Finding the ideal environmental diet

Our food system is polluting the world and destroying wild ecosystems—if we are to survive, we have to shrink its impacts. At the same time, it’s damning much of the world’s population to diseases of undernutrition and overnutrition—if we want to thrive, we have to improve its outputs, or at least change the way we distribute them. So: what should we all be eating if we want to both be healthy and minimise the harm we do to the planet?

This is a deceptively difficult question. Perhaps it sounds like it should be a simple matter of identifying the most ‘efficient’ food—the one that uses the least land per calorie to produce, say—and just eating lots of that? Livestock take up 77% of agricultural land and yet animal source foods only supply 18% of calories—they’re ‘low efficiency’ foods in this crude sense, so we shouldn’t eat them, right? Well, not so fast. Living things are extremely complicated and have extremely complicated nutritional needs. Animal source foods provide more like a third of the global supply of protein and half the fat. They’re rich in essential micronutrients, including some (like the B-vitamin complex) which are nigh-impossible to get from plant-based foods. So can you be sure that the ideal diet wouldn’t include some meat, dairy or eggs?

Pleasingly, these kinds of questions sit at the level of mathematical complexity that is hard for human brains and very easy for computers. So let’s find out.

Limitations: people are not computers, and the world is not one place

I’m taking a very abstract approach here, and I don’t have any delusions about the limitations of that. It’s really hard to get people change what they eat—food is close to all our hearts and is imbued with all sorts of social meanings. The more alien the diet, the harder it is to get people to shift to it, and there’s lots of room to try to get people to eat better without trying to get them to eat perfectly. So the point of calculating the mathematically optimised environmental diet is not to find a precise goal state for the food system—rather, it’s about sorting out what holds up to scrutiny among the big claims that people make about how the food system should change.

This is also a very reductive way to think about food, place and culture. Different places have different growing conditions, different amounts of land available, different population densities—all of these might mean that the real impact of producing a foodstuff is different in some locales than others. Alternatively, even though food miles are not a large part of emissions, they still contribute, so shipping food around the world from the places it’s least impactful to produce would also add complexity. So my one-world approach here is a huge simplification, and in the real world, the right answer will differ between geographical contexts. On top that, social-cultural variation in preferences for food and the cultural meanings attached to food mean that what is feasible or desirable will also vary from place to place. Looking for one, mathematically optimised answer ignores all of this, and that is a big drawback.

I don’t think my approach here is new or ground-breaking (I assume something like this was tried in developing the EAT-Lancet diet), but I’m not aware of this exercise being spelt out in detail anywhere. Nevertheless, this is just a bit of fun and shouldn’t be taken more seriously than it’s meant.


What set me wondering about this was some questions about environmentally-motivated veganism and vegetarianism. In a taste-culture vaccuum, is it always the right answer to be vegan? Is it even always the right answer to be vegetarian? Assuming that it isn’t, when do animal-sourced foods have a place in an environmentally friendly diet? Are they suitable for some demographics with some dietary needs but not others? Or suitable to minimise some environmental impacts but not others? Would the environmentally ideal diet for me be a vegan diet, or would it include some ASFs? To lay my cards on the table, I am a vegan, but I come to veganism first and foremost because I believe it’s incumbent on us to try to reduce the suffering we cause in the world. The assumption that my dietary choice also happens to be the environmental one is a comfortable assumption. But it would be interesting to know whether it was actually right. Are my animal ethics in agreement with my environmental politics, or is there an ethical tension there?

I’m also interested to see quite how far we are from the ideal: how extreme or bizarre does the environmentally optimised diet look? Should we all be eating some incredibly complex list of plants picked from all over the world? All eating little more than beans and grains? And how much does the answer differ depending on how we define our environmental goals?

So we have a set of constraints: this needs to be a healthy diet, so it should conform with all of the nutritional guidelines set out by some authority—both meeting the requirements for nutrients the body needs, and keeping below unsafe intakes of potentially unhealthy things like saturated fats. The problem is to pick the combination of foods which meet those constraints while minimising environmental impacts. I talked to a mathematician friend about this, and he said, “I don’t see why that wouldn’t be a pretty straightforward linear programming problem...?” So I looked up the R implementation of linear programming, and—yes, indeed, he was right.

The nutritional constraints

I could reasonably have used any comprehensive set of dietary recommendations here. I’ve gone for the USDA’s over the WHO/FAO’s for no particular reason—I just had the pdf already open in Acrobat for another project when I started this, and here we go. I won’t spell out all of these because it’s a hideously complicated set of recommendations that is sensitive to a lot of variables in non-linear ways: age, weight, height, level of physical activity, pregnancy (and trimester if pregnant) and breastfeeding (and how long after birth if so) all play roles. Basically, I wrote a very ugly R function that spits out a table of nutritional requirements in response to these demographic variables. Here are the requirements it specifies:

