The life seam · a threshold everyone quotes and everyone defines differently

The Crossover at Twenty-Two Degrees

Below some temperature an ordinary C3 leaf turns light into sugar more efficiently than a maize leaf does. Above it, the maize wins. That temperature is not a property of either plant: it is set by how much CO₂ is in the air, and you can drag it. The 22 °C of the title is one specific published number, Collatz, Berry and Clark's mean warmest-month air temperature at 35 Pa CO₂, and it is a different quantity from the leaf-temperature crossing the chart below computes. Watching those two numbers refuse to be the same is most of what this page is about.

Nothing on that chart was drawn. The C3 curve is φ_C3 = φ_max (C_i − Γ*)/(C_i + 2Γ*), the light-limited branch of Farquhar, von Caemmerer and Berry's 1980 model, evaluated at every pixel; Γ*(T) is Bernacchi's in-vivo Arrhenius function, measured in transgenic tobacco in 2002 and quoted below to the digit. The C4 line is flat because Ehleringer and Bjorkman measured it flat in 1977. The crossing is found by bisection each time you move a slider.

Here is the thing worth noticing before any explanation. The crossing moves, and it moves a long way, and the only thing you changed was the air. Neither plant was modified. A C4 grass is not adapted to heat in the way a camel is adapted to heat; it is adapted to a ratio, and the ratio is one that heat and low CO₂ both push the same way.

What is actually being taxed

Rubisco, the enzyme that attaches CO₂ to a five-carbon sugar and starts the Calvin cycle, does both jobs at a single active site: the same pocket has to accept CO₂ and O₂, and it cannot cleanly tell them apart. (A plant's Rubisco is a Form I hexadecamer with eight such sites; the point is that carboxylation and oxygenation compete at every one of them, not that there is only one.) When it grabs O₂ instead, the product is a two-carbon compound the plant cannot use, and it has to be salvaged through the peroxisome and the mitochondrion at a cost in ATP, reductant, and a quarter of the carbon released back as CO₂. That salvage is photorespiration. The enzyme is not broken; it evolved when there was essentially no O₂ to confuse it with, and, as Tcherkez, Farquhar and Andrews put it in 2006, specificity for a molecule as featureless as CO₂ has to be bought in the transition state, which is exactly where it costs speed.

Two things make the tax worse. Warmth, because O₂ becomes relatively more soluble than CO₂ as water warms and because the enzyme's own specificity falls; and thin CO₂, for the obvious reason. Both are folded into a single number, Γ*, the CO₂ level at which carboxylation and photorespiratory release exactly cancel. It is about 37 ppm at 25 °C and nearly twice that at 45 °C, which is the entire reason the C3 line falls.

C4 plants do not fix carbon differently. They run the same Calvin cycle with the same Rubisco; they simply build a wall around it. PEP carboxylase, an enzyme with no oxygenase activity at all, grabs bicarbonate in the mesophyll and ships a four-carbon acid into the bundle-sheath cells, where it is decarboxylated. Rubisco sits in there breathing CO₂ at several times ambient. It is a pump, and pumps cost energy: about two extra ATP per CO₂. That cost does not care about temperature, which is why the C4 line is flat, and why C4 is not "better". It is a fixed-cost strategy in a variable-cost world.

The dismissal, and the answer

The sophisticated reply to all of this is: yes, obviously, photorespiration rises with temperature, C4 is a warm-climate adaptation, everyone knows. That reply is not wrong, it is just untested. So here is the test. In 1977 Ehleringer and Bjorkman measured quantum yields in two atmospheres, ordinary 21% oxygen and a 2% oxygen mixture that all but abolishes photorespiration. In 2002 Bernacchi and colleagues, using a completely different method (gas exchange on transgenic tobacco with antisense Rubisco, a generation later, on a chloroplastic CO₂ basis) published the temperature response of Γ*. Those two papers never had to agree. Put Bernacchi's constants into Farquhar's equation and it predicts the 1977 ratio.

The C4 leaf does not notice. Take nineteen percentage points of oxygen out of its air and its quantum yield changes by less than the measurement's own scatter, because the pump had already taken the oxygen out where it mattered. The C3 leaf leaps. That is the whole content of the crossover, stated as a fact about oxygen rather than a fact about heat: C3 is paying an oxygen tax, and warmth is only the thing that makes the tax bigger.

