Here is a quote from his Watchmaker book, as provided by a reputable online bookseller:
Chapter 3 - Accumulating small change
We have seen that living things are too improbable and too beautifully 'designed' to have come into existence by chance. How, then, did they come into existence? The answer, Darwin's answer, is by gradual, step- by-step transformations from simple beginnings, from primordial entities sufficiently simple to have come into existence by chance. Each successive change in the gradual evolutionary process was simple enough, relative to its predecessor, to have arisen by chance. But the whole sequence of cumulative steps constitutes anything but a chance process, when you consider the complexity of the final end-product relative to the original starting point. The cumulative process is directed by nonrandom survival. The purpose of this chapter is to demonstrate the power of this cumulative selection as a fundamentally nonrandom process.
This does not suggest to me that he is willing to throw out Darwinian gradualism, and the essence of the quote by Azar is very close to this one. Compare:
"If you throw out gradualism, you throw out the very thing that makes evolution more plausible than creation."
PE is sudden, sequestered change, and Gould came up with it because gradualism did not fit the evidence:
"The modern theory of evolution does not require gradual change. In fact, the operation of Darwinian processes should yield exactly what we see in the fossil record. It is gradualism that we must reject, not Darwinism."
Panda, page 182.
It seems to me that Gould is engaging in double talk somewhat, because he wants to have it both ways, since Darwin is FAMOUS for gradualism, as Dawkin's affirms. But is is also plain to see that he is chucking out gradualism as unworkable re the evidence, which Dawkin's clearly does not want to do.
I would have to say, that the known paragraph and Azar's sentence are congruent. If Dawkin's did not say exactly that, he said something very much like it.
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That quote of Dawkins' is taken so far out of context that I won't dignify it with a response. I strongly suggest you carefully question everything that you read in the Azar book. I also suggest you find that quote (I believe it's from The Blind Watchmaker), read it in context, and then decide if you trust Larry Azar.
Finally, I accept that there are parts of Darwin's original theory that have required modification to better fit the last 150 years of observation. These aspects are minor and do not change the fundamental tenets of the theory. Modification of this type is ubiquitous is science and has occurred for EVERY theory that has ever been proposed.