PUFA 18:2 (linoleic acid)AI
PUFA 18:3 (ɑ-linoleic acid)AI
vitamin ARDAUL
vitamin B6RDAUL
vitamin B12
vitamin CRDAUL
vitamin DAIUL
vitamin ERDA
vitamin KAI
pantothenic acidAI
carbohydrateAMDR (lower)AMDR (upper)
fatAMDR (lower)AMDR (upper)
proteinAMDR (lower)AMDR (upper)
added sugarDGAfrom the "Dietary Guidelines for Americans"
saturated fatDGAfrom the "Dietary Guidelines for Americans"
histidinemg/g proteinborrowed from FAO/WHO/UNU
isoleucinemg/g proteinborrowed from FAO/WHO/UNU
leucinemg/g proteinborrowed from FAO/WHO/UNU
lysinemg/g proteinborrowed from FAO/WHO/UNU
methioninemg/g proteinborrowed from FAO/WHO/UNU
cysteinemg/g proteinborrowed from FAO/WHO/UNU
phenylalanine+tyrosinemg/g proteinborrowed from FAO/WHO/UNU
threoninemg/g proteinborrowed from FAO/WHO/UNU
tryptophanmg/g proteinborrowed from FAO/WHO/UNU
valinemg/g proteinborrowed from FAO/WHO/UNU

AI: adequate intake. AMDR: acceptable macronutrient distribution range. DGA: daily guideline amount. RDA: recommended daily allowance. UL: upper limit.

A few things to point out here. I couldn’t find USDA specifications for individual amino acids, so those are borrowed from the FAO/WHO/UNU. There are some micronutrients (vitamin B12, riboflavin, thiamin, magnesium, etc.) for which the USDA gives RDAs or AIs but doesn’t specify upper limits for intake from food (in some cases a UL is specified but only applies to supplements). There isn’t a real risk of getting too much of these things in normal diets, so presumably it hasn’t been a big priority for anyone to work out the point at which they become dangerous. But if the programme here suggests really abnormal diets, it’s conceivable that these would become problems. There are some things which the USDA gives dietary recommendations for but which aren’t included in the nutritional information of enough foods in the dataset I’m using (see below). For that reason, these have been excluded: molybdenum, chromium, fluoride, iodine, sulfate, boron, nickel, vanadium and biotin. Some of these are really potential contaminants rather than necessary nutrients anyway.

I also haven’t included constraints on trans fats or dietary cholesterol in the programme. On the question of cholesterol, it was previously thought that higher dietary intake was associated with cardiovascular disease, and so older guidelines recommend minimising intake. However, recent work shows that this association is complicated and uncertain, and so since 2015 guidelines have not included a specific recommendation on cholesterol. However, these guidelines don’t reject the idea that high dietary cholesterol could be bad for you. They just assert that the issue is complicated enough that directly advising people to monitor and limit their cholesterol intake is impractical, and the recommended dietary patterns (like the Mediterranean Diet) are low in cholesterol anyway. So if the programme were to end up recommending very high cholesterol diets, that could be a flaw. Trans fats also present a problem: guidelines generally just recommend minimising them, with the ideal daily intake being 0. However, if I set this to have a constraint of zero trans fats, that completely rules out a lot of animal source foods, which undermines the usefulness of the programme to answer my question about the role of ASFs in sustainable, healthy diets. So I haven’t put a constraint on trans fats: again, if the programme ends up recommending diets really high in them, that would be a flaw to address.

The environmental goals

So those are the constraints on what’s an acceptable diet. Our goal is to meet those, but optimise for the best (read: smallest) environmental impacts. In linear programming terms, that’s the objective function or loss function—the mathematical function to be minimised.

But what should that be? Well, there are a large number of ~environmental bad things~ one could choose from—but I think two stand out as most universally central to any analysis of the way our food system is destroying the world, and those are land use and greenhouse gas emissions. The relevance of emissions is obvious. Land use because every bit of land used for agriculture—even in maximally ‘nature friendly’ ways—is taking away habitat from wild species. The most egregious examples are where agricultural use is directly causing ongoing deforestation, but really in the big, zoomed out picture, any land used by agriculture could in an alternate history or future be left to nature. You could also include other environmental impacts here like water use, nitrogen pollution and water eutrophication, other types of pollution, and so on. But I’m starting here with the big two.

With linear programming, we have* to pick just one objective function—so what I’ll be doing here is running all the maths twice, minimising land use and minimising greenhouse gas emissions separately. This will give two different environmentally optimal diets we can compare.

These two kinds of environmental impacts clearly overlap, and I did also consider ways to treat them as a single thing. For example, all land use for agriculture is either virgin land that necessitates deforestation (releasing carbon) or could alternatively be rewilded (sequestering carbon), so you could just translate all land use into a counterfactual carbon sequestration figure and include it in the GHG emissions estimate. I didn’t do this for a couple of reasons. Firstly, conceptually, this fails to capture the entire reason that we might be interested in land use: taking land away from wild ecosystems is not only bad because it entails releasing more carbon; the idea of calculating the moral value of wild ecosystems solely in terms of ecosystems services to humans like carbon sequestration is pretty reductive. Secondly, I wanted to keep this relatively simple and avoid making too many big assumptions. It’d be an interesting future addition to try something like this out.

