This myth has more to do with what people thought their own views contrasted to, than anything Darwin said, but like all myths, there's a hint of truth underlying it.
The problem with this myth is the ambiguity of the term "gradual". It is a weasel word, which can mean one thing at one point and another when the first meaning has no purchase. This is referred to the fallacy of ambiguity in logic: when attacking terms in science, one must make sure the terms stay the same form beginning to end.
"Gradual" can mean one or more of the following things:
Steady: the rate of change is constant
Continuous: There are no large discontinuities
Uniform: the same things are active now as in the past and vice versa
Now, I reckon that Darwin never held to a steady rate of change, and that from the fourth edition of the Origin he was explicit about that. Some people see this as a bit of a backdown on his part in the face of criticisms from Wagner and Mivart and others, but I think he never held to any notion that involves or implied steady rates of change. This undercuts the supposed "phyletic gradualism" claim made by Gould and Eldredge. It may be that in the mid twentieth century some people, notably Mayr and Dobzhansky, were arguing that there was always a more or less set amount of change occurring in every species, but the existence of arguments like Haldane's proposal for a measure of rates of change - the "darwin" - in 1949 suggests otherwise, as did Simpson's book five years earlier Tempo and Mode in Evolution. I think this has been over stated. In fact while there may have been an emphasis on steady change, when pushed, most people accepted variable rates of change. Here's Darwin's comments in the fourth edition:
Species of different genera and classes have not changed at the same rate, or in the same degree. ... [p377]
I believe in no fixed law of development, causing all the inhabitants of a country to change abruptly, or simultaneously, or to an equal degree. The process of modification must be extremely slow. The variability of each species is quite independent of that of all others. Whether such variability be taken advantage of by natural selection, and whether the variations be accumulated to a greater or lesser amount, thus causing a greater or lesser amount, thus causing a greater or lesser amount of modification in the varying species, depends on many complex contingencies,—on the variability being of a beneficial nature, on the power of intercrossing and on the rate of breeding, on the slowly changing physical conditions of the country, and more especially on the nature of the other inhabitants with which the varying species comes into competition. Hence it is by no means surprising that one species should retain the same identical form much longer than others; or, if changing, that it should change less. [p378]
Groups of species, that is, genera and families, follow the same general rules in their appearance and disappearance as do single species, changing more or less quickly, and in a greater or lesser degree. [p380]
We have seen in the last chapter that many species of a group sometimes falsely appear to have come in abruptly in a body; and I have attempted to give an explanation of this fact, which if true would have been fatal to my views. But such cases are certainly exceptional; the general rule being a gradual increase in number, till the group reaches its maximum, and then, sooner or later, it gradually decreases. If the number of the species of a genus, or the number of the genera of a family, be represented by a vertical line of varying thickness, ascending through the successive geological formations in which the species are found, the line will sometimes falsely appear to begin at its lower end, not in a sharp point, but abruptly; it then gradually thickens upwards, often keeping for a space of equal thickness, and ultimately thins out in the upper beds, marking the decrease and final extinction of the species. This gradual increase in the number of the species of a group is strictly conformable with my theory, for the species of the same genus, and the genera of the same family, can increase only slowly and progressively; the process of modification and the production of a number of allied forms necessarily being a slow and gradual process,—one species first giving rise to two or three varieties, these being slowly converted into species, which in their turn produce by equally slow steps other varieties and species, and so on, like the branching of a great tree from a single stem, till the group becomes large. [p380f]
Now let's look at the famous passage he introduced which people quote as being evidence that punctuated equilibrium is not anti-Darwinian:
I have attempted to show that the geological record is extremely imperfect; that only a small portion of the globe has been geologically explored with care; that only certain classes of organic beings have been largely preserved in a fossil state; that the number both of specimens and of species, preserved in our museums, is absolutely as nothing compared with the incalculable number of generations which must have passed away even during a single formation; that, owing to subsidence being almost necessary for the accumulation of deposits rich in fossils and thick enough to resist future degradation, enormous intervals of time have elapsed between most of our successive formations; that there has probably been more extinction during the periods of subsidence, and more variation during the periods of elevation, and during the latter the record will have been least perfectly kept; that each single formation has not been continuously deposited; that the duration of each formation is, probably, short compared with the average duration of specific forms; that migration has played an important part in the first appearance of new forms in any one area and formation; that widely ranging species are those which have varied most frequently, and have oftenest given rise to new species; that varieties have at first been local; and lastly, although each species must have passed through numerous transitional stages, it is probable that the periods, during which each underwent modification, though many and long as measured by years, have been short in comparison with the periods during which each remained in an unchanged condition. [p410f]
It is hard to find a better summary of punctuated equilibrium, especially the bit I have bolded. Certainly, Darwin was changing his emphases over time in response to criticism and suggestions - which any decent thinker ought to do. But in no way did he ever rely on a steady rate of change view.
