Estimating the Perfect Diet for the Environment
Evan Peters
Results Summary
I simulated 1 million daily food diets of 1.8kg of food, using 38 frequently eaten foods, in search of the most environmentally friendly diet that also meets a human’s daily nutritional requirements.
The following diets caused the least damage of the one-million diets simulated, while also satisfying daily nutritional needs.
## [1] "Minimum GHG Diets (kg of food)"| Apples,flesh and skin | Cauliflower, boiled | Eggs, chicken | Sweetcorn, | Nuts, mixed | Porridge oats | Spinach, mature, raw | Sweet potato, flesh only, boiled | Milk, soya, fortified |
|---|---|---|---|---|---|---|---|---|
| 0.103 | 0.026 | 0.141 | 0.247 | 0.312 | 0.292 | 0.256 | 0.146 | 0.277 |
## [1] "Minimum Freshwater Use Diets (kg of food)"| Barley, pearl, raw | Sugar, white | Coffee | Chocolate, dark | Eggs, chicken | Sweetcorn, | Spinach, mature, raw | Peas, boiled | Chicken, meat | Sweet potato, flesh only, boiled | |
|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 0.066 | 0.009 | 0.003 | 0.234 | 0.435 | 0.109 | 0.484 | 0.184 | 0.143 | 0.133 |
## [1] "Minimum Land Use Diets (kg of food)"| Bananas, flesh only | Cassava | Peanuts, kernel only | Sweetcorn, | Nuts, mixed | Porridge oats | Plums | Spinach, mature, raw | Potatoes, flesh and skin | Prawns, king | Milk, soya, fortified | Tomatoes, cherry, raw | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 3 | 0.026 | 0.019 | 0.153 | 0.07 | 0.054 | 0.195 | 0.055 | 0.373 | 0.294 | 0.081 | 0.341 | 0.14 |
## [1] "Minimum Eutrophying Diets (kg of food)"| Apples,flesh and skin | Cassava | Eggs, chicken | Peanuts, kernel only | Nuts, mixed | Onions | Spinach, mature, raw | Milk, soya, fortified | |
|---|---|---|---|---|---|---|---|---|
| 4 | 0.261 | 0.274 | 0.18 | 0.213 | 0.089 | 0.127 | 0.391 | 0.265 |
## [1] "Minimum Overall Environmental Impact Diets (kg of food)"| Apples,flesh and skin | Cassava | Eggs, chicken | Peanuts, kernel only | Nuts, mixed | Onions | Spinach, mature, raw | Milk, soya, fortified | |
|---|---|---|---|---|---|---|---|---|
| 7 | 0.261 | 0.274 | 0.18 | 0.213 | 0.089 | 0.127 | 0.391 | 0.265 |
These diets are not the true optimal diets for each environmental pathway, rather they are the best performing among an evenly distributed, large, and random sample.
Introduction
Last month I worked on finding the environmentally optimal food source for each nutrient, mineral and vitamin necessary for humans. Using the same data, I set out to find the environmentally-optimal daily-diet. The goal is to find diets that satisfy the following conditions:
- Contain all the nutrients necessary for survival.
- Have minimal environmental harm.
Data
The foods chosen for this study:
## [1] "Apples,flesh and skin" "Bananas, flesh only"
## [3] "Barley, pearl, raw" "Beef, mince,(beef herd)"
## [5] "Beef, mince, (dairy herd)" "Beetroot, cooked"
## [7] "Grapes" "Cauliflower, boiled"
## [9] "Sugar, white" "Cassava"
## [11] "Cheese, hard" "Citrus fruit, flesh only"
## [13] "Coffee" "Chocolate, dark"
## [15] "Eggs, chicken" "Tilapia"
## [17] "Peanuts, kernel only" "Lamb, mince"
## [19] "Sweetcorn, " "Milk, whole"
## [21] "Nuts, mixed" "Porridge oats"
## [23] "Onions" "Plums"
## [25] "Beans, butter, boiled" "Spinach, mature, raw"
## [27] "Peas, boiled" "Pork"
## [29] "Potatoes, flesh and skin" "Chicken, meat"
## [31] "Prawns, king" "Rice, wild, raw"
## [33] "Sweet potato, flesh only, boiled" "Milk, soya, fortified"
## [35] "Tofu, soya bean, steamed" "Tomatoes, cherry, raw"
## [37] "Flour, rye" "Wine, red"The data on the environmental impacts for these foods were taken from ourworldindata.org.