* Well, there are more sophisticated methods that allow for multiple objective functions, but I’m starting simple here

The data

Okay, we’re getting there. Next we need two sources of data. First, we need a dataset with the nutritional contents of a large range of foods which represent the options on the menu that the programme is picking from. I’ve used the USDA’s Legacy Foods database. When dealing with meat, things are somewhat complicated by the fact that different parts of the carcass have wildly different nutritional contents, but you can’t produce one without producing all of them, so it doesn’t make sense to include them all as separate options. Instead, I’ve gone to the literature for proportions of different types of offal and meat in carcasses and included nutritional content of meats as weighted averages of the nutritional contents of those components (in other words, these diets are optimised assuming nose-to-tail eating). Strictly speaking, this does mean that there are potential solutions that involve just eating micronutrient-dense offal and actually throwing away other meat (since it isn’t as micronutrient-dense but still counts against nutritional constraints like that on saturated fat). But I think it’s vanishingly unlikely that these solutions would ever turn out to be optimal.

Secondly, we need a dataset with the average land use and GHG emissions of the foods we’re going to include. You could go to the literature and start looking up individual studies of land use for all these things, plus LCAs to get GHG emissions. But there’s a lot of variation between different studies, necessitating calculating averages and estimates of variance—and this work has been done before. So I’ve used the data collected by Poore & Nemecek 2018 for this purpose.

There are some real problems with these data. The biggest one, I suspect, is that Poore & Nemecek’s categories are just too big and collapse too many things. All brassicas not nutritionally equal—is it really reasonable to regard them as having equal environmental impacts per kg? Similarly non-starchy root vegetables, all berries, all nuts, and so on. It’s very possible that some results here are artefacts of particular foodstuffs being unrepresentative of their larger group for environmental impacts. But, given that the alternative is going to involve doing a huge amount of work searching for individual studies of every vegetable—and that then I’ll instead have a problem that the data will be too low-quality, with just n=1 or 2 for many things—I think this is a reasonable compromise to accept. I’ve also explored how big a problem this is by using leave-one-out cross validation, below.

I didn’t include fish at all. The impacts of wild-caught fish on wild ecosystems is clearly a question entirely outside the framework here. If you blindly optimised for land use and included wild-caught fish then you would of course conclude that you should eat as much fish as possible, since their land use would be close to zero. That would be an ad absurdum answer, so it doesn’t make sense to include them here. You could argue that I should have included farmed fish on the basis that it’s more feasible to measure their impacts in terms of land use (including for feed crops) and carbon emissions. However, a great part of what farmed fish are fed is still wild-caught fish. As a result, I think that from the perspective of a land+emissions model, aquaculture still effectively externalises so much of its environmental impact that it would be distorting to include it.

I did then add some more foodstuffs to the list that Poore & Nemecek present in their data. Firstly, I added synthetic vitamin D. You might baulk at the idea of adding synthetic vitamins—many people have an objection to them (whether on the grounds of aesthetics, naturalness, or concerns about the unknowns of ultra-processed foods). But many people already take them, and what role they could and should play in more sustainable food systems is a legitimate question. Secondly, the soymilk I included was fortified with synthetic vitamin B12—most plant milks I have access to in shops is fortified with B12, and the same logic applies, I think. I also added spirulina powder, since another interesting question I think you could try to answer with this kind of modelling is: what place should alt proteins like SCP play in a sustainable diet? For the vitamin D and the spirulina, I looked up LCAs for estimates of the GHG emissions and did some reading online to estimate land use.

How to read the results

So, finally, what does the LP tell us? Well, click the plus sign to expand the bar below and view the result when optimising for emissions for the diet of a 33 year old, female, 64.9kg, 180cm tall, sedentary adult (hi). The top lines give you the headline figures: the land use (in m2 per day) and emissions (in kg CO2-eq per day); the total weight and kcal of food; and the macronutrient breakdown of the diet. At 17% of calories from protein, this is a low-ish protein diet relative to the meat-eating population of the UK (where I am), but pretty typical of vegan diets. The top two pie charts show the contribution of the different components of the diet to environmental impacts: we can see on the left that lentils and almonds are responsible for the biggest chunks of land use, whereas on the right we see that GHG emissions are distributed more evenly across a lot of the components of the diet. In the two bottom pie charts we see the different components of the diet in terms of their uncooked weight (left) and contribution to energy (right). Finally, the bar chart at the bottom gives us some clues as to why this particular set of foodstuffs have been selected. This ‘limiting nutrient’ chart shows us only the nutritional constraints that are within 10% of their maximum or minimum allowable values—these then are the constraints which likely played a bigger role in determining the makeup of the diet. For each of these, the colours show us how much each foodstuff contributed to that nutrient. So, for example, we can see that we’re at the upper limit for fat mostly due to eating a lot of almonds, and we’re exactly meeting our vitamin A requirement mostly through sweet potatoes.