Confusion of this with the next sense is the mediate source, I think, of the confusions this topic engenders. Darwin did hold that change is continuous. He wrote, immediately after the last passage:
Passing from these difficulties, the other great leading facts in palæontology seem to me simply to follow on the theory of descent with modification through natural selection. We can thus understand how it is that new species come in slowly and successively; how species of different classes do not necessarily change together, or at the same rate, or in the same degree; yet in the long run that all undergo modification to some extent. The extinction of old forms is the almost inevitable consequence of the production of new forms. We can understand why when a species has once disappeared it never reappears. Groups of species increase in numbers slowly, and endure for unequal periods of time; for the process of modification is necessarily slow, and depends on many complex contingencies. [p411f]
I have bolded the relevant bits here - Darwin thinks the process is "slow". There's a real problem with notions like "abrupt" and "slow" when discussing matters that are geological or paleontological (van Loon 1999). The notion of rates is highly contextual - what is slow in geology takes hundreds of millions of years. What is slow in genetics can take a century. What is slow for a student depends on the lecturer. Darwin and many since have been a bit vague about this. But I agree with van Loon's argument that such relational comparatives are useless and worse, confusing. Now, at any rate - Darwin had no way to set up metrics other than what is subjectively salient to systematists and paleontologists. But even so, he gets it right - even if a species appears without precursors in the fossil record, it arose from a process that in human terms is very slow indeed. Geological rapidity is genetic imperceptibility, to the point where one needs special analytic techniques to spot real time evolution even now.
This is effectively the view that Gould had. There is continuous, incremental, change, which results in rapid (geologically speaking) evolutionary change. And change need not be constant or steady. Of course, Darwin's explanation of this change is based on natural selection - it doesn't always operate at the same intensity, while punctuated equilibrium relies fundamentally on neutral evolution and drift and other stochastic effects, but it doesn't deny the efficacy of selection even in speciation. It is my own view that selection operates pretty well universally, although the outcomes of that selection are often not what was selected for - such as reproductive isolation from parental populations. This is usually a side-effect of what was selected for: adaptations for novel environments or slightly different ecological relations.
As to uniformity, Stephen Toulmin once remaked (1970) that the uniformitarian versus catastrophism debate in nineteen century geology began with wide differences of views, but that the uniformities got more "abrupt", while the catastrophes got less so over the course of the century, until all that was disputed was terminology. We think the same causes operate now as in the Cambrian, but the conditions and prior states were different then. We only know how novel features might have affected evolution - say, the origin of hard parts or of vision - because we know how they affect organisms and ecological relations now. That's classic uniformitarianism. Darwin was, in this respect, a uniformitarian. He expected explanations of causal processes in the past to resemble closely the processes of today, and his arguments relied almost solely on modern biology. But this did not mean that he expected things to "look like" today's processes. If eyes evolved for the first time, the results would dramatically differ from the evolution of a new eye in modern times.
So to summarise: Darwin was not a steady stater - a "phyletic gradualist" in any reasonable sense. He was a continuity advocate, and he was a uniformitarian. As to continuity, it seems to me that large scale (another relative contextual term that effectively means nothing) change in one sense - say in developmental sequence - will have incremental intermediates between it and its ancestral form, in some other level or fashion (e.g., genetic, regulatory, or timing increments).
Late note: Larry Moran gives an excellent exposition of the punctuated equilibrium theorists' views on this here. However, I do not think that their interpretation of Darwin is itself theory-free.