GHGs, or Greenhouse Gasses, are carbon based emissions embedded in agricultural processes. Measured in kg CO2 equivalents, greenhouse gas emissions are proven to have a warming effect on the earth.
Water Use, measured in cubic meters (or 1000 liters), refers to all the freshwater that went into the production of a kilogram of that food product. This figure is just total water use, and is different from Water Stress Adjusted amounts, which takes into account the relative water stress of a region.
Land Use, measured in square meters, refers to all the land that had to be cleared in order to make a kilogram of that food product. Land use is the most ecologically harmful consequence of agricultural production.
Eutrophying Emissions, measured in kilograms phosphate equivalent, is a measure of how much phosphate is leached into waterways, which has a damaging effect on aquatic life. Phosphates and their equivalents are a part of agriculture’s over-fertilization process.
The nutritional information on each of the foods came from McCance and Widdowsons Composition of Foods integrated dataset 2021.
Data and calculation techniques for environmental damage was taken from the LifeCycle Assessment algorithm ReCiPe 2016.
Creating the Sample
The optimization problem is too complex to solve outright; so I opted for creating a huge amount of random diets and then looking at the best performing among them.
To create random combinations of the 38 foods in our list, I first generated 38-million random numbers between 0 and 1. I then multiplied that list of numbers by a list of 0’s and 1’s, also randomly generated. This multiplication was done to reduce the distinct number of foods in each diet. Then I compressed this 38 million long list of numbers into a matrix with one-million rows and 38 columns. Once in that configuration, I divided each row by its row-sum and multiplied it by the total amount of food I wanted each diet to be, which was 1.8 kg. People eat between 3 and 5 pounds of food daily; 1.8kg is in the middle of those figures.
total_daily_food = 1.8
total_runs = 1000000
random_sample <- matrix(runif(total_runs*38,0,1)*
sample(c(0,1),total_runs*38,
replace = T,
prob = c(.60,.40)),
nrow = total_runs)
normalized_sample <- data.frame((sweep(x,1,(rowSums(random_sample)/total_daily_food),'/')))Which yields results that look like this:
| Apples,flesh and skin | Bananas, flesh only | Barley, pearl, raw | Beef, mince,(beef herd) | Beef, mince, (dairy herd) | Beetroot, cooked | Grapes | Cauliflower, boiled | Sugar, white |
|---|---|---|---|---|---|---|---|---|
| 0.178 | 0.110 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.131 | 0.000 |
| 0.000 | 0.163 | 0.000 | 0.000 | 0.180 | 0.000 | 0.000 | 0.000 | 0.000 |
| 0.000 | 0.060 | 0.000 | 0.132 | 0.128 | 0.000 | 0.112 | 0.000 | 0.000 |
| 0.000 | 0.000 | 0.000 | 0.222 | 0.001 | 0.229 | 0.000 | 0.218 | 0.000 |
| 0.168 | 0.126 | 0.134 | 0.000 | 0.000 | 0.284 | 0.107 | 0.258 | 0.019 |
| 0.000 | 0.000 | 0.086 | 0.165 | 0.228 | 0.000 | 0.081 | 0.078 | 0.043 |
Meaning our first simulated diet has .178 kilograms of apples, .110 kilograms of bananas and 0 kilograms of barley, and so on and so forth 1 million times.
Nutrients
We only want to look at diet’s that are nutritious or meet the Daily Recommended Value (DRV) of each nutrient.
List of nutrients and their DRVs.
