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.
Some believe that the Earth's population has already overshot its carrying capacity.
Human Overshoot Index 
The Overshoot Index assesses the extent to which a country can support itself from its own renewable resources, by measuring per capita consumption against per capita biocapacity. The ecological footprint measures the area of biologically productive land and water required to produce the renewable resources/ecological services for, and absorb the waste of, a given population at a given average level of resource consumption. Biocapacity is the biologically productive capacity of an area - cropland, grazing land, forest, fresh water etc. It does not include non-renewable resources like fossil fuels and other minerals, so tends to underestimate dependency. Ecological footprint and biocapacity are measured in global hectares (hectares with world average biological productivity) per person. 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 is its self-sufficient percentage; the remaining percentage is its dependent percentage. 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 dependency of greater than zero means that a country, region or the world is relying on other countries or non-renewable, unsustainable resources for its current consumption. Countries in overshoot increase their dependency, and the others approach overshoot, 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 (GFN). Countries with populations of under one million have been omitted. GFN’s data are largely from UN sources; their methodology is still admittedly imprecise, but is subject to continuous refinement. 
Other populations 
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.
See also 
- 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
- Optimum Population Trust (10 April 2012). "New index highlights most overpopulated countries". Overshoot Index (Optimum Population Trust). Retrieved 10 April 2012.