Domestic dogs are even more plastic because they don't have to feed themselves and have medical care. When the welfare system abandons them, most will die or fail to breed. The ones with the fewest handicapping traits will have the most offspring.
I mean that mutations are only going to occur at a certain rate, even with animals that have a high tolerance for them. So that led me to think that maybe breeding relies mostly on some other means of altering the genotype in order to result in changes that take place on a timescale that's a little shorter than geological.