++) { transport(); } } 4) Transport Rules Three types of transport are implemented using user-defined edge relations: a) Leaf to Internode Transport (L. 251-258): lf:Leaf ←minDescendants- itn:Internode ::> { if(lf[as] > 0.01) { Keep minimum for leaf maintenance

      float exportable = lf[as] - 0.01;
      float r = DIFF_CONST * exportable;
      lf[as] -= r;
      itn[as] += r;
  }

} This rule ensures leaves retain a minimum amount (0.01) for maintenance while exporting the surplus. b) Internode to Internode Transport (L. 260-268): i_top:Internode ←minDescendants- i_bottom:Internode ::> {

  if((i_bottom[as] - i_top[as])<=0) { 
      float r = DIFF_CONST * (i_top[as] - i_bottom[as]);
      i_bottom[as] :+= r;
      i_top[as] :-= r;
  }
  else if ((i_bottom[as] - i_top[as])>0) { 
      float r = DIFF_CONST * (i_bottom[as] - i_top[as]);
      i_bottom[as] :-= r;
      i_top[as] :+= r;
  }

} This bidirectional transport follows the concentration gradient between successive internodes. c) Internode to Fruit Transport (L. 269-275): itn:Internode -minDescendants→ fr:Fruit ::> {

  if(itn[as]>0) {
      float r = DIFF_CONST * itn[as];
      itn[as] :-= r;
      fr[as] :+= r;
      println("sugar import into fruit: " + r);
  }

} 5) Fruit Set Decision Based on Sugar Availability The model now makes fruit formation dependent on available sugar in the plant (L. 165-172): fl:Flower(t, m), (t >= m) =⇒ {float sugar = sum¹⁾); Tasks for Exploration 1. Run the model and observe sugar flow: Watch how internodes change color as sugar moves through them. 2. Modify DIFF_CONST: Try values between 0.0001 and 0.01. How does this affect: o Speed of sugar movement? o Final fruit size? o Number of successfully developed fruits? 3. Change transport frequency: Modify the condition if(time % 24 == 0) to different values (e.g., % 12 for twice-daily transport). What impact does this have? 4. Adjust maintenance respiration: Change MR from 0.01 to 0.05. How does increased respiration affect fruit development? Key Improvements Over FlowerAging Model Feature FlowerAging Transport Sugar tracking Only in leaves Leaves, internodes, and fruits Transport None Diffusion-based with user-defined edges Fruit growth Fixed size Based on sugar availability Resource competition None Age-based weighting Maintenance costs None Respiration in internodes Visual feedback Leaf color only Leaf and internode color Biological Relevance This transport model introduces key physiological concepts: • Source-sink relationships: Leaves act as sources, fruits as sinks • Phloem transport: Simplified as diffusion along concentration gradients • Competition for resources: Multiple sinks compete for limited assimilates • Maintenance respiration: Realistic metabolic costs • Sink strength: Younger fruits have stronger sink strength The model provides a foundation for exploring how plant architecture and physiology interact to determine yield formation.