← Back

First Principles of Food #1

Sunlight, thermodynamics, and trophic levels
March 5, 2024

All food comes from sunlight

At a first principles level, all of the food we eat is stored sunlight, assembled from air and water. Using photons as an energy source, plants absorb CO₂ from the air, strip the carbon atom off and combine it with water to produce stored carbohydrates.

CO2+2H2O+photons    CxHyOz+O2+H2OCO_2 + 2H_2O + \mathtt{photons} \implies C_xH_yO_z + O_2 + H_2O
Equation 1: Photosynthesis

Depending on the plant, the carbohydrates could be a mix of glucose, cellulose, etc, although the details aren't that important for our sake. Light energy is stored in chemical bonds that we can break to release it. Plants also need nitrogen and some minerals, which is why they've evolved to exchange sugar with symbiotic bacteria for other compounds.

Photosynthesis isn't very efficient

How efficient are plants at turning light energy into chemical energy, in the form of carbohydrates? Not very. While the theoretical efficiency of photosynthesis (energy stored per unit of solar energy received) is about 26%, plants have a practical efficiency of less than 1% on an annual, areawide basis. Some of the most "light-efficient" crops we farm are maize and sugar beets, which can capture about 0.3% and 0.4% of the light energy that falls on a given patch of land, respectively1. So when you eat a plant and metabolize its carbohydrates for energy, >99% of the original solar energy has already been lost.

Not all of Earth's surface is suitable for growing biomass, of course. Zooming out to the global scale, the Earth's surface receives 3x10^24 J/yr of solar energy, while the net primary production of Earth's plant biomass is 4.2x10^21 J/yr – a 0.14% conversion of solar to chemical energy (Source).

Trophic levels

Energy efficiency losses start to become a real problem when we move further up the food chain. I like to think about the food system in terms of trophic levels, which are 1-indexed tiers that indicate how many steps removed a food source is from sunlight. Primary producers (plants) have a trophic level of L1L_1, herbivores L2L_2, carnivores that eat herbivores L3L_3, carnivores that eat other carnivores L4L_4, and so on2. Omnivores (e.g., most humans) might eat from many different trophic levels on a daily basis.

As you move to higher trophic levels, energy is inevitably lost as heat due to the fact that organisms do a lot more than just eat and grow. An animal who eats 1000 kcal of vegetation doesn't actually gain 1000 kcal of edible body mass, since they do lots of other energy-consuming things for survival (or just for fun). The feed conversion efficiency of animals might be 10% under "ideal" (read: highly confined) conditions.

Using an ηsunplants<1%\eta_{sun \rightarrow plants} < 1\% efficiency bound on photosynthesis and an ηLnLn+1<10%\eta_{L_n \rightarrow L_{n+1}} < 10\% upper bound on feed conversion, the fraction of the sun's energy available at level LL is:

η(L)ηsunplants×(ηLnLn+1)L1=1100×110L1=(110)L+1\eta(L) \ll \eta_{sun \rightarrow plants} \times (\eta_{L_n \rightarrow L_{n+1}})^{L-1} = \frac{1}{100} \times \frac{1}{10^{L-1}} = \left(\frac{1}{10}\right)^{L+1}

Equation 2: Energy available at trophic level LL

So L1L_1 herbivores have η(1)1%\eta(1) \ll 1\% of the sun's energy available to eat, L2L_2 carnivores have 0.1%\ll 0.1\%, L3L_3 carnivores 0.01%\ll 0.01\%, and so on. Another way to think about this is that each additional trophic level has an order of magnitude less available energy or carrying capacity to sustain life3.

The land footprint of food

Because virtually all food energy originates from sunlight hitting a leaf, energy requirements and land requirements are effectively interchangeable. Due to the upper bound on photosynthetic efficiency, there is a minimum amount of land required to produce one calorie. Because of energy losses, a calorie consumed from level L+1 generally requires 10x more land to product than a calorie consumed from level L 4.

The carbon footprint of food

You're probably aware that animal products, like meat, dairy, and eggs, tend to have high carbon footprints. That's not a coincidence, and can be largely explained by trophic levels. Chickens are one of the most "efficient" farmed animals, but are only produce about 1 edible calorie for every calorie they're fed. Each calorie of chicken contains the emissions from producing 10 calories of feed, transporting it, farming the chicken, etc. Cows are even less efficient, suggesting that cows5 should require a lot of land, which is indeed the case. In sum, thermodynamics dictates that livestock must be significantly more carbon intensive than the food they eat.

