A temperature-dependent tradeoff

The Temperature Where Grass Changes Its Mind

Warm a C3 leaf and its carbon gain per absorbed photon falls while C4 stays nearly level. The C4 line here is not measured: it is held at the value this model's own C3 equation gives at 22 °C and 340 ppm CO2, so that crossing is the calibration rather than a result. A real C3 and C4 grass pair measured at that CO2 crosses at 22 to 25 °C of leaf temperature (Monson et al. 1982). Lower CO2 moves the model boundary cooler. Physiology predicts a boundary, but fire, water and history decide what occupies it.

Drag the leaf across the crossing. Before it, the C3 route buys more carbon with a photon. After it, the C4 route does. The bend is not drawn: every point is recalculated from the temperature response of photorespiration.

Rubisco admits two gases to the same active site. Its specificity for CO2 over O2 falls as temperature rises, while dissolved CO2 also loses ground to O2. This is a chemical tradeoff, not a mistake. The model tracks it through Γ*, the CO2 compensation point without mitochondrial respiration.

The numerator removes carbon returned by oxygenation. The denominator counts the extra photochemistry needed when oxygenation diverts the cycle. The C4 line represents a CO2-concentrating pump that keeps Rubisco away from this ambient ratio. It is held level at the value produced by the C3 equation at 22 °C and 340 ppm. That is a declared calibration, not an independently fitted universal constant, and it has a consequence worth stating flatly: this model crossing at 22 °C at 340 ppm is arithmetic, not evidence. It was put there. What the model earns is the shape of the response, how the crossing moves when you change CO2, and not the anchor itself.

The anchor is Monson, Littlejohn and Williams (1982), who measured equal quantum yields in a real C3 and C4 grass pair at 22 to 25 °C of leaf temperature in 21% O2 and 340 ppm CO2. Those are this model's own conditions and its own kind of temperature. Collatz, Berry and Clark's better-known 22 °C is not the right anchor for this axis: it is a mean warmest-month air temperature at 35 Pa, which is 350 ppm at a 100 kPa reference, and it appears further down where it belongs, in the climate paragraph.

The boundary is a function, not a latitude

Now use the CO2 slider. The crossing is the root of ΦC3(T,pCO2) − ΦC4 = 0, found afresh by bisection. Less CO2 raises the oxygenation-to-carboxylation ratio at every temperature, so the same equality arrives in cooler air.

The 22 °C crossing is this model's calibrated value at 340 ppm, not a constant carried by every leaf and not something this page discovered. Published crossings do span a range, and here are the two that name their conditions. Monson, Littlejohn and Williams measured Agropyron smithii (C3) against Bouteloua gracilis (C4) in 21% O2 and 340 ppm CO2 and found their quantum yields approximately equal at leaf temperatures between 22 and 25 °C. Fox and colleagues modelled 14, 20 and 24 °C of leaf temperature at 280, 405 and 560 ppmV. Species, C4 subtype and measurement conditions move the equality within that spread.

Collatz, Berry and Clark used the physiological crossover with climate fields and found that a warmest-month mean near 22 °C at 35 Pa pCO2 separated much of the observed C3 and C4 grass abundance. That makes the enzyme model a strong first-order predictor. It does not make a temperature isotherm a sufficient explanation for a grassland.

The direction also appears in altitude and glacial records, with an important correction. A Colombian Andes reconstruction linked Pleistocene C3 and C4 shifts at 2,550 m to temperature and CO2. North American data since the Last Glacial Maximum found low CO2 favoured C4 where cooling was modest, but colder regions still shifted toward C3. A lower crossover is a conditional advantage, not evidence for one global glacial expansion.

Origin is not expansion

The neat story says falling CO2 made C4 grasslands. The chronology refuses to be that neat, but not because C4 arose before the fall. The earliest grass C4 origins sit in the Oligocene CO2 decline.

The pathway was not a one-off invention. A 2011 synthesis recognized 62 independent C4 lineages across flowering plants, while dating the grassland story still requires separating origins from expansion.

The CO2-controlled crossover still has predictive teeth. It says which pathway has the photon economy to compete. Rainfall, nitrogen, fire, herbivory and land use decide whether that advantage becomes a landscape.