I have never understood Punctuated Equilibrium in the manner that Dawkins, in his chapter, spends considerable time refuting. Evolution is gradualist, as Dawkins says, in the sense that there is no such thing as half an animal. A "transitional fossil" can be a confusing concept, giving one the idea that certain animals are "transitional" as opposed to being "normal" (when in fact every living thing is "transitional"). This misunderstanding is exploited by creationists in their tiresome demand for "transitional" fossils.
P.E. is, essentially, a reinterpretation of the fossil record which turns out not to be as radical or revolutionary as Gould portrayed it to be. Dawkins likens the difference between previous interpretations and the Gould-Eldredge proposal as the difference between walking up a hillside and ascending a staircase. There are no "gaps" in the fossil record, only steps.
Dawkins explores Gould and Eldredge's equation: P.E. + Wright's Rule = Species Selection
Wright's Rule: "The proposition that a set of morphologies produced by speciation events is essentially random with respect to the direction of evolutionary trends within a clade." In other words, in an apparent analogy with mutational randomness, if a species of horse shows marked progression toward larger body size, a new species of horse would not necessarily follow this trend, if Wright's Rule is preserved. As many new species would be smaller than the clade as larger. Therefore, Wright's Rule must be tested.
However, Dawkins points out (quoting Gould): "'If Wright's Rule be valid, and new species of horses arise equally often at sizes smaller and larger than their ancestors, then the trend is powered by species selection. But if new species arise preferentially at sizes larger than their ancestors, then we don't require species selection at all, since random extinction would still yield the trend.' Gould here simultaneously sticks his neck out and hands Occam's Razor to his opponents!" Dawkins adds that he can imagine some major speciational trends of the type described by Cope's Rule,* but points out that this is quite different that the original question, that of individual sacrifice behavior or adaptations "for the good of the species." The difference is between the concept of the group as replicator versus the group as a vehicle for replicators.
Palaeontological major trends, such as the length of horses' legs, are simple, requiring only a few replicator replacements, whether we mean genes or species at this point. However, many more replicator replacements are required for the evolution of a complex adaptation such as those that allowed a land mammal to evolve into whales, for example. Even if such a complex phenomenon could be broken down into smaller evolutionary events, the adaptation involves an interrelated web of changes that group-selectionism just could not produce them without yielding, over and over again, a highly unlikely barrage of parallel beneficial trends. (Indeed, this mistaken idea of group-selectionism could be what some creationists imagine evolution to be, leading them to dismiss evolution as improbable.)
The theory of species selection, growing out of that of punctuated equilibria, is a stimulating idea which may well explain some single dimensions of quantitative change in macroevolution. I would be very surprised if it could be used to explain the sort of complex multidimensional adaptation that I find interesting, the 'Paley watch," or 'Organs of extreme Perfection and Complication' kind of adaptation that seems to demand a shaping agent at least as powerful as a deity. Replicator selection, where the replicators are alternative allels, may well be powerful enough. If the replicators are alternative species, however, I doubt if it is powerful enough, because it is too slow. Eldredge and Cracraft (1980, p. 269) appear to agree.
Part 3: Memes