This drastic culling serves its purpose in livestock, but it is impractical and unacceptable in companion animals such as dogs. Nature goes to great lengths to discourage inbreeding. Related animals rarely mate, which prevents genes for diseases and defects from coming together with any great frequency. Wild animals have a variety of behaviors which will eliminate or severely restrict inbreeding. In wolves, the species most closely related to dogs, only the alpha pair will breed.
Pups stay with the pack for their first year.
After that time they must find a place, often low-ranking, within the adult hierarchy. If a yearling cannot accept this or it becomes the brunt of too much negative social interaction, it will disperse. Dispersers may have to travel many miles before they can find an available territory and a mate, if they can find them at all. Those individuals which do not disperse will not be breeders unless they should someday attain alpha status, so the breeding of relatives is unlikely. Sometimes circumstances give animals no choice but to mate with relatives.