The groups never go extinct. But group selection happens when groups are selected against. The math used to argue against group selection assumes from the outset that group selection does not occur. (This is also true of Maynard Smith’s famous haystack model.)
That argument is invalid. Adaptations arise as a result of differential reproductive success. Some haystacks do indeed do better than others in contributing to future haystacks—since they contain more individuals which contribute to the big pool of individuals, from which the next generation of haystacks is produced. So: Maynard Smith’s model is just fine in this respect.
The Harpending and Rogers model from 1987 that you critique works in the same way.
Selection does not require different rates of extinction if there are different levels of reproductive sucecss.
You’re assuming that the benefits of an adaptation can only be linear in the fraction of group members with that adaptation. If the benefits are nonlinear, then they can’t be modeled by individual selection, or by kin selection, or by the Haystack model, or by the Harpending & Rogers model, in all of which the total group benefit is a linear sum of the individual benefits.
For instance, the benefits of the Greek phalanx are tremendous if 100% of Greek soldiers will hold the line, but negligible if only 99% of them do. We can guess—though I don’t know if it’s been verified—that slime mold aggregative reproduction can be maintained against invasion only because a slime mold aggregation in which 100% of the single-cell organisms play “fairly” in deciding which of them get to produce germ cells survives, while a slime mold aggregation in which just one cell’s genome insisted on becoming the germ cell would die off in 2 generations. I think individual selection would predict the population would be taken over by that anti-social behavior.
That argument is invalid. Adaptations arise as a result of differential reproductive success. Some haystacks do indeed do better than others in contributing to future haystacks—since they contain more individuals which contribute to the big pool of individuals, from which the next generation of haystacks is produced. So: Maynard Smith’s model is just fine in this respect.
The Harpending and Rogers model from 1987 that you critique works in the same way.
Selection does not require different rates of extinction if there are different levels of reproductive sucecss.
You’re assuming that the benefits of an adaptation can only be linear in the fraction of group members with that adaptation. If the benefits are nonlinear, then they can’t be modeled by individual selection, or by kin selection, or by the Haystack model, or by the Harpending & Rogers model, in all of which the total group benefit is a linear sum of the individual benefits.
For instance, the benefits of the Greek phalanx are tremendous if 100% of Greek soldiers will hold the line, but negligible if only 99% of them do. We can guess—though I don’t know if it’s been verified—that slime mold aggregative reproduction can be maintained against invasion only because a slime mold aggregation in which 100% of the single-cell organisms play “fairly” in deciding which of them get to produce germ cells survives, while a slime mold aggregation in which just one cell’s genome insisted on becoming the germ cell would die off in 2 generations. I think individual selection would predict the population would be taken over by that anti-social behavior.