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.

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.

Darwinism is not a theory of random chance. It is a theory of random mutation plus non-random cumulative natural selection. . . . Natural selection . . . is a non-random force, pushing towards improvement. . . . Every generation has its Darwinian failures but every individual is descended only from previous generations' successful minorities. . . . [T]here can be no going downhill - species can't get worse as a prelude to getting better. . . . There may be more than one peak.

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.

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.

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.

Darwin believed that the crossing of two types generally led to a blend, and that consequently bisexual reproduction tended to make a species uniform. He therefore had to postulate some cause constantly at work to keep up the inheritable variation within a species. He very naturally looked to the effects of differences of environment. ...It was shown that Darwin had been wrong in supposing that variations due to environment were inheritable. Selection merely picked out the best available line from a given population, and would not, as Darwin had believed, give rise to an unlimited amount of change.

Darwin’s model of evolution . . . , being basically a theory of historical reconstruction, . . . is impossible to verify by experiment or direct observation as is normal in science . . . Moreover, the theory of evolution deals with a series of unique events, the origin of life, the origin of intelligence and so on. Unique events are unrepeatable and cannot be subjected to any sort of experimental investigation.

<nowiki>[</nowiki>Darwin’s] inquiry characteristically confines itself to the process of cumulative change. His results, as well as his specific determination of the factors at work in this process of cumulative change, have been questioned; perhaps they are open to all the criticisms levelled against them as well as a few more not thought of; but the scope and method given to scientific enquiry by Darwin and the generation whose spokesman he is has substantially not been questioned, except by that diminishing contingent of the faithful

Evolution, thus, is merely contingent on certain processes articulated by Darwin: variation and selection. No longer is a fixed object transformed, as in transformational evolution, but an entirely new start is, so to speak, made in every generation.

To this day, and in quarters where they should know better, Darwinism is widely regarded as a theory of ‘chance’.
It is grindingly, creakingly, crashingly obvious that, if Darwinism were really a theory of chance, it couldn’t work. You don’t need to be a mathematician or physicist to calculate that an eye or a haemoglobin molecule would take from here to infinity to self-assemble by sheer higgledy-piggledy luck. Far from being a difficulty peculiar to Darwinism, the astronomic improbability of eyes and knees, enzymes and elbow joints and the other living wonders is precisely the problem that any theory of life must solve, and that Darwinism uniquely does solve.

It [variation and natural selection] would explain, says Mr. Darwin, the unity of type which runs through the whole organic world, and why there is sometimes a fundamental agreement in structure in the same class of beings which is quite independent of their habits of life, for such structure, derived by inheritance from a remote progenitor, has been modified, in the course of ages, in different ways, according to the conditions of existence. It would also explain why all living and extinct beings are united, by complex radiating and circuitous lines of affinity with one another, into one grand system; also, there having been a continued extinction of old races and species in progress, and a formation of new ones by variation, why in some genera which are largely represented, or to which a great many species belong, many of these are closely but unequally related; also, why there are distinct geographical provinces of species of animals and plants, for, after long isolation by physical barriers, each fauna and flora, by varying continually, must become distinct from its ancestral type, and from the new forms assumed by other descendants which have diverged from the same stock.

In Darwin’s version of Darwinism, natural selection played a key role, but so too did various living agencies, notably one that Darwin called “use and disuse” (using or failing to use a limb or organ, which, he assumed, would have heritable effects) and another that he named “sexual selection.”

Evolution must have involved the simultaneous change in many genes, which doubtless accounts for its slowness. Here matters would have been easier if heritable variations really formed a continuum, as Darwin apparently thought, i.e. if there were no limit to the possible smallness of a variation. But this is clearly not the case when we are considering meristic characters. ...the atomic nature of Mendelian inheritance suggests very strongly that even where variation is apparently continuous this appearance is deceptive.