The thing I’m struck by with this first result is that it’s actually a relatively sane diet compared to my expectations. I was expecting something that would be pretty hard to imagine eating (and stay tuned for some examples like that), but this isn’t an impossible day of food. The weirdest thing is getting a third of calories from almonds—but the amount (124g) is physically feasible. I wouldn’t be totally surprised to discover that I had eaten close to that amount of almonds in a day at some point in my life…? (My local cinema used to sell these 150g packs of salted lemon almonds which were super addictive…). And 473g of cauliflower is, let’s be clear, quite a lot of cauliflower. But again, it’s not an amount that sounds really hard to actually eat—to give this some context, the internet seems to regard between 100g and 130g of cauliflower as a ‘serving’.

There are also some obvious structural things worth noting. It’s vegan—perhaps that’s not that surprising to you if you’ve ever read much about sustainable diets (but on that point, stay tuned). All the dietary vitamin D is provided by a supplement, and all of the vitamin B12 is provided by fortified soy milk. If you take away those options, the result changes substantially. Indeed, since soy milk is the only vegan dietary source of B12 on offer here, if soy milk isn’t available then the optimised diet won’t be vegan.

How about if we optimise for land use instead of GHG emissions? Well, click the plus sign below to see the result for the same demographic characteristics but optimised for land.

There’s quite a bit to say here. Firstly, note that the diet isn’t vegan! We’re eating 49g of egg—about equivalent to one small chicken’s egg per day. Oddly, this doesn’t seem to be because egg uniquely represents the most land-efficient source of any nutrient in particular. It’s providing about a third of the choline in the diet, and then a small part of the B12, vitamin D, and some other bits here and there. This is a pattern we’ll see a lot throughout these results.

Secondly, it’s completely different to the GHG emissions-optimised diet. In the low-land diet, we’re getting most of our calories from maize flour, spirulina, cabbage, palm oil and beet sugar. In the low-emissions diet, we were getting most of our calories from almonds, rye bread and sweet potatoes. There is no overlap there at all. Indeed, the only ingredient that is found in both diets in any quantity is (fortified) soymilk, which is there to be a source of B12. This, too, is going to be a pattern we see a lot of: it really matters whether you want your diet to be climate-friendly or land-use-friendly.

Thirdly, something you may already have spotted in the last paragraph, in addition to a potentially impractical quantity of cabbage, this diet has us eating a lot of spirulina. I mean really a lot. To put it in context, 113g of spirulina per day is at least ten times the vague recommendations for consumption written on spirulina packets (where a ‘serving’ is often defined as 3g or 7g) and nearly six times the largest amount I’ve come across being administered in a clinical trial (here’s an example with 19g/day—but the vast majority of trials are giving participants 10g/day or less). This isn’t an outlier, either: because the estimate of land use for spirulina production I came up with is really extremely low, the programme will recommend diets with as much spirulina as other nutritional constraints allow whenever you’re optimising for land use. So is this merely a deeply unpalatable idea, or actually dangerous?

My initial thought was that this high a spirulina intake might be a problem due to high levels of nucleic acids, which contain high levels of purines, which would lead to excess uric acid production and eventually gout and kidney stones. The USDA doesn’t have a guideline for maximum safe intake of nucleic acids or purines (that I’ve found), and neither nucleic acids nor purines are recorded in the nutritional information for any of the other foods I’ve included—so this doesn’t offer a very consistent way to fix this problem. What’s more, when I read about this further, I learnt that my “high purine intakes lead to gout” understanding was out of date or simplistic: there are many foods which are high in purines which are not associated with gout or kidney stones, so although high intake of algae/seaweeds (along with meat) is associated with these negative health outcomes, this can’t straightforwardly be the right explanation. Nevertheless, there is a 40-year old WHO/FAO recommendation to limit consumption of nucleic acids from single-celled proteins (like spirulina) to 2g per day, which equates to an intake of spirulina of 40g per day. As ad-hoc as this feels, I haven’t come up with anything better, so I’ve included this in the nutritional constraints. That gives the revised diet optimised for land-use for the same demographic characteristics below.

This actually results in some pretty big changes. The carrots and a bit of that huge quantity of cabbage from the first version are replaced by a large amount of chard. Smaller changes include eating more maize flour and a bit more palm and rapeseed oil and soymilk, a bit less soy oil and eggs. Overall, this looks like a somewhat saner diet than the first version—although, to be clear, still pretty extreme. I’m not convinced it’s possible—and it certainly wouldn’t be fun—to eat almost a kilo of cabbage per day.

Frivolous aside: find your own environmentally optimal diet!

So what should you be eating to minimise your GHG emissions or your land-use footprint? Look up your personalised recommendation below! Nb. this isn’t being calculated live, and I’ve only pre-rendered 16k combinations. So I couldn’t include as many small gradations of height/weight/etc. as would be nice. Just choose options as close to your demographics as possible.

