What is Earth's Carrying Capacity?
This is the last, for now, of my series on sustainability as it relates to human population and wealth. By no means am I done with the topic, but I want to move on to some other topics in the coming weeks. Today we’ll consider how many people can sustainably live on the Earth or beyond.
Here are the posts in the sustainability series:
Internal Limits to Growth, where we consider whether societies, as they become wealthier, cannibalize their wealth base through consumption and leisure.
Peak Oil, the idea that crude oil production will peak and decline due to geologic constraints, causing economic dislocation.
What Thomas Malthus wrote in his famous 1798 “An Essay on the Principle of Population”.
Paul Ehrlich’s The Population Bomb and problems therein.
Planetary Boundaries: what the concept is and some of its weaknesses.
Mineral Resources are Abundant, with special attention to copper.
Carrying capacity and theoretical limits to growth (this post).
For the sake of reference in reading the following estimates, current world population is about 8.2 billion people.
Carrying capacity is tricky to estimate, and I’ll say at the outset that I don’t find any of the following estimates to be convincing. The various papers differ widely in what limiting factor(s) to population growth they consider, what assumptions they make about future technology, and what practical constraints they consider on population size. As Cohen (1995) explains, an early estimate of carrying capacity comes from Antoni von Leeuwenhoek, the inventor of the microscope, in 1679. He assumed that the population density of Holland at the time was the limit, and if the whole world had that density, it could support 13.4 billion people. That’s not much worse than the other estimates I’ll consider, which are only a small fraction of all the estimates that have been made.
The Dynamic Nature of Carrying Capacity
“How many people can the Earth support” is very sensitive to the assumptions one makes about technology and lifestyle, as Shepon et al. (2018) find with diet in the United States. They consider the effect of substituting all meat and animal products with plant-based alternatives. Animal products are less ecologically efficient than plant products due to the feed conversion ratio: typically 2-20 calories of plant intake yields 1 calorie of meat or animal product. Shepon et al. (2018) find that the United States could support 350 million more people on the same land with an entirely plant-based diet, compared to what they take as a population of 300 million at the time of the paper.
Mottet et al. (2017) find that only about a third of grassland used to produce animal feed is land that would be suitable for human agriculture, and 86% of livestock feed would not be edible for humans. It is not clear how Shepon et al. (2018) account for this in their calculations. They also make no attempt to consider the economic, political, and cultural limitations of a shift to a vegan diet. Therefore, I would consider Shepon et al. (2018) to be more of a thought experiment than a serious proposal.
Peters et al. (2016) perform a similar analysis. They consider 10 dietary scenarios, including a baseline scenario in which Americans retain the same diet as today and one that reduces fat and sugar intake, as well as eight other scenarios. They find carrying capacity to be the lowest with the baseline scenario at 402 million people, and it is the highest under the lacto-vegetarian diet at 807 million people. Due to considerations above, they don’t find a strict vegan diet to be the most ecologically efficient. Carrying capacity is based on current land use requirements of diets. Because they don’t account for improving technology, their figures should be taken as lower bounds.
As discussed by Binder et al. (2020), most carrying capacity estimates are based on trying to determine the most stringent limiting factor on population and then estimating that factor’s limit, analogous to Liebig’s law of the minimum, which holds that plant growth is constrained by whatever the most limited resource is. In other words, if a plant is constrained by water availability, then more sunlight or more nutrients will not assist growth. However, Cohen (1995) notes that this approach does not consider interactions between constraints, does not consider how technology can lift constraints, and has other limitations.
Ecological Limits to Growth
Estimates of carrying capacity based in ecological considerations tend to be the most pessimistic. Lianos and Pseiridis (2016) is an example of that, with an estimated world carrying capacity of 3.1 billion people. Their estimate is based on the ecological footprint idea, introduced by Rees (1992) and estimated by the Global Footprint Network (2011). In brief, the ecological footprint is an estimate of the usage of various resources and ecological services, and it is compared to biocapacity, or the world’s ability to provide the resources and services. You may have heard of “Earth Overshoot Day”, the date on which humanity has supposedly used the Earth’s biocapacity for the year and is thus in ecological deficit.
