One of the most important presuppositions of Darwin's entire thesis is gradualism, the idea that mutations to the genome can cause minor variations in the organism's properties, which can be accumulated piecemeal, bit by bit, over the eons to create the complex order found in the organisms we observe.

No one can believe in transmutation who is not profoundly convinced that all we know in paleontology is as nothing compared to what we have yet to learn, and they who regard the record as so fragmentary, and our acquaintance with the fragments which are extant as so rudimentary, are apt to be astounded at the confidence placed by the progressionists in data which must be defective in the extreme. But exactly in proportion as the completeness of the record and our knowledge of it are overrated, in that same degree are many progressionists unconscious of the goal towards which they are drifting. Their faith in the fullness of the annals leads them to regard all breaks in the series of organic existence, or in the sequence of the fossiliferous rocks, as proofs of original chasms and leaps in the course of nature, signs of the intermittent action of the creational force, or of catastrophes which devastated the habitable surface; and they are therefore fearless of discovering any continuity of plan (except that which must have existed in the Divine mind) which would imply a material connection between the outgoing organisms and the incoming ones.

When something dies, it is usually disassembled, digested, and decomposed. Only rarely is anything ever fossilized, and even fewer things are very well-preserved. Because the conditions required for that process are so particular, the fossil record can only represent a tiny fraction of everything that has ever lived. Darwin provided many environmental dynamics explaining why no single quarry could ever provide a continuous record of biological events, and why it would be impossible to find all the fossilized ancestors of every lineage. But despite this, he predicted that future generations, -having the benefit of better understanding- would discover a substantial number of fossil species which he called “intermediate” or “transitional” between what we see alive today and their taxonomic ancestors at successive levels in paleontological history. In fact, in the century-and-a-half since then, we’ve found millions of evolutionary intermediaries in the fossil record, much more than Darwin said he could reasonably hope for. There are three different types of transitional forms and we have ample examples of each. But creationists still insist that we’ve never found a single one, because what they usually ask us to present are impossible parodies which evolution would neither produce nor permit.

It seemed obvious to [Darwin] that, if his theory of evolution [were] correct, fossils ought to provide incontrovertible proof of it, since each stratum should contain links between the species of earlier and later strata, and if sufficient fossils were collected, it would be possible to arrange them in ancestor descendent sequences and so build up a precise picture of the course of evolution. This was not so in Darwin’s time, and today, after more than another hundred years of assiduous fossil collecting, the picture still has extensive gaps.

Darwin's theory of evolution was simple, beautiful, majestic and awe-inspiring. But because it contradicts the allegorical babblings of a bunch of made-up old books, it's been under attack since day one. That's just tough luck for Darwin. If the Bible had contained a passage that claimed gravity is caused by God pulling objects toward the ground with magic invisible threads, we'd still be debating Newton with idiots too.

There can be no question that Darwin had nothing like sufficient evidence to establish his theory of evolution. . . . His general theory, that all life on earth had originated and evolved by a gradual successive accumulation of fortuitous mutations, is still, as it was in Darwin’s time, a highly speculative hypothesis entirely without direct factual support and very far from that self-evident axiom some of its more aggressive advocates would have us believe. . . . One might have expected that a theory of such cardinal importance, a theory that literally changed the world, would have been something more than metaphysics, something more than a myth.

I published that theory [of speciational evolution] in a 1954 paper…and I clearly related it to paleontology. Darwin argued that the fossil record is very incomplete because some species fossilize better than others... I noted that you are never going to find evidence of a small local populatlon that changed very rapidly in the fossil record... Gould was my course assistant at Harvard where I presented this theory again and again for three years. So he knew it thoroughly. So did Eldredge. In fact, in his 1971 paper Eldredge credited me with it. But that was lost over time.

We have always thought that Mr. Darwin has unnecessarily hampered himself by adhering so strictly to his favourite "Natura non facit saltum." We greatly suspect that she does make considerable jumps in the way of variation now and then, and that these saltations give rise to some of the gaps which appear to exist in the series of known forms.

Physiologic facts concerning the origin of species in nature were unknown in the time of Darwin. . . The experience of the breeders was quite inadequate to the use which Darwin made of it. It was neither scientific, nor critically accurate. Laws of variation were barely conjectured; the different types of variability were only imperfectly distinguished. The breeders' conception was fairly sufficient for practical purposes, but science needed a clear understanding of the factors in the general process of variation. Repeatedly Darwin tried to formulate these causes, but the evidence available did not meet his requirements. Quetelet's law of variation had not yet been published. Mendel's claim of hereditary units for the explanation of certain laws of hybrids discovered by him, was not yet made. The clear distinction between spontaneous and sudden changes, as compared with the ever-present fluctuating variations, is only of late coming into recognition by agriculturists. Innumerable minor points which go to elucidate the breeders' experience, and with which we are now quite familiar, were unknown in Darwin's time. No wonder that he made mistakes, and laid stress on modes of descent, which have since been proved to be of minor importance or even of doubtful validity.

One of the principal claims of Mr. Darwin's theory to acceptance is, that it enables us to dispense with a law of progression as a necessary accompaniment of variation. It will account equally well for what is called degradation, or a retrograde movement towards a simpler structure, and does not require Lamarck's continual creation of monads; for this was a necessary part of his system, in order to explain how, after the progressive power had been at work for myriads of ages, there were as many beings of the simplest structure in existence as ever.

I have attempted to show that the geological record is extremely imperfect; that only a small portion of the globe has been geologically explored with care; that only certain classes of organic beings have been largely preserved in a fossil state; that the number both of specimens and of species, preserved in our museums, is absolutely as nothing compared with the incalculable number of generations which must have passed away even during a single formation; that, owing to subsidence being necessary for the accumulation of fossiliferous deposits thick enough to resist future degradation, enormous intervals of time have elapsed between the successive formations; that there has probably been more extinction during the periods of subsidence, and more variation during the periods of elevation, and during the latter the record will have been least perfectly kept; that each single formation has not been continuously deposited; that the duration of each formation is, perhaps, short compared with the average duration of specific forms; that migration has played an important part in the first appearance of new forms in any one area and formation; that widely ranging species are those which have varied most, and have oftenest given rise to new species; and that varieties have at first often been local (emphasis not Darwin's). All these causes taken conjointly, must have tended to make the geological record extremely imperfect, and 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. For he may ask in vain where are the numberless transitional links which must formerly have connected the closely allied or representative species, found in the several stages of the same great formation. He may disbelieve in the enormous intervals of time which have elapsed between our consecutive formations; he may overlook how important a part migration must have played, when the formations of any one great region alone, as that of Europe, are considered; he may urge the apparent, but often falsely apparent, sudden coming in of whole groups of species. He may ask where are the remains of those infinitely numerous organisms which must have existed long before the first bed of the Silurian system was deposited: I can answer this latter question only hypothetically, by saying that as far as we can see, where our oceans now extend they have for an enormous period extended, and where our oscillating continents now stand they have stood ever since the Silurian epoch; but that long before that period, the world may have presented a wholly different aspect; and that the older continents, formed of formations older than any known to us, may now all be in a metamorphosed condition, or may lie buried under the ocean.

I absolutely stand by my comment that Charles Darwin’s theory of evolution is not scientific. There is hardly any evidence to substantiate the theory. Great scientists of the world came out to say there is no evidence available in the world which can prove the theory of evolution is correct.

Since we proposed punctuated equilibria to explain trends, it is infuriating to be quoted again and again by creationists—whether through design or stupidity, I do not know—as admitting that the fossil record includes no transitional forms. Transitional forms are generally lacking at the species level, but they are abundant between larger groups.

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.”