Optimise for:
Physical activity:

* How is this being defined? I don’t really know. The USDA talks about “gender groups”, “sex”, “boys and girls” and “men and women” pretty much interchangeably, while citing papers that talk about both “sex differences” and “gender differences”. For some things, I guess what is relevant is sex hormone profile (testosterone vs. oestrogen dominant) because of the way it tends to affect body composition; in others, it’s probably about what reproductive organs you have and whether you currently have periods; in others, I suspect that we don’t know. For most nutrients it doesn’t actually change the recommendations a huge amount, although because it changes the recommendation for total calorie intake, it does often change the optimised diet quite a lot.

Patterns across results

Okay, that was a fun tangent. Something you might have noticed if you explored those results much, though, is that they’re pretty volatile. As you play with the settings, you’ll find individual foodstuffs appearing and disappearing from the diet, sometimes even in quite large quantities. So how can we summarise patterns across environmentally optimised diets for many different demographics? How can we identify overall takeaways?

To start with, I’ve run the programme again, this time on 54k people with more realistic population demographics. To construct this population I took the means and standard deviations for adult men and women’s heights in the UK and sampled a regular sequence of 15 quantiles from 0.01 to 0.99 from these distributions, then combined these three regular sequences of BMIs from 18.5 to 35.5 (giving three equal-sized groups of “healthy weight”, “overweight” and “obese” people, in line with UK population statistics), and a regular sequence of ages from 18 to 90. Weights are calculated from BMIs and heights, giving a nice double-peaked, long-right-tailed distribution. We can then do some stats to summarise what diets the programme usually suggests across this population.

The boxplots below then show the amount of different foodstuffs included in diets optimised by weight and by kcal. Click the first + to see diets optimised for emissions, and the second to see diets optimised for land use. Only foodstuffs which occurred in at least 1% of diets were included in these figures.

So, some things are really consistent across the minimum-emissions diets. They’re mostly getting the largest single part of their energy intake from almonds, but also sizeable amounts from wheat bread, sweet potatoes and kidney beans. As a result of those almonds, these are almost all quite high fat diets—generally they’re all knocking up against that 35% acceptable macronutrient distribution range for proportion of energy from fat. In terms of weight, they all include a lot of cauliflower: the median is a ridiculous 510g. There is a huge range of maize flour intakes, ranging from diets which get almost half their calories from this source to many (38%) which have no maize flour at all. Oranges are similar, except even the diets which include really extreme amounts of oranges by weight aren’t getting a majority of calories from this source—the largest energy intake from oranges is 530kcal. Then there are some oddities like pistachios, which are entirely absent from 97% of diets, but in a handful make up a really large chunk of calorie intake, particularly in the diets with the highest total calorie intake (try looking up m / 18y / 1.81m / 112kg / very active in the library above).

You will notice that eggs do occur in a small minority of these diets (1.4%). So to return to one of the questions I started with: when should(n’t) you be vegan if minimising for emissions with these data? Well, all of those 1.4% are among the 18 year olds in the data: there’s a sharp discontinuity in the USDA recommendations between 18 and 19, with the requirements for a lot of micronutrients dropping, and the higher micronutrient requirements of 18 year olds (and presumably younger people—but I haven’t run the programme on children’s diets at all to check) lead to micronutrient-dense eggs being a GHG-efficient foodstuff for that group. Within that group, it’s only the heavier (weight>70kg, and much more reliably so for weight>100kg) and taller (height>1.5m) individuals for whom the programme tends to suggest eggs.

As we already guessed from looking at the individual results above, the suggested diets are a lot weirder when optimising for land use. A bit like the cauliflower in the emissions-optimised diets these consistently contain a large quantity of cabbage. But where “a large quantity of cauliflower” typically meant half a kilo, this time the median weight of cabbage is over a kilo per day (still under 15% of calories per day, though—cabbage really isn’t energy dense). Most land-optimised diets also include a lot of chard by weight. If we think about the diets in terms of energy intake, we see that most of the energy in the land-optimised diets is coming from maize flour and palm oil.

Quite unlike the emissions-optimised diets, the vast majority (93.8%) of the land-use-optimised diets include eggs and a tiny handful (0.2%) include milk. The strongest predictor of being recommended a vegan diet among this set of results is bodyweight, with the programme suggesting a vegan diet for 18% of people in the 93-103kg bodyweight group, rising to 86% of those in the 134-145kg bodyweight group.

Land vs. emissions

The biggest factor determining what the optimised diet looks like is whether you’re optimising for land or emissions. This is an intuitively obvious result—of course you’ll get a different result if you optimise for a different thing—and easy to demonstrate statistically (whatever clustering method you choose, the choice of loss function determines the top level clusters). However, what’s interesting here is quite how different these diets are. Your average emissions-optimised diet has a lot of nuts, grains, vegetables and some pulses, is vegan, and probably doesn’t contain any spirulina. Your typical land-optimised diet includes added sugars (generally the full 10% of energy intake allowed by the DGA), more added oil (particularly palm oil), and most often the maximum amount of spirulina allowed by the constraint on SCP nucleic acids (40g). It wasn’t obvious to me in advance that the diets would be quite this different, but what this shows is that the list of foodstuffs which provide nutrients most efficiently by land use don’t overlap much with the list of foodstuffs which provide nutrients most efficiently by GHG emissions.

