Number of? Not what I was saying. But the Variablilty present in the original dogs has been bred down to specific traits.
Breeding for a ‘pure’ trait will remove the variability that was initially present. AND, in any case, it is still a dog.
You said "The genes for all the secialized forsm are present in the original." What did you mean by that, if not that the original had more genes than the specialized forms do? Where was the "variability that was initially present" stored, if not in the genes?