In this article, we consider theoretical limits to human population. Binder et al. (2020) observe that an estimate of the world’s “carrying capacity” generally finds a single limiting factor to growth. That limiting factor might be the world’s photosynthetic capacity, the problem of waste heat disposal, or something else. Estimates of carrying capacity differ widely in part because researchers differs in which limiting factor(s) they consider.
The above is an application of Liebig’s law of the minimum–popularized by Liebig (1840)–to carrying capacity. However, Cohen (1995) notes several limitations of application of the law. It does not account for heterogeneous needs of a population; it does not account for potential fluctuations in availability of limiting resources; it assumes that resources needs grow linearly with population, which has not generally been observed; it does not account for interactions between various resources, such as freshwater needs for irrigation; and it does not account for adaptive responses such as technological innovations in the face of threatened resources shortages.
As recounted in Cohen (1995), an early estimate of Earth’s carrying capacity came in 1679 from Antoni van Leeuwenhoek, the inventor of the microscope. Van Leeuwenhoek estimate that the would could support 13.4 billion people, which he derived by estimating that all the world’s landmass would have the same population density as Holland at the time.
The Dynamic Nature of Carrying Capacity
One difficulty in estimating how many people can live on the Earth is that per-capita resource consumption is itself the complex product of economic and cultural forces, as noted in Cohen (1995). For example, Shepon et al. (2018) find that the United States could feed an additional 350 million people, approximately the current population of the country, by replacing meat and animal products for food with plant-based analogues. This is based on the fact that animal products tend to have a low feed conversion ratio, which is the ratio between the number of calories the animals require to the number produced, and thus it is more ecologically efficient for people to eat plants directly. Shepon et al. (2018) estimate that the carrying capacity of the United States would be about 650 million people in this way, though they do not estimate how much of a shift to a plant-based diet would be economically, politically, or culturally feasible.
Peters et al. (2016) perform a similar analysis. They consider two baseline diets for the United States–one that it is the same as today’s prevailing diet, and one in which fat and sweetener intake is reduced–and eight additional dietary scenarios. They find that carrying capacity is at a minimum with today’s diet, at 402 million people, and highest with a lacto-vegetarian diet at 807 million people. Carrying capacity is calculated with the assumption that the American (lower 48 states) agricultural system is closed and with today’s land use requirements by food commodity. When the possibility of technological advancement is considered, these numbers should be taken as lower bounds for the nuumber of people who could be supported. As with Shepon et al. (2018), the higher number of people that could be fed with more plant-based diets in Peters et al. (2016) is based on the fact that plant-based diets have higher feed conversion ratios then diets based on meat and animal products.
Ecological Limits to Growth
Lianos and Pseiridis (2016) offer one of the more pessimistic estimates of optimum population size of 3.1 billion people worldwide, less than half of the estimated world population of 7.3 billion at the time of the paper. This estimate is first based on the ecological footprint, introduced by Rees (1992). This metric was assessed by the Global Footprint Network (2011) to have exceeded the Earth’s biocapacity since 1976, at which time the world gross domestic product was $5618 per capita and world population was 4.15 billion. They then perform a regression on the ecological footprint with respect to per-capita GDP and population to find a tradeoff between these two factors, with an increase of per-capita GDP of 1.88% being equivalent to a 1% increase in population. Then, noting that world average GDP per capita was $11,000 at the time of the paper, world population must be 3.1 billion to maintain an ecological footprint within the Earth’s biocapacity.
There are several reasons to be skeptical of the pessimistic conclusion of Lianos and Pseiridis (2016), beyond the obvious reason that world population has long exceeded 3.1 billion people with no obvious ecological catastrophe. The paper’s regression is based on a variant of the IPAT equation developed in, for instance, Ehrlich and Holdren (1972), which holds that the ecological footprint is the product of population, affluence, and technology. Technology is a residual term and cannot be measured directly, and so its effect is abstracted into the relationship between per-capita GDP and population as noted above. The estimate of Lianos and Pseiridis (2016) thus assumes no further role for technology to reduce ecological impact of human activity for a given population and affluence level.
Furthermore, the concept of the ecological footprint, on which the analysis of Lianos and Pseiridis (2016) is based, is itself a flawed indicator. As Blomqvist et al. (2013) explain, ecological footprint at a world level is driven mostly by the insufficiency of world forests to serve as a carbon sink. The metric is arbitrary, and modest changes could yield a world that is in ecological surplus rather than deficit–that the world ecological footprint is less than biocapacity–or that the overshoot is nearly infinite, in that no number of “Earths” would be sufficient to offset the ecological footprint.
Photosynthetic Limits to Growth
Binder et al. (2020) find that the ability to feed the population, and the world’s capacity to conduct photosynthesis in particular, is the limiting factor on population growth. They find that at least 200 billion people can live with currently demonstrated technology, and with ideal technology, the carrying capacity is in the “tens of trillions”. Although they note that no studies to that point had considered the availability of essential micronutrients, including nitrogen, phosphorus, potassium, calcium, magnesium, and, sulfur, they find that photosynthetic capacity, rather than micronutrient availability, is a binding constraint on population growth.
Binder et al. (2020) note that their analysis does not account for all conceivable limitations on growth. For example, it does not allow for sustenance of potentially ecologically necessary species that are not humans or plants. It also does not account for quality of life considerations, such as whether such extreme population levels would allow adequate personal space or travel opportunities, and whether one would consider the ecological impacts to be acceptable.
de Wit (1967), an earlier work that attempted to estimate the world’s carrying capacity based on photosynthetic capacity, finds a limit of 1.022 trillion people. The estimate was made by dividing the world’s land into 10 degree latitude bands and estimating the potential yield of each, assuming that photosynthesis can convert a quarter of incoming solar energy into human food. He takes human daily caloric needs as 2740 kilocalories per day. The limit is reduced to 146 billion people if one assumes 750 square meters of living and other non-agricultural land use per person, and it is further reduced to 79 billion people if 1500 square meters of non-agricultural land are considered per person.
