If evolution really weren’t based on heritable and permanent changes in DNA sequence, that would be surprising, and at least a major change in perspective. The “revolution” proponents argue that this does happen in two ways.
First, there is cultural evolution: stuff is passed on not by genes, but by learning. This, of course, is nothing new: Dawkins wrote about memes—units of cultural inheritance—way back in 1976, drawing a parallel between genetic and cultural evolution. But that was a parallel, and one that I don’t find terribly enlightening. But cultural inheritance is of course important in some species, including all animals that teach their young. The authors give some examples:
In addition, extra-genetic inheritance includes socially transmitted behaviour in animals, such as nut cracking in chimpanzees or the migratory patterns of reef fishes.
So what’s new? Yes, we can model how this works, but learning it itself an evolved ability, and modeling social evolution will involve things beyond the purview of evolutionary theory. Cultural evolution is not genetic evolution, and hence not part of the SET, which rests on changes in genes. Cultural evolution is important, but it’s no more part of SET than is the “evolution” of changes in automobile style over the years.
First let's look at the idea that "modeling social evolution will involve things beyond the purview of evolutionary theory".
Surely modeling DNA evolution involves things beyond the purview of evolutionary theory. It involves modeling aerodynamics, photosynthesis, echolocation, turbulence, biochemistry, structural stability, osmosis - and all manner of other things.
The idea that modeling cultural evolution goes beyond evolutionary theory while modeling DNA evolution does not seems like simply a basic confusion about the explanatory role that evolutionary theory plays.
As for: "Cultural evolution is not genetic evolution, and hence not part of the SET [Standard Evolutionary Theory], which rests on changes in genes" - that goes to the definitions of 'genes' and 'genetics'. If you have 'genetics' as the study of heredity, and 'gene' as the unit of heredity - as I favor - then cultural evolution is indeed genetic evolution, and does indeed involve changes in genes.
This is an argument about terminology. However, even without the terminological debate, defining the domain of evolutionary theory in terms of DNA genes - as Coyne curiously proposes - doesn't make any sense. Ultimately, this idea will be ditched as being based on an outdated classification scheme. Our ancestors weren't based on DNA, or descendants won't be based on DNA, and many modern evolving systems are not based on DNA. A DNA-based classification scheme is simply an impoverished one. It is deeply unscientific to divide evolutionary theory into evolution based on DNA genes and other kinds of evolution.