Ronald Fisher: Selection

“[We are now] in a position to judge of the validity of the objection which has been made, that the principle of Natural Selection depends on a succession of favourable chances. The objection is more in the nature of an innuendo than of a criticism, for it depends for its force upon the ambiguity of the word chance, in its popular uses. The income derived from a Casino by its proprietor may, in one sense, be said to depend upon a succession of favourable chances, although the phrase contains a suggestion of improbability more appropriate to the hopes of the patrons of his establishment. It is easy without any very profound logical analysis to perceive the difference between a succession of favourable deviations from the laws of chance, and on the other hand, the continuous and cumulative action of these laws. It is on the latter that the principle of Natural Selection relies.”

Ronald Fisher book The Genetical Theory of Natural Selection

On the objection (still often made by creationists) that the theory of evolution predicts evolution occurs "only by chance", Ch. 2, p. 37.
The Genetical Theory of Natural Selection (1930)

Law , Hope , Nature , Sense

“In organisms of all kinds the young are launched upon their careers endowed with a certain amount of biological capital derived from their parents. This varies enormously in amount in different species, but, in all, there has been, before the offspring is able to lead an independent existence, a certain expenditure of nutriment in addition, almost universally, to some expenditure of time or activity, which the parents are induced by their instincts to make for the advantage of their young. Let us consider the reproductive value of these offspring at the moment when this parental expenditure on their behalf has just ceased. If we consider the aggregate of an entire generation of such offspring it is clear that the total reproductive value of the males in this group is exactly equal to the total value of all the females, because each sex must supply half the ancestry of all future generations of the species. From this it follows that the sex ratio will so adjust itself, under the influence of Natural Selection, that the total parental expenditure incurred in respect of children of each sex, shall be equal; for if this were not so and the total expenditure incurred in producing males, for instance, were less than the total expenditure incurred in producing females, then since the total reproductive value of the males is equal to that of the females, it would follow that those parents, the innate tendencies of which caused them to produce males in excess, would, for the same expenditure, produce a greater amount of reproductive value; and in consequence would be the progenitors of a larger fraction of future generations than would parents having a congenital bias towards the production of females. Selection would thus raise the sex-ratio until the expenditure upon males became equal to that upon females.”

Ronald Fisher book The Genetical Theory of Natural Selection

On natural selection acting on sex ratio: Fisher's principle, Ch. 6, p. 141.
The Genetical Theory of Natural Selection (1930)

Children , Sex , Nature , Parent

“We may consequently state the fundamental theorem of Natural Selection in the form : The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time.”

Ronald Fisher book The Genetical Theory of Natural Selection

Defining the fundamental theorem of natural selection, Ch. 2, p. 35.
The Genetical Theory of Natural Selection (1930)

Nature , Time

“Natural selection is a mechanism for generating an exceedingly high degree of improbability.”

Ronald Fisher

Reported by J. S. Huxley in Evolution in Action, London: Chatto and Windus, 1953.
1950s

Nature

“Professor Eddington has recently remarked that 'The law that entropy always increases — the second law of thermodynamics — holds, I think, the supreme position among the laws of nature'. It is not a little instructive that so similar a law [the fundamental theorem of natural selection] should hold the supreme position among the biological sciences.”

Ronald Fisher book The Genetical Theory of Natural Selection

On the fundamental theorem of natural selection, Ch. 2, p. 36.
The Genetical Theory of Natural Selection (1930)

Law , Nature , Thinking , Science

“Natural Selection is not evolution.”

Ronald Fisher book The Genetical Theory of Natural Selection

Preface, opening sentence, p. vii.
The Genetical Theory of Natural Selection (1930)

Nature