As stated, in a punctuated fashion. Organisms can be in stasis, adapted well to their environment for long periods of time, but can undergo rapid evolutionary change ( rapid in the geological sense ) with the proper environmental selection pressure.
Punctuated Equilibrium, I believe is the answer.
It is called Punctuated Equilibrium. Some Evolutionary apologists, notably Richard Dawkins, have down played this aspect of Neo-Darwinistic theory.
Punctuated equilibrium
This is the idea called punctuated equilibria, by paleontologists Stephen Jay Gould and Niles Eldredge. It explains the patterns seen in the fossil record.
Yes. Evolution via punctuated equilibrium still depends on natural selection. In punctuated equilibrium there are long periods in which most species are well-suited to their environments, and so there is is little selective pressure to change. These periods are punctuated by times of more rapid environmental change and greater stress, which results in greater selective pressure for populations to change.