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Stephen Jay Gould

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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.”
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"The Episodic Nature of Evolutionary Change", p. 182

 
Stephen Jay Gould

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At the core of punctuated equilibria lies an empirical observation: once evolved, species tend to remain remarkably stable, recognizable entities for millions of years. The observation is by no means new, nearly every paleontologist who reviewed Darwin's Origin of Species pointed to his evasion of this salient feature of the fossil record. But stasis was conveniently dropped as a feature of life's history to he reckoned with in evolutionary biology. And stasis had continued to be ignored until Gould and I showed that such stability is a real aspect of life's history which must be confronted-and that, in fact, it posed no fundamental threat to the basic notion of evolution itself. For that was Darwin's problem: to establish the plausibility of the very idea of evolution, Darwin felt that he had to undermine the older (and ultimately biblically based) doctrine of species fixity. Stasis, to Darwin, was an ugly inconvenience.

 
Niles Eldredge
 

I want to argue that the “sudden” appearance of species in the fossil record and our failure to note subsequent evolutionary change within them is the proper prediction of evolutionary theory as we understand it. […] Evolutionary “sequences” are not rungs on a ladder, but our retrospective reconstruction of a circuitous path running like a labyrinth, branch to branch, from the base of the bush to a lineage now surviving at its top.

 
Stephen Jay Gould
 

The fossil record implies trial and error, an inability to anticipate the future, features inconsistent with an efficient Great Designer.

 
Carl Sagan
 

The species with eyes appears suddenly, capriciously as it were, and it is this species which changes the environment by creating its visible aspect. The eye does not come into being because it is needed. Just the contrary; because the eye appears it can henceforth be applied as a serviceable instrument. Each species builds up its stock of useful habits by selecting among, and taking advantage of, the innumerable useless actions which a living being performs out of sheer exuberance.

 
Jose Ortega y Gasset
 

Evolution is a theory of organic change, but it does not imply, as many people assume, that ceaseless flux is the irreducible state of nature and that structure is but a temporary incarnation of the moment. Change is more often a rapid transition between stable states than a continuous transformation at slow and steady rates. We live in a world of structure and legitimate distinction. Species are the units of nature's morphology.

 
Stephen Jay Gould
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