If you ask most people what constitutes overgrazing, they will tell you, "putting too many animals on the land." While that's not totally incorrect, it is misleading.
The reality is that it's possible to overgraze with only one animal. Having more animals will accelerate overgrazing; but overgrazing is not so much how many animals are present, but how those animals are managed.
What constitutes overgrazing is failure to move or rotate animals in harmony with forage growth. Proper grazing management is a matter of moving animals before they have the opportunity to regraze lush regrowth.
It used to be the "proper" stocking rate was determined by percentage utilization. (Unfortunately, this is still used in some government-controlled grazing management situations.) The goal was/is for range managers to determine how many animals it takes to reach that level of utilization. If you exceed that rate you are overgrazing; under that rate, you are not.
Unfortunately, that concept is fundamentally flawed. Grazing animals don't utilize a percentage of any given forage. They will eat palatable grasses down to the ground, while unpalatable plants are left untouched.
This concept (percentage utilization) will slow the amount or intensity of overgrazing, but it still permits damage to the more palatable and nutritious species. Similarly, it used to be believed that given the "proper" stocking rate, animals could continually graze in one pasture.
Not true. Continuous grazing ensures that the higher quality forage in a pasture will be stressed. If stocking rate is light, the changes in forage composition will occur gradually over time. If grazing pressure is light enough, the changes may be so gradual as not to be noticed and/or blamed on other factors (weather patterns, etc.).
It also used to be thought that grazing management was an art. Through experience and perception a manager would intuitively know the "proper" stocking rate. While experience is a valuable tool in grazing management, for the most part it is based on straightforward science.
Allow Regrowth To Rest
The most important aspect to understand is that when grass is grazed, the leaf area will regrow; utilizing energy reserves stored in the crown and roots. After regrowth, it takes three to six weeks for most species to replenish those reserves. If regrazed prior to replenishment, the plant will die. That's overgrazing.
Proper grazing management is rotating the animals before they can graze regrowth. This is why continuous grazing in the same pasture ensures overgrazing. Even if there is only one animal in the pasture, they will preferentially seek out lush green regrowth. Over time, the more nutritious and palatable plants will be replaced by less nutritious plants.
The question always asked is, "when should the animals be moved?" Unfortunately, there is no hard and fast answer for that.
The need for movement will depend upon the weather. During peak growing season, movements may be often. In winter, when there is no plant growth, one pasture can be used until spring.
Likewise, during warm weather if drought is present, animals can be left for relatively long periods. Once it rains however, movement must be quick. If not, the pasture will be devastated.
Another common misconception, especially among environmentalists, is that only domestic livestock overgraze. That is most emphatically not true. In fact, many wild ungulates are more selective and therefore more prone to overgrazing than cattle.
As an example, the American buffalo is often said to be "easier on the land" than cattle. Absolutely not true. If you watch buffalo graze, they use their lips as prehensile organs; whereas cattle use the tongue. As a result, buffalo can be (and are) more selective than cattle.
Buffalo are, however, much more athletic, and will readily climb rough or steep terrain, thereby utilizing a pasture more thoroughly than cattle. But leave them in a pasture too long, and they will graze and regraze lush regrowth.
The bottom line is that there is nothing special about wild ungulates. It makes no difference whether the animals are buffalo, elk, deer or cattle. They will instinctively seek out the lushest, most nutritious forage available. Unmanaged and non-rotated, they will deteriorate range quality.