Considering the most agriculturally productive use of land, Franck et al. (2011) find that Earth can sustain 282 billion people. In a scenario that saves rain forests and boreal forests, the carrying capacity is 150 billion. A scenario that cultivates pasture to feed animals can support up to 96 billion people. They further find that with 750 and 1500 square meters respectively of non-agricultural land per person, carrying capacity is reduced to 89 and 54 billion people respectively, without forest conservation or animal agriculture. They take caloric needs of 2803 kilocalories per day, the world average as of 2002 as reported by the Food and Agriculture Organization of the United Nations, compared to 2740 kcal/day as used by de Wit (1967). Franck et al. (2011) do not account for other possible limitations on population growth, such as freshwater availability, macronutrients and micronitruients, crop protection, energy, and transportation of food.
Thermodynamic Limits to Growth
Amidst anxiety about population growth in the 1960s, Fremlin (1964), considers, somewhat whimsically, the maximum human population that Earth could support from a heat disposal perspective. Considering a 37 year population doubling time, which was observed at the time, Fremlin identifies five future phases of population growth, culminating in stage 5, which sees a world population of 60 quadrillion people after 890 years. At that level, heat production of 100 watts from the human body would overwhelm the Earth’s heat capacity, despite macro-engineering projects such as hermetically sealing the planet’s outer surface and using heat pumps to dispose of waste heat.
Fremlin (1964) does not consider migration into space as solution, both regarding it as infeasible, and even if it were feasible, other planets in the Solar System would allow only up to 200 years of additional population growth. Fremlin’s analysis only considers heat generated by human bodies and not the heat generated by industrial production of goods necessary for human survival and comfort, which West (2017) estimates at 11,000 watts for a contemporary American. The analysis of Fremlin (1964) also does not consider some other obvious practical problems, such as that a population of 60 quadrillion people would be equivalent to a density of 120 people per square meter, requiring that the world be covered with skyscrapers thousands of stories tall to provide individuals with adequate living space. Even then, individual travel would be greatly restricted for reasons of space and heat generation. Briefly considering the two most potential Malthusian fears, Fremlin regards neither the ability to produce enough food nor the availability of raw materials as likely constraints on population growth.
Badescu and Cathcart (2006) perform a similar analysis to Fremlin (1964), but they operate with more stingent restrictions on the tolerable level of waste heat. Again with bodily waste heat as the limiting factor, Badescu and Cathcart (2006) find a maximum human population of 0.3 to 1.7 quadrillion people, or 1.3 quadrillion if a maximum ambient temperature of 300 kelvin (27 °C or 80 °F) is accepted. With a planetary-scale system of heat pumps to evacuate excess heat considered, the limit rises to 1.6-4.0 quadrillion people. Like Fremlin (1964), Badescu and Cathcart (2006) consider bodily heat production of 100 watts per person and do not consider heat resulting from technology. The authors note that the macro-engineering solution affords 74 additional years of population growth, using the same 37 year doubling time as Fremlin (1964) despite the fact that population growth had slowed considerably by 2006.
Beyond Earth and Biology
All papers discussed above assume, implicitly or explicitly, two aspects of future civilization. First, civilization will be confined to Earth, and thus carrying capacity and the carrying capacity of the Earth are synonymous. Second, civilization will be inhabited by beings that are similar to modern humans, and thus with the same physical needs. Both of these assumptions could be false under plausible trajectories of future technology.
Kardeshev (1964) developed what is now known as the Kardeshev scale. As explained by Carrigan (2010), the scale has gone through several refinements and extensions, such as the interpolation of values as conducted by Carl Sagan. Under the Kardeshev scale, a Type I civilization is one that harvests the equivalent of the solar energy flux to Earth. A Type II civilization harvests the equivalent of the energy output of the Sun. A Type III civilization harvests the equivalent of the energy output of all objects in the Milky Way galaxy, including stars and black holes. According to Zhang et al. (2023), under Sagan’s interpolation, human civilization comprises a Type 0.7276 civilization, almost a factor of 1000 lower than the threshold for a Type I civilization.
Genta (2024) assesses that interstellar travel requires substantial advances in engineering and perhaps substantial advances in basic science, with “slow” generation ships, requiring crew hibernation times of hundreds of years, the most scientifically feasible today. There is, however, no obvious scientific barrier to interstellar travel and eventual human settlement of the Milky Way galaxy, and even intergalactic travel may be possible, as Fogg (1988) assesses. Thus there is the potential for a staggering sustainable human population across the Milky Way and neighboring galaxies.
Bostrom (2013) estimates that the future universe could support at least 10^34 biological life-years, which if spread over a billion years, implies that 10^25, or 10,000,000,000,000,000,000,000,000 (10 septillion) people are alive at a given time, dwarfing any estimate of the carrying capacity of Earth. If human minds are implemented in computational hardware rather than in neuronal wetware, then that estimate grows to at least 10^54 future life-years, or 10^45 minds at a given time over a billion years.
Price (2019) suggests a variant of Lee Smolin’s theory of cosmological natural selection, whereby the knowledge and technology of intelligent life is the vector by which the universe can “reproduce”, spawing daughters universes that themselves develop intelligent life. By this mechanism, the offspring of future human civilization is potentially infinite. At io9, Dvorsky (2015) considers other possibilities for infinite descent of intelligent life in the universe.
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