HELENA, Mont. — The battle to save the so-called gray ghosts — the only herd of caribou in the lower 48 states — has been lost.

A recent aerial survey shows that this international herd of southern mountain caribou, which spends part of its year in the Selkirk Mountains of northern Idaho and Washington near the Canadian border, has dwindled to just three animals and should be considered “functionally extinct,” experts say.

The Selkirk herd had been disappearing for the last several years.

In 2009, the herd, the southernmost in North America, had about 50 animals and was declining. Wildlife officials in Canada began a last-ditch effort to protect them by killing wolves, which occasionally preyed on the few caribou that remained.

But the root cause of the extirpation of this herd and the decline of others in Canada is extensive industrial development in British Columbia, experts say.