Something that you might notice here is that, certain idiosyncracies aside (like suggesting that you should eat a kilo of cabbage per day), the diets optimised for land use look more like modern, Western diets, with the higher quantities of added fats and sugar, and techno-ingredients like spirulina, whereas the diets optimised for GHG emissions look a bit more like the healthy diets that we’re all advised to move towards. This makes a lot of intuitive sense. Our current system does penalise production systems for land use quite consistently, since land is a valuable, scarce commodity. All other things being equal, it’s in the financial interests of corporate food producers to encourage us to eat foods which don’t take as much land to produce per kcal (like refined sugar and oils). GHG emissions are more complicated here in this regard. Fossil fuels cost money, so in a sense there is an economic penalty applied to production systems which overuse them. However, economies of the post-industrial period are pretty much defined by abundance of fossil fuels, so this only a small economic penalty. Other mechanisms of GHG emissions in food production aren’t really economically penalised at all (at least on the time scales that markets are sensitive to). So it makes sense modern diets in the Global North have more in common with land-optimised diets than emissions-optimised diets.

Flaws in the loss functions

Kilos of CO2-equivalent emissions and simple land use in production are not perfect measures of environmental impacts—even of GHG emissions and wild habitat loss. There are definitely some perverse results here due to peculiarities in the data. Palm oil is a case in point. Palm oil is pretty efficient source of fat, calories and vitamin E simply in terms of the area of land it uses—accordingly, it turns up a lot in the diets designed to minimise land use. But this doesn’t take into account the fact that a lot of the land that palm oil is grown on is recently deforested rainforest, and so among the most destructive kinds of land use possible.

Another example here is the use of almonds. Poore & Nemecek’s figures end up with nuts actually sequestering carbon per weight of output, so an emissions-optimised diet will always include as much nuts as possible given other nutritional constraints (generally the limits on saturated fats or total dietary energy from fat are what kick in to limit nut intake). But of course, even if you accept these figures, you could argue that it misses the point, since the problem with almonds is famously blue water use.

How much do individual foodstuffs matter? What’s making the biggest difference?

I think an obvious question in response to all of these concerns is: how much difference does it make if we exclude certain foodstuffs? If we took out palm oil, what then? Is the huge quantity of cabbage in the land-optimised diets due to something really special about cabbage, and both the optimised diets and the impact they have on the world would change totally if we removed the option of including cabbage? Or, perhaps more pertinently, if it turned out that Poore & Nemecek’s figures for cabbage were wrong, what difference would that make? If, in a hypothetical future when spirulina production was hugely scaled up it turned out that the average land use was way higher than I estimated, would that render these results useless? In other words, how much of this is achieved by just eating huge amounts of some outlier foodstuffs, and how much flexibility is there?

To try to answer this question, I’ve run the stats again (although on a much smaller population group of just 864 people for each of land and emissions, but again a realistic sample group). For every person, I’ve run the programme multiple times, each time excluding one of the foodstuffs.* We can then see how much difference it makes to the environmental impacts not to be able to use each foodstuff: how much extra land we’d need, or how much extra emissions it would cause.

*I’ve only excluded foodstuffs that were actually used at least once in the previous runs. So that’s maize, sweet potato, plantain, apple, chard, leek, cauliflower, spinach, lentil, chickpeas, kidney beans, almonds, cashews, pistachios, hazelnuts, brazilnuts, broccoli, rapeseed oil, beet sugar, wheat bread, rye bread, peas, soymilk, tofu, soybean oil, orange, eggs, dried spirulina and synthetic vitamin D in the emissions diets, and maize, apple, chard, onion, cabbage, carrot, cauliflower, sunflower kernels, pine nuts, pecans, brazilnuts, rapeseed oil, tomatoes, beet sugar, lettuce, wheat bread, rye bread, soymilk, tofu, soybean oil, palm oil, milk, eggs, dried spirulina and synthetic vitamin D in the land use diets.

The results are in the two expandable sections below. Most individual ingredients don’t make a massive difference to the outcome when optimising for emissions. For example, kidney beans occur (in small quantities) in 98% of the diets optimised for emissions, but if they are excluded it only increases the GHG emissions of diets by a mean average of 2.5% (median 2.2%). This isn’t because there is a simple one-for-one switch available kidney beans—this becomes clear if we return to the first emissions-optimised diet we calculated above:

foodstuffemissions-optimised dietemissions-optimised diet excl. kidney beans
sweet potato351g230g
rye bread171g0g
kidney beans43g0g
rapeseed oil6g3g
synthetic vitamin D5μg5μg
wheat bread0g168g

Because almost everything in the diet has many nutritional functions, swapping out any one thing necessitates many small adjustments. The result is just a 1.5% increase in the GHG emissions.

