An example of punctuated equilibrium is human evolution, in which species seem to remain stable for very long spans of time and then abruptly develop into new species, or in the rapid evolution of species isolated on islands. Punctuated equilibrium is a modified version of Darwin's law.
The punctuated equilibrium theory states evolution often happens in abrupt, quick bursts punctuated by long periods of little or no change. This often happens in times of abrupt and catastrophic environmental change or when a small population, isolated from the rest of the species, rapidly develops into a more fit specimen and outcompetes its original population.
This theory is partly supported by observed microevolution. For example, the peppered moth was colored primarily white until Britain's Industrial Revolution caused its habitat to blacken with soot. The regular white moths, deprived of natural camouflage, were eaten by predators, while rarer black moths of the same species flourished.