The authors then bring in IPAT, a decomposition of ecological impact—the ecological footprint as measured by the GFN in this case—as a product of population, affluence, and technology. “Technology” is a residual term, much like total factor productivity in the Solow-Swan growth model, and it cannot be estimated directly. Instead, it is estimated indirectly, since all other parameters in the equation are known. Lianos and Pseiridis (2016) perform a regression and find that an increase of affluence (GDP per capita) of 1.88% has an equivalent impact of a 1% growth in population. The GFN shows that the world passed an ecological footprint of 1 biocapacity in 1976, when world GDP per capita was $5618 and population was 4.15 billion. Since GDP per capita was $11,000 at the time of the paper, under the regression, population should be 3.1 billion so that the ecological footprint is equal to biocapacity.
There are two obvious problems with this analysis. First, the regression assumes away any role for technology, and so it is not possible under the analysis for more ecologically friendly technology to raise carrying capacity. Indeed, a higher standard of living will only reduce the carrying capacity. Rather than, say, clean energy production, Lianos and Pseiridis (2016) are enthusiastic proponents of population control. The second problem, as discussed in more detail by Blomqvist et al. (2013), is that the ecological footprint metric itself is based on arbitrary assumptions and tells us little about the actual ecological impact of human civilization. Indeed, the very fact that the world has supposedly been in overshoot for nearly 50 years, according to the GFN, without obvious ecological consequences should itself be cause for suspicion about the usefulness of the metric.
Photosynthetic Limits to Growth
One of the more obvious limits to growth is the world’s capacity to grow enough food. This is the concern that preoccupied Malthus and is at the center of Malthusian readings of history. Simply taking average yields around the world and multiplying by the amount of arable land will not give a good estimate of carrying capacity because yields have been going up over time, and there is no reason to suppose that this trend will stop any time soon.
Binder et al. (2020) estimate that the world’s carrying capacity is more than 200 billion people using currently demonstrated technology, and with ideal technology, it is in the “tens of trillions”; the most optimistic technology scenario tops out above 170 trillion. Their model is based on a world consisting only of human and plants, so that humans appropriate the entire net primary productivity. They find that, while no other authors had seriously considered the availability of critical micronutrients, including nitrogen, phosphorus, potassium, calcium, magnesium, and, sulfur, as a limiting factor, photosynthesis is a more stringent constraint than micronutrients. Likewise, they find that freshwater availability will be a constraint after photosynthetic capacity, and there isn’t even any discussion of desalination.
Earlier, de Wit (1967) found a photosynthetic carrying capacity of 1.022 trillion people. This estimate is based on diving the world’s land mass into bands comprising 10 degrees of latitude and estimating the potential yield of each, assuming that photosynthesis converts a quarter of incoming sunlight into human-edible food. The limit is reduced to 149 billion if we assume that each person needs 750 square meters of non-agricultural living space and other facilities (about 5.4 people per acre), and 79 billion if 1500 square meters are assumed (2.7 people per acre).
Franck et al. (2011) refined the analysis of de Wit (1967), using a more granular model of solar insolation, and found an ultimate carrying capacity of 282 billion people. If we insist on conserving rainforests and boreal forests, the number is reduced to 150 billion, and if we insist on a diet of entirely animal products (without forest conservation), the limit is 96 billion. With 750 and 1500 square meters of nonagricultural space per person (without forest conservation or animal products), the limits are 89 billion and 54 billion respectively. Franck et al. (2011) note, but do not account for, limitations in freshwater supply, macronutrients or micronutrients, and transportation of food, though we saw that Binder et al. (2020) do not consider the first two constraints to be binding.
Thermodynamic Limits to Growth
Maybe we can produce all the food we need with fusion-powered bioreactors or Star Trek-style replicators. The human body operates at about 100 watts of power at rest, and so this is the body’s heat production. There can only be so many bodies in the world before the heat produced by them is intolerable, and there is where extreme carrying capacity estimates based in thermodynamics come into play.
