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As far as I know for evolution to work mutations are necessary. Mutations are the raw material on which natural selection works.
But mutations are always completely random and human beings have no control over it.Then my question is how artificial selection works? Would it have been possible to domesticate dogs from wolves, if there would have been no mutations in wolves to begin with?
Both natural selection and artificial selection require genetic variation in the underlying population to work. The exact source of this genetic variation is not particularly important theoretically. In reality this genetic variation originally comes from mutations of various sorts (not just point mutations, but also duplications, recombinations, etc.). If you had no genetic variation then artificial selection would not be effective.
You might be interested in Stephen Jay Gould's essay "A Dog's Life in Galton's Polyhedron" (found in the collection "Eight Little Piggies"), where he explains that domestic dogs have very little variation in skull length (relative to body size), but large variation in skull width. It seems that it is very difficult to artificially select for dogs whose skull and body don't have the correct ratio, even though you can wildly change the sizes of dogs, the width of their skulls, the length of their legs, etc.
You seem to have a few different concepts in there...
But mutations are always completely random and human beings have no control over it.
Aside from the fact that mutations are not completely random (not always, at least), it is not true that humans have no control over them. Imagine you grow plants, and you start to cross those plants that have a larger stalk, allowing them to be more resistent to wind: you are effectively selecting a certain mutation. Surely, you cannot choose which specific sequence you want to mutate, but still you are enriching your population of plants with a specific mutation. Nowadays of course you can specifically mutate the genome in the lab, but that is a different matter.
Would it have been possible to domesticate dogs from wolves, if there would have been no mutations in wolves to begin with?
Note that artificial selection has been used to generate the different breeds of dogs, by breeding animals with specific characters.
However, domestication is a different matter. Wolves and dogs are the same species (Canis lupus) and domestication is not strictly dependent on selective breeding. You can domesticate an adult animal without inducing mutations in its DNA. Probably epigenetics plays an important role there, and epigenetic patterns could possibly be transmitted to the offspring.
Of course, then you will use selective breeding to expand the domesticated population, and to select those traits you are interersted into. With artificial selection you are just selecting the mutations you want, the way you generate them is irrelevant to the matter: for instance you can irradiate plants to enhance mutation rate, and consequently the appearance of new favorable traits.
Accumulated mutations over generations will make up the genetic variation present in a population for a species. For example, wolves naturally had a certain amount of genetic variation, or diversity, before humans started domesticating wolves. They still do, but to a lesser extend now since their populations have decreased.
Artificial selection is different from natural selection in that is forced artificially by us, humans, upon a species, like wolves, to change the traits to our liking. The first few traits that were artificially selected from wolves were probably related to their behavior: being more submissive and less erratic in their behavior. Then different people started crossing different breeds with interesting traits to try and combine the desired traits into new breeds.
One of the consequences of such dramatic breeding efforts is a decrease in haplotype diversity in dog breeds and higher incidence of undesired diseases. That is, during the crossing of breeds, part of the natural variability in the original populations was lost, and the resulting breeds only had one identical haplotype (in both copies) for many areas of the genome where there used to be two distinct ones, and if that haplotype was bearing an allele for a recessive disease, it showed up in homozygosis. This is the reason why for many important species of plants and animals, there are efforts to try and keep the original wild populations alive, in case we need to draw from the genetic diversity when the domesticated breeds need more.
