Here is an extended quote from Stephen Jay Gould’s “The Episodic Nature of Evolutionary Change,” pp. 181-182, in which he explains the problems with the fossil record, and how he believes his pet theory of “punctuated equilibrium” purportedly solves this “uncomfortable paradox.” Of course, you can take these facts regarding the fossil record and draw quite different inferences.
The extreme rarity of transitional forms in the fossil record persists as the trade secret of paleontology. The evolutionary trees that adorn our textbooks have data only at the tips and nodes of their branches; the rest is inference, however reasonable, not the evidence of fossils. Yet Darwin was so wedded to gradualism that he wagered his entire theory on a denial of this literal record:
The geological record is extremely imperfect and this fact will to a large extent explain why we do not find interminable varieties, connecting together all the extinct and existing forms of life by the finest graduated steps. He who rejects these views on the nature of the geological record, will rightly reject my whole theory.
Darwin’s argument still persists as the favored escape of most paleontologists from the embarrassment of a record that seems to show so little of evolution directly. In exposing its cultural and methodological roots, I wish in no way to impugn the potential validity of gradualism (for all general views have similar roots). I only wish to point out that it is never “seen” in the rocks.
Paleontologists have paid an exorbitant price for Darwin’s argument. We fancy ourselves as the only true students of life’s history, yet to preserve our favored account of evolution by natural selection we view our data as so bad that we never see the very process we profess to study.
For several years, Niles Eldredge of the American Museum of Natural History and I have been advocating a resolution to this uncomfortable paradox. We believe that Huxley was right in his warning. The modern theory of evolution does not require gradual change. In fact, the operation of Darwinian processes should yield exactly what we see in the fossil record. It is gradualism we should reject, not Darwinism.
The history of most fossil species includes two features particularly inconsistent with gradualism:
1. Stasis. Most species exhibit no directional change during their tenure on earth. They appear in the fossil record looking much the same as when they disappear; morphological change is usually limited and directionless.
2. Sudden appearance. In any local area, a species does not arise gradually by the steady transformation of its ancestors; it appears all at once and “fully formed.”
This summary of the fossil record has been the accepted view of paleontologists for more than 20 years now, as confirmed by Donald Prothero in 2009. See here.