And the prediction is not a fit. Nothing in Bernacchi's tobacco experiment knew about Ehleringer's 1977 gas exchange. One free choice enters, the assumed intercellular CO₂, and the instrument shows you exactly how much it buys: the value that makes the agreement exact is printed above, and the 1977 atmosphere itself was 333.84 ppm (published, NOAA Mauna Loa annual mean).

The same two curves, as a bill

Turn the quantum yields upside down and they become photons per CO₂, which is what a leaf actually pays. Now the crossover stops being a crossing of curves and becomes something blunter: a rising tax meeting a fixed toll.

Two numbers on that panel deserve staring at. The first is the C3 ceiling: about thirteen photons per CO₂ even with photorespiration abolished. The thermodynamic floor is eight (four electrons per CO₂, two photons per electron), so a real leaf in ideal air already wastes about a third of its light before the oxygen problem starts. The second is the surcharge: the C4 pump costs a flat five-and-a-half photons per CO₂, at every temperature, forever. Below the crossing that is money thrown away.

Zhu, Long and Ort put the same accounting in whole-leaf energy terms in their 2010 review, and their figure is a useful reality check because it is not derived from anything on this page. It also contains an arithmetic step that does not close, which the panel below recomputes rather than hides.

Does it put C4 where C4 actually is?

A crossover temperature is a claim about a leaf. Turning it into a claim about the Earth needs three more assumptions, and the honest way to present them is to hand them over. This instrument runs the criterion of Collatz, Berry and Clark (1998) over the real world: WorldClim 2.1 monthly climate normals, aggregated here to 2° cells, asking of each land cell how many months are both warm enough and wet enough for a C4 grass to beat a C3 grass on light-use efficiency.

Three things the map cannot know. It does not know that C4's real competitor in the warm wet tropics is not C3 grass but trees, which shade grass out entirely. It does not know about fire: Bond, Woodward and Midgley ran a dynamic global vegetation model with fire switched off and reported that "Without fire, closed forests would double from 27% to 56% of vegetated grid cells, mostly at the expense of C₄ plants but also of C₃ shrubs and grasses in cooler climates." And it does not know about grazers, or about maize, which is a C4 crop occupying land no physiological criterion put it on. The physiology sets an envelope. Disturbance decides what lives in it.

The clock that fires seventeen million years early

If the crossover explains where C4 grows, it ought also to explain when C4 took over. The textbook story: CO₂ fell during the Cenozoic, the crossover temperature fell with it, and somewhere in the late Miocene it dropped below tropical growing-season temperatures and the grasslands took the world. Cerling and colleagues proposed exactly that in 1997 on the strength of a sharp shift in the carbon isotopes of fossil tooth enamel: "Between 8 and 6 million years ago, there was a global increase in the biomass of plants using C4 photosynthesis as indicated by changes in the carbon isotope ratios of fossil tooth enamel in Asia, Africa, North America and South America."

The instrument below drives the same model with the actual proxy record, all 4,726 Cenozoic CO₂ estimates in the CenCO2PIP compilation that fall in the last 40 million years, each one a published reconstruction from boron isotopes, alkenones, stomata, paleosols or leaf-wax carbon. Nothing is smoothed for you: the running median is computed in your browser and the window is yours to set.

The model fires early, by a lot, and it keeps firing early no matter which knob you move inside its defensible range. That is not a bug in this page; it is the actual state of the question, and the literature has been arguing about the gap for thirty years.

