In population dynamics and population ecology, overshoot occurs when a population exceeds the long term carrying capacity of its environment. The consequence of overshoot is called a crash or die-off.
An attempt to apply this concept to human experience is Overshoot: The Ecological Basis of Revolutionary Change, by William R. Catton, Jr. Also see Limits to growth: The 30-year update, by Meadows, Randers & Meadows, which updates the 1974 book, The Limits to Growth. The Limits to Growth simulation showed in several scenarios how overshoot could happen based on an assumption of hard limits to resources, but did not deal with questions of substitution of limited resources with renewable resources.
Measuring Human Overshoot
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Globally, we can measure how much the human economy demands against what the biosphere can renew. One accounting approach is the Ecological Footprint. Footprint accounting measures the demand on biocapacity, i.e., area of biologically productive land and water required to produce the ecological services (including resource regeneration and waste absorption) for a given population. Biocapacity encompasses the biologically productive capacity of all of the planet's surface areas - cropland, grazing land, forest, fresh water etc. Footprint accounts include non-renewable resources like fossil fuels and other minerals in as far as their use puts a demand on biocapacity. Some demands are difficult to measure and are not included in the accounts - hence the results tend to underestimate dependency. Ecological Footprint and biocapacity are measured in global hectares (hectares with world average biological productivity). Thus increased productivity would reduce dependency; while increased population or consumption per head would increase it.
The percentage of an area’s Footprint supported from its renewable resources shows its overall resource dependence within or above its areas'regeneration rate. A percentage over 100 percent indicates local overuse or net dependence on ecosystems elsewhere. Similarly, the percentage of an area’s population supported from its renewable resources is its sustainable population at current consumption levels with current technology; the remaining percentage is its overshoot population. A country's biocapacity deficit increases as either their population or their per capita consumption grows; and faster if both grow.
Overshoot Index of various countries
A detailed list of countries and their main figures to compute the Overshoot (overpopulation) index has been computed by The Optimum Population Trust. All source data is from The Ecological Footprint Atlas 2010, based on 2007 figures, produced by the Global Footprint Network. Countries with populations of under one million have been omitted. Global Footprint Network’s data are largely from UN sources; their methodology is still admittedly imprecise, but is subject to continuous refinement. 
The eradication of disease can trigger overshoot when a population suddenly exceeds the land's carrying capacity. An example of this occurred on the Horn of Africa when smallpox was eliminated. A region that had supported around 1 million pastoralists for centuries was suddenly expected to support 14 million people. The result was overgrazing, which led to soil erosion.
- Meadows, Donella; Jørgen Randers, & Dennis Meadows (2004). Limits to growth: The 30-year update. White River Junction, VT: Chelsea Green Publishing Company. p. 337. ISBN 1-931498-51-2.
- Ryerson, W. F. (2010), "Population, The Multiplier of Everything Else", in McKibben, D, The Post Carbon Reader: Managing the 21st Centery Sustainability Crisis, Watershed Media, ISBN 978-0-9709500-6-2
- Brown, L. R. (2011). World on the Edge. Earth Policy Institute. Norton. ISBN 978-0-393-08029-2.
- Optimum Population Trust (10 April 2012). "New index highlights most overpopulated countries". Overshoot Index (Optimum Population Trust). Retrieved 10 April 2012.