## Nutrient Value Unit
## 1 PROT 50.0 g
## 2 FAT 72.0 g
## 3 CHO 0.3 g
## 4 KCALS 2000.0 kcal
## 6 CHOL 300.0 mg
## 7 NA 2300.0 mg
## 8 K 4700.0 mg
## 9 CA 1300.0 mg
## 10 MG 420.0 mg
## 11 P 1250.0 mg
## 12 FE 18.0 mg
## 13 CU 0.9 mg
## 14 ZN 11.0 mg
## 15 CL 2300.0 mg
## 16 MN 2.3 mg
## 17 SE 55.0 B5g
## 18 I 150.0 B5g
## 19 RET 0.0 B5g
## 20 CAREQU 0.0 B5g
## 21 RETEQU 0.0 B5g
## 22 VITD 20.0 B5g
## 23 VITE 15.0 mg
## 24 VITK1 120.0 B5g
## 25 THIA 1.2 mg
## 26 RIBO 1.3 mg
## 27 NIAC 16.0 mg
## 28 TRYP60 0.0 mg
## 29 NIACEQU 0.0 mg
## 30 VITB6 1.7 mg
## 31 VITB12 2.4 B5g
## 32 FOLT 400.0 B5g
## 33 PANTO 0.0 mg
## 34 BIOT 30.0 B5g
## 35 VITC 90.0 mgSome nutrients were excluded from the study. Sodium and Chloride were removed because all of the foods in the data are unsalted. We can just assume you can add some salt to any of the given diets and be sufficient in those minerals. Iodine was excluded for the same reason; most people consume iodized salt. And vitamin D is excluded because most people get it from being in the sun.
Environmental Impacts
Thanks to OurWorldinData, we have data on four environmental impacts per kilogram of each of our foods. Units in order listed are kg CO2e, m2 of land, m3 of water, kg phosphate equivalent.
| Nutrient.Food.Name | GHG | Land.use.per.kilogram..Poore…Nemecek..2018. | Eutrophying.Emissions | Freshwater.withdrawls |
|---|---|---|---|---|
| Apples,flesh and skin | 0.43 | 0.63 | 0.00145 | 0.1801 |
| Bananas, flesh only | 0.86 | 1.93 | 0.00329 | 0.1145 |
| Barley, pearl, raw | 1.18 | 1.11 | 0.00233 | 0.0171 |
| Beef, mince,(beef herd) | 99.48 | 326.21 | 0.30141 | 1.4512 |
| Beef, mince, (dairy herd) | 33.30 | 43.24 | 0.36529 | 2.7143 |
| Beetroot, cooked | 1.81 | 1.83 | 0.00541 | 0.2177 |
| Grapes | 1.53 | 2.41 | 0.00612 | 0.4196 |
| Cauliflower, boiled | 0.51 | 0.55 | 0.00501 | 0.1194 |
| Sugar, white | 3.20 | 2.04 | 0.01692 | 0.6201 |
| Cassava | 1.32 | 1.81 | 0.00069 | 0.0000 |
| Cheese, hard | 23.88 | 87.79 | 0.09837 | 5.6052 |
| Citrus fruit, flesh only | 0.39 | 0.86 | 0.00224 | 0.0827 |
| Coffee | 28.53 | 21.62 | 0.11052 | 0.0259 |
| Chocolate, dark | 46.65 | 68.96 | 0.08708 | 0.5406 |
| Eggs, chicken | 4.67 | 6.27 | 0.02176 | 0.5777 |
| Tilapia | 13.63 | 8.41 | 0.23512 | 3.6913 |
| Peanuts, kernel only | 3.23 | 9.11 | 0.01414 | 1.8523 |
| Lamb, mince | 39.72 | 369.81 | 0.09713 | 1.8028 |
| Sweetcorn, | 1.70 | 2.94 | 0.00403 | 0.2157 |
| Milk, whole | 3.15 | 8.95 | 0.01065 | 0.6282 |
| Nuts, mixed | 0.43 | 12.96 | 0.01915 | 4.1338 |
| Porridge oats | 2.48 | 7.60 | 0.01123 | 0.4824 |
| Onions | 0.50 | 0.39 | 0.00324 | 0.0143 |
| Plums | 1.05 | 0.89 | 0.00243 | 0.1535 |
| Beans, butter, boiled | 1.79 | 15.57 | 0.01708 | 0.4357 |
| Spinach, mature, raw | 0.53 | 0.38 | 0.00227 | 0.1025 |
| Peas, boiled | 0.98 | 7.46 | 0.00752 | 0.3966 |
| Pork | 12.31 | 17.36 | 0.07638 | 1.7958 |
| Potatoes, flesh and skin | 0.46 | 0.88 | 0.00348 | 0.0591 |
| Chicken, meat | 9.87 | 12.22 | 0.04870 | 0.6600 |
| Prawns, king | 26.87 | 2.97 | 0.22722 | 3.5154 |
| Rice, wild, raw | 4.45 | 2.80 | 0.03507 | 2.2484 |
| Sweet potato, flesh only, boiled | 0.43 | 0.33 | 0.00161 | 0.0284 |
| Milk, soya, fortified | 0.98 | 0.66 | 0.00106 | 0.0278 |
| Tofu, soya bean, steamed | 3.16 | 3.52 | 0.00616 | 0.1486 |
| Tomatoes, cherry, raw | 2.09 | 0.80 | 0.00751 | 0.3698 |
| Flour, rye | 1.57 | 3.85 | 0.00716 | 0.6475 |
| Wine, red | 1.79 | 1.78 | 0.00457 | 0.0789 |
We now have everything we need to find the best and worst diets for each environmental impact!