• The CO₂-threshold hypothesis (Cerling et al. 1997) says a falling CO₂ crossed a threshold at 8 to 6 Ma. Pagani, Freeman and Arthur tested it directly two years later with alkenone-based pCO₂ and found the opposite: "Alkenone-based pCO₂ estimates for the late Miocene indicate that pCO₂ increased from 14 to 9 million years ago and stabilized at preindustrial values by 9 million years ago. The estimates presented here provide no evidence for major changes in pCO₂ during the late Miocene." No threshold was crossed at the moment the enamel changed.
• The aridity hypothesis, which Pagani's own paper suggested as the alternative, was tested by Polissar and colleagues in 2019 with African leaf-wax carbon and hydrogen isotopes plus dust. C4 ecosystems "expanded synchronously across Northwestern and East Africa after 10 million years ago. This was not accompanied by substantial changes in palaeohydrology or dust deposition, precluding aridification as a causal factor." That paper then argues back for CO₂, at 10 Ma rather than 7.
• The lag itself. Christin and colleagues dated the 17 to 18 independent grass C4 lineages by Bayesian molecular clock and put the first transition, in the Chloridoideae, at 32.0 to 25.0 Ma. C4 grasses existed for roughly twenty million years before they dominated anywhere. Whatever explains the expansion has to explain the delay, and a threshold model that fires the moment the threshold is crossed cannot.
• Fire and grazers are the leading candidates for what fills the gap. Bond's fire-off experiment above is the quantitative version of that argument.

This page picks no winner. What it can do is show you that the physiological clock and the isotope clock are not the same clock, and let you fail to make them agree.

Is Rubisco a bad enzyme?

The popular version says Rubisco is the worst important enzyme in biology: slow, and confused about its own substrate. The specialist version, argued by Tcherkez, Farquhar and Andrews in 2006, is that "all Rubiscos may be nearly perfectly adapted to the differing CO₂, O₂, and thermal conditions in their subcellular environments, optimizing this compromise between CO₂/O₂ specificity and the maximum rate of catalytic turnover." Those cannot both be right, and the thing that separates them is data.

In 2019 Flamholz and colleagues re-examined the trade-off with kinetic measurements from about 300 organisms instead of the roughly 20 the classical picture rested on. The instrument below is that dataset, 256 enzymes with both a carboxylation turnover number and a specificity, plotted and refit in your browser. Then you get to invent a better one.

Notice what happens when you drag specificity up. Γ* falls, photorespiration falls, the crossover temperature climbs and C3 keeps its advantage further into the heat. But the classic correlation says you pay in turnover, and the relative-assimilation tile prices that: a leaf contains a finite mass of Rubisco, so halving the turnover halves the carboxylation capacity whatever the specificity does for you. Somewhere the trade turns negative. Where it turns depends on a correlation whose strength the 2019 dataset materially weakened, which is exactly why the C4-rice and better-Rubisco engineering programmes are live rather than settled.

What it is worth, now

C4 is rare and enormous at the same time. Sage counted "over 45" independent origins in 19 families of angiosperms in 2004, and by 2011 Sage, Christin and Edwards listed "62 recognizable lineages of C4 photosynthesis", 36 of them in the eudicots and 26 in the monocots, "with a minimum of 18 lineages being present in the grass family and six in the sedge family". Evolution invented this pump, independently, at least sixty-two times. It is one of the most convergent complex traits known.

And it does a fifth of the work. Luo and colleagues mapped C4 vegetation against satellite observations and optimality theory and found that "global C4 vegetation coverage decreased from 17.7% to 17.1% of the land surface during 2001 to 2019", the net of C4 natural grass being lost as rising CO₂ favours C3 against C4 cropland (mostly maize) being gained, and estimated that "C4 vegetation contributed 19.5% of global photosynthetic carbon assimilation". Maize, sorghum, sugarcane, millet and the world's worst weeds are C4. Rice, wheat, soy, barley and essentially every tree are C3; C4 trees do exist, and they make a short and exotic list, including the Hawaiian tree Euphorbia species Pearcy and Troughton measured in 1975. That is why there is an international project trying to install a C4 pump into rice: at 30 °C and 387 ppm the pump is worth 6.0% of incident sunlight against C3's 4.6% (published, Zhu, Long & Ort 2010), and rice grows on the hot side of the crossing.

The last line of that paragraph is also the live experiment. The crossover model predicts that as CO₂ rises the crossing temperature rises with it, and C4's advantage retreats. Luo's satellite record shows exactly that, at 0.6 percentage points of land cover in eighteen years, and that 0.6 is a net figure: maize expansion was adding C4 cropland over the same period, so the CO₂-driven loss of natural C4 grass is larger still. The model on this page is being tested in real time, and so far it is passing on the sign.