How many humans can the earth support?

Background/Question/Methods

The carrying capacity of earth for human beings has been debated for many years. Most estimates fall in the range from 4 billion to 16 billion. To provide a baseline for such discussions, I estimated the carrying capacity for a human population composed of hunter-gathers. I combined estimates of home range size for primates of different sizes with the calculated metabolic mass of the primate to estimate the amount of primate metabolic mass that can be supported per unit area. Metabolic mass was calculated as mass raised to a power of 0.75. Metabolic mass of primate per unit area was then divided by the metabolic mass of a 60 kg human (21.6 kg^0.75) to give the number of humans that could be supported per unit area of land. The area of arable land that could support primates was estimated to be 110 million km².

Results/Conclusions

The mean metabolic mass from several studies of primates in the tropics ranged from 28.5 kg^0.75/km² to 44.9 kg^0.75/km². The carrying capacity of the earth for humans operating as hunter-gatherers without energy subsidies can then be estimated as 28.5 * 110 million / 21.6 = 145 million for a lower bound to 44.9 * 110 million / 21.6 = 229 million as a upper bound. These estimates are likely to be overestimates as they assume that all arable land has the same carrying capacity as the tropical habitats where the primate home range data were collected. Mean population density of Native Americans before the European invasion was has been estimated to be 0.75/km². Multiplying by 110 million arable km² gives a carrying capacity of 80 million. Although these estimates may be high the current population of earth  (7 billion) is 30-87 times as large, which gives some perspective on the degree to which human society depends on supplemental food provided by agriculture and fisheries.