Results by Environmental Impact
GREENHOUSE GASSES
This diet emits the least GHGs AND is nutritionally sufficient from our sample of 1 million:
| Apples,flesh and skin | Cauliflower, boiled | Eggs, chicken | Sweetcorn, | Nuts, mixed | Porridge oats | Spinach, mature, raw | Sweet potato, flesh only, boiled | Milk, soya, fortified |
|---|---|---|---|---|---|---|---|---|
| 0.103 | 0.026 | 0.141 | 0.247 | 0.312 | 0.292 | 0.256 | 0.146 | 0.277 |
With emissions of only 2.46kg of CO2e, we see lots of fruit and veg, with a notably huge amount of Nuts. This tracks with our understanding of nuts as one of the most carbon-efficient foods in the world.
The diet that emits the most GHG is this one, with 58kg of CO2e in a day’s worth of food.
| Barley, pearl, raw | Beef, mince,(beef herd) | Beef, mince, (dairy herd) | Grapes | Cassava | Cheese, hard | Tilapia | Milk, whole | Nuts, mixed | Peas, boiled | Prawns, king | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 8 | 0.017 | 0.414 | 0.185 | 0.011 | 0.23 | 0.301 | 0.096 | 0.1 | 0.085 | 0.318 | 0.042 |
One can see that it’s mostly animal products, which tracks with our understanding of the carbon-intensity of animal based foods.
It’s worth taking a moment to consider the difference between these two diets. Both provide a human with the essential nutrients one needs to survive, but the difference in GHG impact is nearly 25 fold…
To determine whether or not these low GHG diets were just a random happening, I ran pairwise t-test’s on low emitting diets vs high emitting diets. This will tell us which foods are statistically significant in their presence among low GHG and high GHG, nourishing diets.
What this plot shows is that simulated diets with more foods like nuts, spinach and eggs are among the bottom percentile of GHG emitting diets. On average, nuts appear 70 grams more in low emitting, well nourishing diets than non-low emitting diets.
On the other end of the spectrum is beef, chocolate and lamb.
Said another way; low-GHG simulated diets, that are nutritionally complete, have statistically lower amounts of these foods.
Finally, here’s a plot of the distribution of a simulated diet’s GHG
emissions with some summary statistics, giving some perspective on those
minimum and maximum emitting diets.
WATER USE
The simulated diet that uses the least water and is nutritious is this one:
| Barley, pearl, raw | Sugar, white | Coffee | Chocolate, dark | Eggs, chicken | Sweetcorn, | Spinach, mature, raw | Peas, boiled | Chicken, meat | Sweet potato, flesh only, boiled | |
|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 0.066 | 0.009 | 0.003 | 0.234 | 0.435 | 0.109 | 0.484 | 0.184 | 0.143 | 0.133 |
And the one that uses the most while being nutritious is this:
| Cheese, hard | Chocolate, dark | Eggs, chicken | Nuts, mixed | Spinach, mature, raw | |
|---|---|---|---|---|---|
| 9 | 0.702 | 0.22 | 0.093 | 0.449 | 0.336 |
Again we check for statistical differences among food groups for low water use vs. high water use diets.
