Yes, but over a very long time. I was surprised to learn that the Burro Deer (o.h. eremicus !) was actually living in the same areas as it does today and was being eaten by the local natives long before the Desert Bighorn ever showed up down there. 100,000 yrs. ago ? Nobody seems to be sure.
They, the Burro Deer, get every bit as big as the big Rocky Mtn Mule Deer. But their markings are quite different. Way different. Much smaller, dingy white rump patch. Brown, not black, skull cap. Brownish grey, not grey winter coat, but very similar red summer coat. Sometimes the antlers are a pale yellow in color.
I know of no DNA comparisons of them and the RM variety.
I can assure you their diets are much different. I seriously doubt you could transplant either into the other's habitat. E
