“As many more individuals of each species are born than can possibly survive; and as, consequently, there is a frequently recurring struggle for existence, it follows that any being, if it vary however slightly in any manner profitable to itself, under the complex and sometimes varying conditions of life, will have a better chance of surviving, and thus be naturally selected. From the strong principle of inheritance, any selected variety will tend to propagate its new and modified form.”

"Introduction", page 5 http://darwin-online.org.uk/content/frameset?pageseq=20&itemID=F373&viewtype=image
On the Origin of Species (1859)

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Charles Darwin 161
British naturalist, author of "On the origin of species, by… 1809–1882

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“As many more individuals of each species are born than can possibly survive; and as, consequently, there is a frequently recurring struggle for existence, it follows that any being, if it vary however slightly in any manner profitable to itself, under the complex and sometimes varying conditions of life, will have a better chance of surviving, and thus be naturally selected.”

From the strong principle of inheritance, any selected variety will tend to propagate its new and modified form.
"Introduction", page 5 http://darwin-online.org.uk/content/frameset?pageseq=20&itemID=F373&viewtype=image
On the Origin of Species (1859)

Charles Darwin photo

“Owing to this struggle for life, any variation, however slight and from whatever cause proceeding, if it be in any degree profitable to an individual of any species, in its infinitely complex relations to other organic beings and to external nature, will tend to the preservation of that individual, and will generally be inherited by its offspring.”

Source: On the Origin of Species (1859), chapter III: "Struggle For Existence", page 61 http://darwin-online.org.uk/content/frameset?pageseq=76&itemID=F373&viewtype=image
Context: Owing to this struggle for life, any variation, however slight and from whatever cause proceeding, if it be in any degree profitable to an individual of any species, in its infinitely complex relations to other organic beings and to external nature, will tend to the preservation of that individual, and will generally be inherited by its offspring. The offspring, also, will thus have a better chance of surviving, for, of the many individuals of any species which are periodically born, but a small number can survive. I have called this principle, by which each slight variation, if useful, is preserved, by the term of Natural Selection, in order to mark its relation to man's power of selection.

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“Protoplasm is protean; any simple protoplasm can become any complex form of life under mutation and selection.”

Source: Beyond This Horizon (1948; originally serialized in 1942), Chapter 13, “No more privacy than a guppy in an aquarium”, p. 126

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“Where natural selection slackens, new forms may arise which would not survive under more rigid competition”

Source: The Causes of Evolution (1932), Ch. IV Natural Selection, pp. 104-106.
Context: Where natural selection slackens, new forms may arise which would not survive under more rigid competition, and many ultimately hardy combinations will thus have a chance of arising.... Thus the distinction between the principal mammalian orders seems to have arisen during an orgy of variation in the early Eocene which followed the doom of the great reptiles... Since that date mammalian evolution has been a slower affair, largely a progressive improvement of the types originally laid down in the Eocene.
Another possible mode of making rapid evolutionary jumps is by hybridisation.... hybridisation (where the hybrids are fertile) usually causes an epidemic of variation in the second generation which may include new and valuable types which could not have arisen within a species by slower evolution.

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