Five plant root systems share one common mycorrhizal network (CMN): a fungus whose hyphae physically link every root. Each trade round every root pays a carbon ration Ci (sugar from photosynthesis) into the network. The fungus then allocates a fixed phosphorus pool Ptotal back to the roots.
Reciprocal rewards ON (partner choice):
w_i = C_i^k
P_i = P_total · w_i / Σ_j w_j
Reciprocal rewards OFF (naive mutualism):
P_i = P_total / n
With k > 0 the fungus preferentially routes phosphorus to roots that pay more carbon — a "biological market". Isotope-tracing experiments (Kiers et al., Science 2011) showed real arbuscular mycorrhizal fungi do exactly this: root fragments experimentally starved of light (and so unable to pay carbon) receive measurably less phosphorus than well-lit, carbon-paying neighbours on the very same fungal network.
This 2D edition runs the identical allocation formula as the 3D version but represents it two ways at once, both drawn flat in the plane rather than as a spatial hub-and-roots scene: a Sankey-style flow diagram (left) shows carbon ribbons flowing into a central pool node and phosphorus ribbons flowing back out, each ribbon's width set directly by Ci or Pi; a carbon-vs-phosphorus phase plot (right) scatters every root's (Ci, Pi) pair each round, building up a trail whose slope and scatter directly reveal the live Pearson correlation r between payment and reward.
- Carbon sliders — set how much sugar each root pays into the network per round. Drop one to ~0–2 to simulate a shaded, cheating root.
- Partner-choice strength k — 0 makes allocation ignore payment entirely (equal split); higher k rewards big payers more steeply.
- Reciprocal rewards toggle — switch the market off to see cheaters get exactly the same phosphorus as generous roots.
- Click any root's node or ribbon in the flow diagram (or its point cluster in the phase plot) to inspect its exact trade numbers.