However, there are some exceptions. Excluding synthetic vitamin D increases the emissions of the diets by a mean of 45% (median increase 35%); excluding fortified soymilk increases emissions by a mean of 101% (median 96%). The reason is very straightforward: all other sources of vitamin D and vitamin B12 in the programme are animal source foods. In these cases, the programme does have to make a one-to-one switch to an ASF, and these have dramatically higher carbon footprints than everything else. You could see this as being a weird artefact of the particular list of foods I’ve included: if I’d included a vitamin-D-fortified breakfast cereal, then excluding vitamin D supplements wouldn’t look like such a problem! If I’d included vitamin B12 tablets, then excluding fortified soymilk wouldn’t be a problem! But on balance I think these artefacts are very helpful in that they show us unambiguously how much optimisation for emissions turns on micronutrient supplementation to be able to avoid including animal source foods.

The picture is similar, although not quite as dramatic, when optimising diets for land use. The two foods which have the biggest effect when excluded are the same, and for the same reasons. Excluding spirula also has a big effect, although the reasons for this are a bit more complicated than vitamin D and vitamin B12 and more like the kidney beans example above. Here’s how the first land-use diet given above changes when you can’t include spirulina at all:

foodstuffland-optimised dietland-optimised diet excl. spirulina
beet sugar53g0g
dried spirulina40g0g
palm oil36g28g
soybean oil3g0g
rapeseed oil2g6g
synthetic vitamin D5μg5μg
wheat bread0g2g

The problem is just that spirulina is an extremely land-efficient source of a bunch of things (protein, potassium, thiamin, riboflavin, niacin, most indispensible amino acids), which is why we’ve already had to think about how to limit it. When you take it out, you have to rethink how to meet a whole series of nutritional constraints. Again, you could view this as undermining the value of this exercise—just an oddity of the very low land-use I’ve calculated for spirulina production—but I think there is a useful message here, which is that SCPs (and probably microorganism-derived foods in general, since that category includes the synthetic micronutrients already discussed) can offer dramatic improvements on land-use efficiency compared with traditional sources of nutrients.

Finally, removing palm oil from these diets also has quite a big effect. The reason here is a bit harder to work out, since if you compare the before and after excluding palm oil, no new foodstuffs actually get added to replace it.

foodstuffland-optimised dietland-optimised diet excl. palm oil
beet sugar53g3g
dried spirulina40g40g
palm oil36g0g
soybean oil3g20g
rapeseed oil2g0g
synthetic vitamin D4μg4μg

There are two things going on here. Firstly, palm oil is just a more land-efficient source of fat than anything else included in the dataset. The next best thing is soy oil, which takes about 4x as much land per gram of fat. Palm oil is also quite a land-efficient source of calories: in the diet with palm oil we’re getting 27% of calories from fat, whereas in the diet excluding palm oil we’re exactly meeting the 20% minimum AMDR for fat through soy oil. A side effect of having to include quite a bit of soy oil just to meet the AMDR is that we’re exceeding the adequate intakes of linoleic and ɑ-linoleic acid by large margins, whereas the diet with palm oil only meets those AIs. In short: palm oil is a very land-efficient crop, and if we can’t use it then it introduces a range of other inefficiencies too.

How much food can you really expect people to eat?

As already observed several times, many of these diets involve eating really ridiculous weights and volumes of food. Is it really physically possible to eat a kilo of cabbage per day? How about 3kg of onions, or 2kg of tomatoes, all of which do occur with the right combination of demographics? How much difference does it make if we got rid of all these really extreme cases by introducing a limitation on the total weight of food?

Calories are such a universally useful measure of overall food intake that it’s quite hard to find studies of the weight or volume of food which people eat per day. One study that gets cited quite a bit (...more than it deserves, given the tiny n and unrepresentative sample population) has some data that we can use to calculate weights of food eaten. From my back-of-the-envelope calculation, people in that study ate between about 17g and 20g of food per kg bodyweight per day. So what weight of food is currently being included in these diets?

they’re certainly averaging higher than 20g/kg, but not as dramatically so as I’d expected. I suspect that this isn’t really the reason that many of these diets look impractical. The problem with a diet that asks you to eat 1.8kg of food per day of which 1.2kg is cabbage is not really the headline 1.8kg number. Nevertheless, I’ve struggled to find a clear reason to rule out the large amounts of brassicas. You’d need to adapt to such high fibre intakes gradually, but poverty diets in some parts of the world really do seem to include similar intakes. Certainly I haven’t found any clear advice on a ceiling for fibre intake. So, here we are—back to limiting overall diet weight.

