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Ronald Fisher

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[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.
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On the objection (still often made by creationists) that the theory of evolution predicts evolution occurs "only by chance", Ch. 2, p. 37

 
Ronald Fisher

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"What is it that makes natural selection succeed as a solution to the problem of improbability, whereas chance and design both fail at the starting gate? The answer is that natural selection is a cumulative process, which breaks the problem of improbability up into small pieces. Each of the small pieces is slightly improbable, but not prohibitively so. (pg.153)

 
Richard Dawkins
 

With highly civilised nations continued progress depends in a subordinate degree on natural selection; for such nations do not supplant and exterminate one another as do savage tribes. Nevertheless the more intelligent members within the same community will succeed better in the long run than the inferior, and leave a more numerous progeny, and this is a form of natural selection. The more efficient causes of progress seem to consist of a good education during youth whilst the brain is impressible, and of a high standard of excellence, inculcated by the ablest and best men, embodied in the laws, customs and traditions of the nation, and enforced by public opinion. It should, however, be borne in mind, that the enforcement of public opinion depends on our appreciation of the approbation and disapprobation of others; and this appreciation is founded on our sympathy, which it can hardly be doubted was originally developed through natural selection as one of the most important elements of the social instincts.

 
Charles Darwin
 

The giraffe's neck supposedly supplies a crucial example for preferring natural selection over Lamarckism as a cause of evolution. But Darwin himself (however wrongly by later judgement) did not deny the Lamarckian principle of inheritance for characters acquired by use or lost by disuse. He regarded the Lamarckian mechanism as weak, infrequent, and entirely subsidiary to natural selection, but he accepted the validity of evolution by use and disuse. Darwin does speculate about the adaptive advantage of giraffe's necks, but he cites both natural selection and Lamarckism as probable causes of elongation.

 
Stephen Jay Gould
 

Lastly, isolation, by checking immigration and consequently competition, will give time for any new variety to be slowly improved; and this may sometimes be of importance in the production of new species. If, however, an isolated area be very small, either from being surrounded by barriers, or from having very peculiar physical conditions, the total number of the individuals supported on it will necessarily be very small; and fewness of individuals will greatly retard the production of new species through natural selection, by decreasing the chance of the appearance of favourable variations.

 
Charles Darwin
 

There will still be the question why Tuscany, although it abounds in hot springs, does not furnish a powder out of which, on the same principle, a wall can be made which will set fast under water. ...The properties of the soil are as different and unlike as are the various countries. ...Hence it is not in all the places where boiling springs of hot water abound that there is the same combination of favourable circumstances... For things are produced in accordance with the will of nature; not to suit man's pleasure, but as it were by a chance distribution.

 
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