Carrying Capacity of the Earth Energy and Area limits on Human Population Note: Most of the numbers in these slides are order-of-magnitude estimates Martin Taylor 2011/05/19

Available Land Area World Land Area x 10 6 sq km. Antarctica and Greenland 16 x 10 6 sq km Sahara, Gobi and Arabian deserts total roughly the size of Australia, 8 x 10 6 sq km. Available habitable land area ~125 x 10 6 sq km. Most of these slides assume all habitable land is optimum habitat for humans.

The World

Fig. 2. The scaling across trophic levels of per-individual area (N–1, triangles, dashed line) and individual home range size (H, circles, solid line). W Jetz et al. Science 2004;306: Published by AAAS Carnivores Omnivores Herbivores 50 kg individual needs ~ 15 sq km ~ 1 sq km ~0.2 sq km

Basic carrying capacity of the Earth World habitable area is approximately 125 x 10 6 sq km. Assume it is all optimum habitat. A 70 kg mammal requires Sustainable number of individuals Carnivore15 sq km8.3 million Omnivore1 sq km125 million Herbivore0.2 sq km750 million How can the world sustain 60 times as many humans? Or should we ask whether it can?

Where are the limits? An organism is a self-organized structure that maintains its structure in a low-entropy state using a through energy flow The fundamental limit must be the ability of the organism to use the available energy sources. Vegetation uses solar energy, whereas animals use food that contains chemical structures ultimately derived from vegetation. The areal footprint of an animal ultimately is a measure of how much vegetation is used to generate its food. Jetz et al. compute that for animals in an optimum habitat, the habitat provides approximately 2188 w/km 2 to a herbivore, 408 w/km 2 to an omnivore and 32 w/km 2 to a carnivore, independent of body size.

How about arable land? 10% of the land surface is arable land, 16 x 10 6 km 2 1% is actually in crops, 1.6 x 10 6 km 2 If cropland were only as productive as wild land, and if it was the only source of energy, we would expect the carrying capacity for a 50kg omnivore to be 1.6 million people. Since this is a little over.02% of the existing population, something is wrong with the assumptions or the calculation. What? Data from the CIA World Factbook

Agriculture doesnt necessarily increase biological productivity From Foley et. al, Proc Natl Acad Sci USA, 2007 July 31, 104(31)

What about Humans? Assuming that before the invention of controlled fire, humans were subject to the same constraints as other mammals, we can assume they used approx 400w averaged over a day. However, at a rough approximation, an active person of 50 kg in present day USA is said to need about 2500kcal/day = 4kwh = 170w (to a first approximation). Why the difference? Contemporary humans live in sheltered houses, have heating and cooling systems, and eat cooked meat, all of which reduce the requirements for food energy. But these and other energy offsets provided by civilization require their own energy sources.

Accommodating more people Humans get a far larger share of the food energy from cropland or pastureland than they would have done in the pre-fire wild environment. Photosynthesis captures about 3 x J per year, which is a power level of about 0.8 w/m 2 (Wikipedia). Omnivores get approximately 4 x w/m 2 from food derived from plants. (Jetz et al.) Hence a wild omnivore sharing with other species gets about about 5 x of the photosynthetic production. Haberl et al. estimate humans use 23.8% of the potential net primary productivity, or 500 times what a wild omnivore would expect. Hence a human should need about 800 m 2 for food.

Area Limit If an omnivore human needs 800 m 2 for food and the arable land is 12.5 x m 2, then the maximum population that could possibly be fed is about 16 billion. However…

How much power do we need? To sustain a life-style equivalent to a pre-fire person, we would need about 400w per person. But A person in France, Germany or Japan now uses about 5 kw A person in the USA now uses about 10 kw Taking the European value, 7 billion people would use 35 x 10 9 kw generated over 125 x 10 6 sq km The average power requirement to give 7 billion people a European standard of living is roughly 3 w/m 2 over the habitable land surface of the Earth.

Land area requirements Assuming all the power we use comes directly from the sun, and biophotosynthesis is as efficient as we can achieve overall. To sustain a European lifestyle requires 3w/m 2, or about 7.5 x 10 3 m 2 of photosynthesis. With a habitable land area of 125 x m 2, this allows for a total population of 16 billion. To achieve this would require the elimination of all other animals except for those we eat, and turning the whole habitable surface of the Earth into high-quality cropland. We need power sources with a higher areal energy density than photosynthesis.

Adding other power sources We probably cant reduce the need for biological sources of the 170 w we need to get from food, but for the rest of the 5 kw that seems to be needed for a European life style, how do other sources compare in area efficiency? The main suggestions for carbon-neutral energy sources are: o Nuclear as a bridging source for a century or two And sustainable over the long term o Wind o Solar voltaic o Tide o Bio-fuel

Power of the Tide Bow wave of the tide breaking from an islet off the north coast of Scotland

Meeting tides Tides from north and south breaking against one in the North Sea

Areal power densities Solar cells can achieve efficiencies up to 43% in the laboratory, compared to 2-5% for photosynthesis. Available solar power is about 340 w/m 2, so at 30% efficiency solar cells could achieve about 115 w/m 2. Current standard is about 80 w/m 2 in Southern Ontario. Nuclear Power. A by-eye estimate of the area covered by the Darlington power station suggests it takes about 1 sq km to produce 3.5 x 10 9 w., or 3500 w/m 2. Tidal power takes very little land area, but may interfere with ocean life. Wind power takes up only the area of an access road if the turbines are located in cropland, none if located in the sea. Guess the average access road to be 3 x 300m, or about 1000 m 2, and the turbine averages 200 kw (1.5Mw x 15%). The energy density is around 200 w/m 2. Estimates omit the area dedicated to mining, manufacture and transport.

Wind Power A wind farm in the North Sea

Land area needed from other Sources For 7 x 10 9 humans using 5 kw per person, we need 3.5 x w from 1.25 x m 2 land surface. To supply this much power the land area requirements are very roughly… For nuclear, m 2, or about 8 x of the land surface. For solar photovoltaic, 4 x m 2 or 3% of the land surface. Perhaps half could be on rooftops, which takes nothing out of biological production. For wind turbines, 2 x m 2, or 0.2% of the land surface, less if in the sea. For solar, wind, and tide, some land must be dedicated to energy storage and transmission. Contrast these numbers with biofuel, which is limited by photosythetic efficiency to about 10% of the efficiency of solar photovoltaic. Biofuel crops would need at least 30% of the land surface, almost all of which would have to be taken from food production, since only about 30% of the land area is arable or pastureland.

Conclusions We cannot afford to compromise the sources of food if the existing population is to be maintained. Hence… We should not be considering biofuels as a major source of power We need power sources of high areal energy density (w/m 2 ) Wind and tide seem better than solar Nuclear from uranium might serve as a bridging technology, (but nuclear from thorium is likely to be longer lasting, less subject to diversion of fissile material, safer, and create less difficulty with waste disposal).

References CIA World Factbook 2011, < world-factbook/ Foley et. al, Proc Natl Acad Sci USA, 2007 July 31, 104(31) Haberl, H. et al., Human appropriation of net primary production., Science, 14 June 2002, Hargreaves, R and R. Moir, Liquid Fluoride Thorium Reactors, American Scientist, 2010, 98, Jetz, W. et al. Science 2004;306: Kazimi, M. S., Thorium Fuel for Nuclear Energy, American Scientist, 2004, 91,