Fremlin (1964) considers five future stages of population growth, based on the 37 year world population doubling time that was observed at the time. After 890 years, world population would reach an absolute limit of 60 quadrillion people (about 7 million times the current level), at which time heat would become unmanageable, despite macroengineering projects such as hermetically sealing the upper atmosphere and a planetary-scale system of heat pumps.
Fremlin’s (1964) is meant to be somewhat whimsical, and he is not really arguing that a world population of 60 quadrillion is feasible, let alone desirable. Like many authors at the time, he was concerned about rising population rates, and wanted to show that even absurd numbers, which would be unmanageable by any conceivable technological solution, would be reached on a time scale relevant to civilization under exponential growth. Fremlin is dismissive of migration into space—apparently regarding that as less realistic than hermetically sealing the atmosphere—and he argues that the solar system would allow at most another 200 years of population growth at the observe rate.
Another obvious practical problem is that, as Fremlin (1964) notes, a population of 60 quadrillion people is equivalent to a density of 120 people per square meter, and so the surface of the earth would have to be covered with towers thousands of stories tall to provide individuals with adequate living space. Not addressed is, as West (2017) observes, the average American requires 11,000 watts for their technological artifacts, 100 times more than direct bodily energy consumption. The extreme situation described by Fremlin would probably require much more, and so I would knock down his carrying capacity estimate by at least three orders of magnitude. Incidentally, Fremlin asserts that there are enough minerals in the Earth’s crust so that mineral availability would not be an obstacle to even a population of 60 quadrillion.
Badescu and Cathcart (2006) conduct a similar analysis, but they use a more restrictive value for the tolerable level of waste heat. They find a limit of 0.3 to 1.7 quadrillion people, with 1.3 quadrillion the limit if a maximum ambient temperature of 300 kelvin (27 °C or 80 °F) is accepted. The limit increases to 1.6 to 4.0 quadrillion if a planetary-scale system of heat pumps is used, which they say buys 74 years of population growth using the 37 year doubling time as in Fremlin (1964), despite the fact that world population growth had slowed considerably by 2006.
This is a major peeve of mine. So many authors, including as recently as West (2017), treat world population growth as though it were an inexorable exponential progress, apparently not having gotten the memo that population growth is slowing, and all credible predictions are that population will peak and decline at some point in the 21st century, or the early 22nd century at the latest.
Beyond Earth and Biology
All papers I have discussed so far assume, mostly implicitly, that the future human population will be confined to Earth, and that humans of the future will be biologically similar, with the same physical and metabolic needs, as modern humans. While neither of these things will change imminently, it is foreseeable that both of these assumptions could be rendered false on timeframes relevant to attaining high carrying capacity estimates.
The famous Kardeshev scale, introduced by Kardeshev (1964) and refined and extended by various authors, including Carl Sagan, as explained by Carrigan (2010), is a three point scale to describe the energy usage of future hypothetical civilizations. A Type I civilization would use the equivalent of the solar energy flux to Earth. Zhang et al. (2023) find that under Sagan’s refinement, human civilization today is a Type 0.7276. Due to the logarithmic nature of the scale, this represents an energy consumption nearly 1000 times less than a Type I civilization. If human civilization develops to Type I, then the energy budget will probably consist of widespread use of nuclear fission and/or fusion, massive solar arrays, including in space, and substantial human presence on the Moon, in cislunar space, on Mars, and elsewhere in the solar system.
Only about one part in 10 billion of solar energy output reaches Earth. A Type II civilization would harness the equivalent of the energy output of the Sun. The nature of such a civilization, if “civilization” is even the right word, is less comprehensible to us than our civilization would be to a prehistoric hunter-gatherer tribe. An article from Slate suggests that, by dismantling the gas giants, it would be possible to build a Dyson sphere or a Dyson swarm around the Sun that would capture a substantial portion of the solar energy output. There would be sufficient energy, raw materials, and living space to support up to 100 quintillion people (more than 1000 times the figure of Fremlin (1964)).
