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What is the name of the hypothesis that evolution occurs at a slow constant rate?

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Darwin's classic theory of evolution assumed that evolution is a slow, contunuous process, by which new species evolve and emerge. This is referred to at times as "organic evolution" and the "synthetic theory of evolution", or just the Darwinian theory of evolution. A newer theory, proposed originally by Niles Eldridge and Stephen Jay Gould is known as "punctuated equilibria", a model in which the evloution of new species occurs only periodically, in relatively rapid spurts. See "Time Frames the Rethinking of Darwinian Evolution and the Theory of Punctuated Equilibraia, Simon & Schuster, 1985"  The slow, constant process has also been called "gradualism."
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What is the hypothesis that evolution occurred slowly but steadily called?

  I think the attribution you are looking for is "Darwins' theory of evolution". He wrote several books hypothesizing his theories, the most pertinent to your question bei

What rate does evolution occur?

there are two different rates that evolution could occur at. the first kind is gradual, which is small changes over time. the other kind is fast and it occurs when there is a