Distribution and summary statistics for water use among simulated diets
LAND USE
The simulated diet that uses the least land and is nutritious is this one:
| Bananas, flesh only | Cassava | Peanuts, kernel only | Sweetcorn, | Nuts, mixed | Porridge oats | Plums | Spinach, mature, raw | Potatoes, flesh and skin | Prawns, king | Milk, soya, fortified | Tomatoes, cherry, raw | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 3 | 0.026 | 0.019 | 0.153 | 0.07 | 0.054 | 0.195 | 0.055 | 0.373 | 0.294 | 0.081 | 0.341 | 0.14 |
And the one that uses the most while being nutritious is this:
| Beef, mince,(beef herd) | Beef, mince, (dairy herd) | Grapes | Cauliflower, boiled | Cheese, hard | Lamb, mince | Nuts, mixed | Porridge oats | Pork | Rice, wild, raw | Flour, rye | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 10 | 0.31 | 0.062 | 0.253 | 0.319 | 0.299 | 0.258 | 0.151 | 0.01 | 0.038 | 0.036 | 0.065 |
Significant differences among foods:
A HUGE jump in spinach present in low land-use diets. Makes sense as 1kg of spinach takes only 0.38m2 of land. Compare to 1kg of chicken at 12m2 or beef from a beef herd 326m2. We see Prawns and Tilapia for the first time as well, which also makes sense considering the production of those two foods don’t take up too much land either.
Distribution and summary statistics for water use among simulated diets:
EUTROPHICATION
The simulated diet that has the least eutrophying emissions and is nutritious is this one:
| Apples,flesh and skin | Cassava | Eggs, chicken | Peanuts, kernel only | Nuts, mixed | Onions | Spinach, mature, raw | Milk, soya, fortified | |
|---|---|---|---|---|---|---|---|---|
| 4 | 0.261 | 0.274 | 0.18 | 0.213 | 0.089 | 0.127 | 0.391 | 0.265 |
The simulated diet that has the most eutrophying emissions and is nutritious is this one:
| Apples,flesh and skin | Beef, mince,(beef herd) | Beef, mince, (dairy herd) | Cauliflower, boiled | Cheese, hard | Tilapia | Peanuts, kernel only | Potatoes, flesh and skin | Prawns, king | Rice, wild, raw | |
|---|---|---|---|---|---|---|---|---|---|---|
| 11 | 0.354 | 0.24 | 0.189 | 0.246 | 0.176 | 0.314 | 0.157 | 0.013 | 0.104 | 0.007 |
Significant differences among foods:
Eggs and Cheese don’t use fertilizer (directly), so their presence among low eutrophication diets makes sense. Nut’s and groundnuts also are known as low fertilizer crops, so their increase among these diets is sensible as well.
Distribution and summary statistics for eutrophication use among simulated diets:
TOTAL ENVIRONMENTAL IMPACT
The best diet, if you combined all the environmental factors into one is this one:
| Apples,flesh and skin | Cassava | Eggs, chicken | Peanuts, kernel only | Nuts, mixed | Onions | Spinach, mature, raw | Milk, soya, fortified | |
|---|---|---|---|---|---|---|---|---|
| 7 | 0.261 | 0.274 | 0.18 | 0.213 | 0.089 | 0.127 | 0.391 | 0.265 |
This score is arrived at by distilling the environmental damages down to two endpoints: damage to human health (measured by loss of healthy life years, or DALYs) and damage to ecosystems (as measured by species extinction rate, or species-years).
DALY stands for Disease Adjusted Life Year, and one unit is equal to a year of healthy life.
A Species-year relates to the amount of animal species likely to go extinct over the course of a year.
You can see the distributions for damages here:
That’s it for now.
Next Steps
A big shortcoming of this study is the lack of breadth among foods. Further research should include a larger corpus of food data to tease out reliance on any single food in this smaller corpus as a source of niche-vitamins/minerals. Similarly, there should be penalties for ‘overshooting’ daily recommended values; for example, having 1000% of your daily vitamin C is wasteful. Perhaps someway to tease out the realism of some of the suggested simulated diets; for example, 500grams of spinach is likely not going to be a part of anyone’s daily food intake. Lastly, algorithms can be designed to find optimal replacements for foods in a diet that take both nutrients and environmental harm into account.