If that’s not enough, the Sun is only one of 100 billion stars in the Milky Way, though one of the larger stars. A Kardeshev Type III civilization would harness the equivalent of the energy output of all the stars, black holes, and other objects in the Milky Way. Genta (2024) assesses that interstellar travel would require substantial engineering advances and maybe substantial basic scientific advances, though a “slow” generation ship, in which the crew hibernates for centuries, would require the least amount of basic scientific advancement. At least, there is no obvious reason to rule it out. Fogg (1988) assesses that even intergalactic travel is feasible.
Bostrom (2013) finds that within the bounds of established physics, the future universe could support at least 10^34 future biological human life-years. Over a billion years, that is 10^25, or 10 septillion, people who would live at a given time throughout the Virgo Supercluster. If we move beyond biology and allow for uploaded minds to “live” on computational substrates, Bostrom’s lower bound increases to 10^54 future life-years, or 10^45 simulated people at a given time over a billion years.
If that is still not enough, various extensions of the Kardeshev scale envision a Type IV civilization, which would harness the energy equivalent of the output of all objects in the observable universe, in which the Milky Way is just one of up to 2 trillion galaxies. Now we’re getting into the realm of speculative physics such as faster-than-light travel and harvesting of dark energy.
And if even that is still not enough, George Dvorsky at io9 (Slate) speculates on such ideas as Lee Smolin’s cosmological natural selection, the creation of “basement universes” through directed cosmic inflation, the Transcension Hypothesis of Smart (2012), Pierre Teilhard de Chardin’s Omega Point, and James Gardner’s Selfish Biocosm. Under such extremely speculative ideas, human progeny may be literally infinite.
Conclusion on Sustainability
Now that we’ve had our fun with some wild speculation, it is time to bring this discussion of sustainability to a close.
Without invoking speculative physics, we expect that, somewhere and somehow, there must be a limit to growth to human civilization or whatever posthuman successor may arise. What is that limit, and what will impose it? Over the last few months, we’ve looked at several hypotheses, including self-cannibalization through consumption and leisure, fossil fuel depletion, mineral depletion, ecological collapse, limits to food supply, various other “overpopulation” concerns, existential risk, and some theoretical limits. We haven’t looked at everything. Depopulation through subreplacement birthrates is a concern about which I have written many times, though I would classify that as an internal limit to growth. We haven’t considered in detail some existential risks, such as misaligned artificial intelligence, a natural or bioengineered pandemic, and whether population growth might exacerbate these risks by increasing the number of people who have the potential to become an omnicidal maniac.
But on the other side of the ledger of the many things we can worry about, for centuries various authors have warned about a collapse resulting from the alleged unsustainability of civilization, and so far all such predictions have turned out to be wrong, sometimes comically so. It would be tempting to treat all such predictions today as the boy who cried wolf, forgetting that at the end of that parable, there actually was a wolf.
Still, my conclusion is that, especially with demographic trends as they are, the world will not face any genuine limit to growth under any plausible scenario and under any time frame that is relevant for making policy. The most rational course of action is to put such anxieties aside and focus on real problems facing the world today, none of which are overpopulation or overconsumption. Indeed, as I hope to further discuss at a later time, more people and higher standards of living are the solutions to our problems, not the causes.
Even more fundamentally, our civilization faces three major inflections points, which, though not imminent, are closer on the horizon that any fundamental limits to growth. One of those three inflection points is a breakout to a spacefaring civilization, in which a significant number of people live sustainably and independently away from the surface of the Earth. Another is a substantial transition to a transhuman or posthuman lifeway, through genetic engineering, cybernetic engineering, mind uploading, or some combination thereof. The final inflection point is the advent of artificial intelligence that is capable of conducting most or all economically relevant tasks now performed by humans. Once one of these three things happens, the other two will likely happen soon after. Then, civilization will be so transformed that most of what I have discussed in the last few months will be moot.
Finally, and perhaps I should have discussed this earlier, so much of this discussion is rooted in value systems that are often left unspoken. The difference between people who believe in sharp limits to growth, and that degrowth and population control are proper policies, and those who believe in the possibility and moral imperative of open-ended growth, is not merely one of scientific claims. There are fundamental differences of values for which scientific claims are little more than proxies. A debate about the route makes little sense unless we know what the destination is.