This 2D version computes the same real ecological effect from the leaf up, using the actual biochemistry rather than a fitted curve. The Farquhar-von Caemmerer-Berry model describes net CO2 assimilation A as Rubisco carboxylation minus photorespiration minus dark respiration:
C3: A = Vcmax · (Ci − Γ*) / (Ci + Kc·(1 + Oi/Ko)) − Rd, Ci ≈ 0.7 · Ca
C4: A = min( Vpmax · Ca/(Ca + Kp), Vcmax4 ) − Rd
Kc = 404 μmol/mol, Ko = 278 mmol/mol, Oi = 209 mmol/mol, Γ* = 42.75 μmol/mol
Kp = 80 μmol/mol (PEP carboxylase, C4 mesophyll) Rd = 1.5 μmol·m⁻²·s⁻¹
C3 Rubisco is not CO2-saturated at today's ~420 ppm, so A keeps climbing with Ca — that's the "fertilization" part. C4 plants (maize) run PEP carboxylase as a CO2-concentrating pump that already saturates Rubisco in the bundle sheath at pre-industrial CO2, so A barely moves — the field on the right stays flat as you drag the slider.
The nutrient side uses two independent, mechanistic dilution pathways instead of one blended empirical curve:
biomassRel = A(Ca) / A(400ppm)
N-uptakeRel = 1 + 0.35·f_N (soil nitrogen supply, ~fixed by roots)
gs_rel(Ca) = max(0.3, 1 − 0.15·ln(Ca/400)) (stomatal closure under high CO2)
ZnFeUptakeRel = gs_rel(Ca) · (1 + 0.15·f_N) (mass-flow delivery via transpiration)
Protein index = 100 · N-uptakeRel / biomassRel
Zn/Fe index = 100 · ZnFeUptakeRel / biomassRel
- Assimilation, A — the instantaneous carbon-fixation rate at the current CO2; it drives biomass, and biomass is the denominator that dilutes everything else.
- Stomatal conductance — elevated CO2 lets leaves partially close their stomata (documented ~20% conductance drop at doubled CO2 in FACE meta-analyses, Ainsworth & Rogers 2007). Less transpiration means less mass-flow delivery of soil zinc and iron to the root surface — a second, independent reason those minerals dilute faster than protein.
- Nitrogen fertilization — raises the soil nitrogen supply feeding the grain, partly offsetting protein dilution; it barely helps Zn/Fe, since those depend on water flow, not fertilizer.
- Growing season day — scrubs the field through a logistic growth curve; plant size in the field view tracks cumulative assimilation up to that day.
This is a deliberately different computational path from the 3D version of this simulator (which fits a single empirical log-yield/log-dilution curve from FACE trial summaries): here, yield and dilution both emerge from separately modeled leaf gas-exchange biochemistry and stomatal water relations, and they still reproduce the same measured pattern — Zhu et al. (2018, Science Advances) and Myers et al. (2014, Nature) found C3 grain losing several percent of protein, zinc and iron per 100 ppm CO2 rise near 550 ppm, roughly matching the indices above.