Herepton claims to be quoting from Milton "Shattering Myths of Darwinism". I have not attempted to verify the quotes, nor have I attempted to verify Milton's quotes from Mayr.
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"Darwin was well aware of one central fact that dominated all animal and plant breeding experiments - then and now. No one has ever bred a new species artificially - and both plant and animal breeders have been trying for hundreds of years, as have scientists."
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"Mayr: 'any drastic improvement under selection must seriously deplete the store of genetic variability....The most frequent correlated response of one-sided selection is a drop in general fitness. This plagues virtually every breeding experiment.' Mayr,
Animal Species and Evolution (1963)
"This limit to the amount of genetic variability available in a species, Mayr termed "genetic homeostasis." IT IS THE NATURAL BARRIER encountered not only by geneticists attempting to breed fruit flies, and the French botanists attempting to increase the sugar PAGE 136:
content of the beetroot, but by all plant and animal breeders throughout the ages.
I expect that what is stated in the quoted text is mostly correct. The question is on whether this provides a basis to question ToE.
Most of the quoted text deals with artificial selection, rather than with natural selection. With artificial selection, what is mainly being tested are the limits of selection alone. If a selection is being made from within a range of variation already present, then it seems obvious enough that what can be achieved is limited by the variation that is present. The only way to go beyond those limits, is for more variation to be introduced.
The quoted text also comments on "drastic improvement". You will mainly get drastic change when selection pressures are high. Again, you will see a reduction of variation.
In the real environment, evolutionary changes are mostly slow. There is plenty of time for new variation to arise from mutations, at the same time that selection pressures might be removing some variants. Thus the population can change, while retaining a significant amount of variation.
My own suspicion is that during times of equilibrium (relatively little change in morphology), there is nevertheless continual genetic change. Roughly speaking, a period of apparent equilibrium could be a period where variation is built up in the population. The occasional drastic change from selection will tend to reduce variation, but the variation will be replaced during a future period of equilibrium.
As a consequence, the barriers are temporary. As additional variation is incorporated into the genome, the barriers are pushed back.
In short, I don't see that the barriers mentioned constitute a problem for evolution.