Loon, A.J. van. "The Meaning of ‘Abruptness’ in the Geological Past." Earth-Science Reviews 45 (1999): 209–14.
Toulmin, S. "Does the Distinction between Normal and Revolutionary Science Hold Water?" In Criticism and the Growth of Knowledge, edited by I. Lakatos and I. Musgrave. Cambridge UK: Cambridge University Press, 1970.
I think this series is excellent.
One thing with this argument. I agree with your assessment that Darwin did not consider all species to evolve at the same rate (rather clear from the quotes, except the fourth which is about the expansion of generic diversity and not transformation itself). However, this does not preclude phyletic gradualism within lineages. The process could be "steady" within each lineage even if those lineages evolve at differing speeds, like a highway versus a city avenue. Now, whether Darwin also rejected relative constancy of rates within lineages is another question -- it is entirely possible, though I don't think the quotes address it.
Thanks Ryan. Darwin has a number of other comments about variable rates of change for difference genera (i.e., lineages), such as this:
"This gradual increase in the number of the species of a group is strictly conformable with my theory, for the species of the same genus, and the genera of the same family, can increase only slowly and progressively; the process of modification and the production of a number of allied forms necessarily being a slow and gradual process,âone species first giving rise to two or three varieties, these being slowly converted into species, which in their turn produce by equally slow steps other varieties and species, and so on, like the branching of a great tree from a single stem, till the group becomes large." 
This suggests that he thinks the relative rates of speciation are or can be constant in a genus and family. I can't locate the other comments I have seen, so I suspect they're in other books.
You allude to this a bit, but... I've always thought that Darwin's gradualism had more to do with his very oft-repeated assertions that that the variations that selection acted on were "slight." Larger variations would mean that selection is far less causally important.
Your post is great, but...
...none of your definitions of "gradual" are quite the definition Darwin used. Trace the origin of the word "gradual" and then read this from Kevin Padian:
It seems to me that the "gradualism" in "phyletic gradualism" is more about what happens within lineages, and not different speeds of change among lineages, so really I don't think we can say Darwin was not a gradualist in the mostly-slow-and-constant-rate-within-specific-lineages type, at least not based on the quotes we have seen. However, I agree that he was NOT a all-lineages-evolve-at-the-same-rate gradualist (how could he be when he mentioned living fossils?).
Another excellent post, John.
Last month, inspired by an earlier post of yours, I wrote a post entitled 'The Surprise Punctuationist' which also quoted from the fourth edition of Origin:
In it, I described my hunch that Darwin clarified his views in the 4th edition of Origin to make it quite clear that his own theory of evolution by means of Natural Selection was perfectly adequate for explaining the apparently punctuated nature of species formation, without recourse to Oswald Heer's 'monsters'. At the time, Heer's view of new species formation was being presented in the international literature as a rival to CD's theory of slow evolution by natural selection.
It is hard to find a better summary of punctuated equilibrium ...
The quoted passage has very little to do with punctuated equlibria. You are making the same mistake that Daniel Dennett and Richard Dawkins make. You are assuming that the key thing about PE is that evolution takes place in fits and starts. You are also assuming that phyletic gradualism = constant speedism.
The important thing about PE is that evolutionary change is coupled to speciation by cladogenesis. If you don't know much about speciation, I'll be glad to teach you! :-)
In PE, it's not just that morphological change takes place rapidly, it's that it takes place when new species are rapidly forming. In the absence of speciation events (by splitting) a species remains basically unchanged for millions of years.
Phyletic gradualism refers to the idea that one species gradually turns into another by accumulating change. This change may be slow and constant or it may occur in bursts. That's not what is important in phyletic gradualism. What's important is that a species changes bit by bit over time until it no longer resembles its ancestors.
I think it's pretty clear that this is the sort of change Darwin was usually thinking about in Origins. You can comb his book for quotes but you'll never find a prominent thread that ties evolution to speciation events. What you'll find is an emphasis on varieties, subspecies, and races that gradually become new species over a long period of time. In some cases only one of the varieties survives. What you'll find is an emphasis on gradual change within a lineageânot necessarily at a constant speed.
That's not the same as punctuated equilibria.
