My chihuahua was rescued on the streets of San Francisco after an unknown period of time fending for himself. He was a little underweight but not dramatically so. No signs of previous ownership (no chip, no collar, not neutered) so he was possibly just dumped somewhere at a young age (they estimated he was 1-1.5 yrs when found).

He fiercely guards food and will snap at anyone that reaches for him. He hunts insects including flies and cockroaches (he caught at least a few of those on our walks).

I don’t think he’d be as effective as a rat terrier, but I suspect he could hunt and kill field mice and maybe small rats.

German shepherds are interstingly often very inbred. From talking to my girlfriend (this is her field), it sounds like it's unlikely that any purebred dogs would be able to adapt well to an actual wilderness