Summary
All evolution, of course, must be gradual, in that each generation must not be too unlike the previous generation, or mating would be impossible. Punctuated equilibrium is not saltationism, a defunct theory that states that speciations occur in single large steps. Rather, punctuated equilibrium states that populations remain stable for long periods of time, evolving little or not at all; these periods of time are called stases.
In the most common occurrence of speciation, according to punctuated equilibrium, small, isolated populations evolve rapidly, so that speciation takes place over about ten thousand to a million years. This period of time is a geological instant, but it still allows plenty of time for gradual change at a fast rate to produce a new species.
Punctuated equilibrium explains how large, stable populations can produce new species:
the large population itself doesn't change, but small isolated "pocket" populations might, resulting in branching rather than linear species histories. It also explains the relative scarcity of transitional forms, particularly between species (rather than between larger groups), in the fossil record. If transitional forms only exist for a few thousand years, often in a small geographical location different from its later range, then the odds are against fossils being formed, found, and described.
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