Gould may not have been right about everything but he was a pretty competent student of the history of biology. When he devotes several pages of The Structure of Evolutionary Theory to refuting what you have just claimed, I think it does him a great disservice not to address the points he raises, even ifâespecially ifâyou disagree.
Well I didn't until just now have the Brick unearthed from the boxes in my room, but I fail to see much that really does more in that section than reassert Gould's interpretation, which I think is simply not supported by the "duelling quotations" of Darwin's own writings. Others may have been anageneticists, holding that speciation occurred when enough change had been accrued, but not, I think, Darwin himself. The very notion of cladogenesis is founded on Darwin's ideas, although the term waited for Rensch in the 1950s. Darwin did hold that most change occurred - in many cases - at the time of speciation, as the bolded text on p410 above showed. If he didn't happen to be an allopatric speciationist, that is no never mind with respect to punctuated equilibrium theory, unless allopatric speciation happens to be the sole reason why the PE pattern would be seen in the fossil record. For my money, that is simply question begging: if speciation occurs as Darwin said, the same pattern would be observed I think. And he gives in that chapter the "speciation outside the bedding plane" argument that G&E gave too.
As it happens, I think that Trémaux in 1866 invented PE theory. He was an allopatrist. And a strict adaptationist, but that's besides the point.
I know you think very highly of Gould as a historian - I am less sanguine. Whenever a biologist starts to do scientific history, they cannot help but use it to make triumphalist or revolutionary points in their own professional favour. He's very well read, but I think not so good at reading.
I should comment on a few other responses too.
Nick: I think that my meanings are in fact based on the senses Darwin himself used, and I'm not so convinced Kevin has it right there.
Roberta: I think that saltation was foremost in Darwin's mind. He had no mechanism by which a saltative change could be adaptive. But the sense of "slight", "insensible" and the like are terms that are highly relative and contextual, and we see him in later editions and in the later books allowing for larger "slight" variations. I don't think he's being inconsistent, but he changes emphasis a lot. Whether Huxley affected him I can't say.
Richard: That's a fantastic piece. I hadn't seen it before. In addition to Heer I add Trémaux, and deprecate the Falconer letter, which is what Gould thought was the origin of Darwin's punctuatedness. So far as I can tell that letter is pretty vacuous.
John, again, I don't think it was so much that he was "worried" about saltation per se, but again, that it undercuts the role of natural selection. Note that they would not need to be adaptive, any more than a slight variation would need to be adaptive. The adaptive ones tend to be retained, the maladaptive tend to get weeded out, and the neutral ones tend to fluctuate.
Yes, in later editions he relaxes his views of slight variation, but that was because of all the criticism he received concerning blending (i.e., why don't all of these slight variations just wash each other out?). He didn't really have an answer, and so was forced to relax his views on slight variations.
Of course, we see the term "slight" as relative and contextual, but again, just do a quick search in the Origin to see just how many times he uses the word. It's a quite a lot. And again, I think this is the sense in which (it's always been the sense in which I've understood) Darwin was a gradualist. It tends to imply that evolution by natural selection will be slow and thus require long periods of time, though as you say it doesn't commit him to saying that the rate of evolution is always the same.
The Great Darwin Myth
Talking of myths.There is a persitent myth that Darwin originated the theory of natural selection. However,both Darwin and Wallace admitted that they were beaten to the idea by Patrick Matthew and Charles Wells. My latest research also shows that none of the ideas(as opposed to examples)given in "On the Origin of Species " are novel to Darwin(search Google for "wainwrightscience" for more details) Best Wishes,Prof.Milton Wainwright,Dept.Molecular Biology and Biotechnology,University of Sheffield,UK.
I just remarked on Sandwalk that some day all instances of "slow and gradual" with reference to evolution will be replaced by "incremental," and I'll be a happy man. :)
I think Darwin was an incrementalist, Incrementalism is the idea that a series of slight, or incremental, changes can produce large and unexpected results. One sees this in operation in Darwin's final book on earthworms.
Padian's definition of "gradual" is based on contemporary definitions in sources from Darwin's time.
Gould certainly interprets history with his own opinions in mind, but he has done a much better job than most other biologists who delve into history of science. He did make the effort to understand sources in the context of when they were written, rather than cherrypicking quotes (e.g., Ernst Mayr).