Implications for climate change

What I'm building towards is an amoral, first-principles intuition for why food choices matter for climate change. Because of Equation 2, the world can support at least an order of magnitude more herbivores (L1L_1s) than carnivores (L2L_2s). Equivalently, we could support the same number of herbivores using an order of magnitude less land, emissions, and other resources.

We are already running into the practical limitations of inefficient food production, simply because there are a lot of people and finite arable land. Most people are unaware that half of Earth's land is used for agriculture, that 80% of agricultural land is dedicated to livestock farming6. Flying over the midwestern United States actually provides a pretty accurate picture of how Earth's surface has been terraformed to capture sunlight and turn it into food. As the world's population grows and more people improve their quality of life, we'll need more land to produce more calories. That land comes from somewhere, and historically it has cost us valuable carbon storing ecosystems, like grasslands and forests.

Eating closer to the sun

In my view, the math of trophic levels implies only one plausible direction for decarbonizing the food system: eating lower on the food pyramid7. In 2018, Poore & Nemecek published an important paper which showed that shifting to plant-based diets would cut emission in half, and reduce land use by three-quarters. Reforesting that land, by the way, would remove an estimated 800 gigatons of CO2 from the atmosphere! Another important study by Eisen & Brown found that phasing out animal agriculture, over a period of 15 years, would effectively pause global warming for 30 years.

We should be very skeptical of any climate solution that promises decarbonization without any material change to how food energy is produced. Examples abound, like carbon neutral milk, regenerative grazing8, and feed supplements. These are solutions that partially help, partially confuse consumers, but will never scale to fully address climate change due to the basic rules of thermodynamics.

Eating lower on the food pyramid doesn't mean eating grass, as the straw-man counterargument often goes. Some of us might voluntarily change our diets, but most people probably won't have to make many sacrifices at all. Alternative proteins (meat, dairy, and eggs, produced without animals) recombine plant ingredients from L1L_1 to mimic foods from L2L_2, L3L_3, and so on! As alternative proteins approach price and taste parity, we'll be able to eat many of the foods we already enjoy for a fraction of the environmental cost.

Outperforming photosynthesis

A plant-based diet is much more energy- and land-efficient than an omnivorous diet, but it still runs up against the poor efficiency of photosynthesis (well below 1%, as we saw above). Is photosynthetic efficiency a hard upper bound on the efficiency of food production? Short answer: no! In the next post, I'll explore a NASA-inspired food production technology that can outperform the efficiency of photosynthesis.

Footnotes

  1. See the supplemental data from this paper. For comparison, a modern solar panel has a theoretical efficiency of ~32%, a ~20% efficiency under ideal conditions, and more like a 5% efficiency if you factor in cloudy days, suboptimal sun angles, etc. At 5% efficiency, solar panels are still about 10x more efficient than most plants.

  2. Decomposers like mushrooms make the picture slightly more complicated, since they can recycle energy from higher trophic levels down to lower levels.

  3. Carrying capacity is why you'd probably find far fewer carnivores in a given area of land, and maybe why they tend to be more solitary than herbivores?

  4. The “food pyramid” is actually an apt metaphor, as you need a very wide area of the base (photosynthesis) to support the increasingly narrow levels above.

  5. Cows and other ruminant animals are infamous for their methane emissions, which is more due to the idiosyncrasies of their digestive biology than a consequence of trophic levels.

  6. Despite using the majority of farmland, livestock only supply 17% of the world's calories and 38% of its protein.

  7. Reducing food waste is critical too, of course, since about one-third of food is wasted. However, I want to re-emphasize the point that livestock are the largest source of food waste by far, since most of the calories they eat are lost from the human food supply as heat. Counterintuitively, reducing the number of farmed animals actually leads to a net increase in food, since feed crops become available for direct human consumption.

  8. Regenerative grazing may promote soil carbon, but proponents fail to acknowledge the fine print and limitations: it requires way more land, and the cows grow more slowly, which means they'll produce more methane in their lifetime. The push for regenerative grazing also implies a false choice between factory-farmed beef and sustainable beef. There is a third option, where we turn pastureland back into its natural state and eat something else.