This assumes high genetic heredity of fertility decisions. Binary fertility does seem largely like it has a strong genetic component, but once it's there, the decision to have two children versus six children seems to be influence overwhelmingly by non-genetic factors. Once industrialization took root, fertility fell quite heavily. Since there would be rather strong selective pressures favoring "have more kids when resources are available," this suggests that such an impulse, if genetic, is very easily outweighed by other factors.

If it's memetic rather than genetic, the argument requires extraordinary stability, for which I see little evidence.