Same-ish problem here in Norway. The arctic fox is nearly extinct whereas the common red fox is thriving like never before. There are only an estimated 110 individuals left in the whole of the Fenno-Scandinavia :-(.
It's a difficult matter tbh. Should you really be shooting red foxes to favour the arctic ones? One could argue that the dominance of the red fox is just nature taking it's course but on the other hand nature's been so beat up and influenced by mankind that you might as well argue that it's our doing.
-edit-
I care :-D.