The effect of different limitations are found in the figures below. The headline is that limiting overall weight of food intake to 20g per kg bodyweight per day usually has a meaningful but modest effect on the emissions of a diet. The mean 7% increase in emissions is about the same as the effect of removing cauliflower from diets (though the median here is just 3%, whereas removing cauliflower causes a median increase of 7%). Putting more modest constraints on total food intake like 22.5g/kg or 25g/kg has smaller effects still. However, there are sets of demographics (and so nutritional requirements) where these constraints have really substantial effects on emissions. These tend to be diets for shorter people where the total calorie intake and the weight of the person are both very low, and so adding another bodyweight-based constraint pushes the programme towards recommending more micronutrient dense foods. Crucially—perhaps you saw this one coming—adding the weight constraint means that the optimised diet includes eggs. Below is one of the most extreme examples (age 75 / weight 48kg / height 1.489m (i.e. the 1% height quantile) / f / sedentary), where constraining the weight of food to 20g/kg results in a 61% increase in minimum emissions.

foodstuffemissions-optimised dietemissions-optimised diet constrained to 20g food/kg bodyweight
sweet potato118g0g
wheat bread85g98g
rapeseed oil1g0g
synthetic vitamin D15μg12μg
dried spirulina0g18g
pigeon pea0g121g

The diets optimised to minimise land use were more extreme and stranger anyway, so, unsurprisingly, trying to make them a little saner by constraining the weight of food has bigger consequences. Some notable differences:

  • Even limiting food intake to 30g/kg bodyweight actually has an appreciable effect, with a mean 3.6% (median 2.8%) increase in land use
  • For the strictest constraint, keeping total food intake to 20g/kg bodyweight, this raises land use by a mean of 23%, up there with the effect of excluding fortified soymilk or synthetic vitamin D
  • ...however, it’s worth noting that this is dragged way up by outliers: the median increase is only 9%

Here’s an example of one of those outliers—the same demographics as above (age 75 / weight 48kg / height 1.489m / f / sedentary), where constraining food intake to 20g/kg bodyweight results in a 160% increase in land use. Unlike in the parallel example when optimising for emissions, this doesn’t result in us going from a vegan to a non-vegan diet, because the land-use optimised diet already included eggs. But it does involve trippling the intake of eggs. It’s worth pointing out that even this, the ‘worst’ diet for land use looked at so far, is still only using 3.456㎡ land/day, which equates to 0.13ha/year. For context, the world average agricultural land use per person in 2018 was 0.63ha. So we’re still talking about extremely land-use efficient diets here compared to how our food system feeds people in reality.

foodstuffland-optimised dietland-optimised diet constrained to 20g food/kg bodyweight
dried spirulina40g40g
palm oil20g0g
soybean oil9g0g
synthetic vitamin D14μg13μg
kidney beans0g43g
pigeon pea0g61g
sunflower kernels0g5g
wheat bread0g5g

Some conclusions

So, did I answer any of my questions? Here are some takeaways I’ve got from doing this exercise:

  • There are some exceptions to the good rule of thumb that a vegan diet is always best for the world—but in the majority of cases, veganism is the right answer (and meat-eating is never a good idea, at least in terms of the environmental impact metrics and nutritional needs looked at here)
  • But the exceptions to the veganism rule of thumb do represent a real and interesting point of tension between ethical veganism and environmentally motivated eating. Specifically, if your focus is not on climate change and greenhouse gas emissions but narrowly on the biodiversity crisis and land use, there is an argument in these data that many people should be eating eggs (though not really any other ASFs). This problem is made much more acute by the fact that the way you get to the conclusion that eggs are a very land-use-efficient source of nutrients is by assuming the cruel, high-density indoor version of chicken farming
  • We should stop talking about alternative proteins. Bear with me here, because this might have come a bit abruptly. But something that has struck me is that wherever a vegan diet isn’t the optimal answer, it really doesn’t have much to do with protein (or specific amino acid) requirements. It has to do with vitamin B12, vitamin D, and occasionally some other micronutrients. The “problem” with plant-based foods is not that they’re too low protein, but that they’re not micronutrient-dense enough. My takeaway from this is that alternative/plant-based meats are potentially a great idea for helping people transition to sustainable diets, but that we’re missing the point if we argue about whether they have enough protein. What we should be ensuring is that they’re all fortified with all the micronutrients that it’s harder to get from plants
  • We should all be eating really large amounts of green vegetables like brassicas, primarily because they’re a great way of getting a bunch of micronutrients, both from the perspective of GHG emissions and land use
  • There is a real tension between emissions and land use. I started this exercise thinking about the land sparing-land sharing debate and wondering about the trade-offs involved in “nature friendly” farming. I didn’t actually pursue those questions at all here because I didn’t come across a good enough source of data for outputs, emissions and land use with organic, agroecological, etc. methods. But the big discrepancy between the results for land use and emissions suggest that there might be big trade-offs there too: the optimised diet for land use here is going to be close to identical to an optimised land-sparing diet, whereas an optimised land-sharing diet might have a little in common with the diet optimised for emissions.

If you’re reading this, hopefully you found the exercise entertaining! Do email / tweet me and tell me what I’ve done wrong / what else I should do with this. There are any number of further places I could have gone... I just ran out of steam.