There was a time when spotted leopards could really stretch out. They roamed 13.5 million square miles of habitat in Africa, the Middle East and Asia, which were full of prey that provided plenty of food.

But a study announced Wednesday by National Geographic says that has changed dramatically. The big cat’s territory in those areas has shrunk 75 percent, to just 3.3 million square miles, and stands to shrink even more because of booming human populations, along with farming and other development to feed and house them.

The finding of a greatly diminished habitat is giving rise to the fear that the iconic cats, so stealthy that they are nearly invisible in the animal kingdom, are vanishing for real. Until now, the prevailing wisdom has been that leopard populations were doing fine and aren’t considered candidates for protection as threatened or endangered.

The lack of visibility was attributed to the leopard’s famous stealth. Unlike other big cats, researchers rarely try to estimate spotted leopard populations because they can’t find enough for a reliable count. But Andrew Jacobson went in a different direction to assess whether the animals were under threat for a study published Monday in the journal Peer J.

Jacobson and his co-authors focused on where the animals roam. The researchers reviewed more than a thousand historic documents to determine the historic and current range. In its announcement, National Geographic called the study “the first known attempt to produce a comprehensive analysis of leopards’ status across their entire range and all nine subspecies.”

The outlook for a cat with such a huge loss of territory isn’t good. It affects the amount of prey that the cats can select and forces them to roam in unprotected areas where they can be hunted for trophies or poached for their desirable coats. Without a healthy portion of food, cubs can’t survive to adulthood.

“If the leopard becomes hemmed in by development, young males try to disperse when they reach adulthood,” Jacobson said. Not only are they vulnerable to being shot, but they sometimes wander into foreign habitats and die, he said, because they’re unaccustomed to the terrain.

Leopards have recently been observed in major cities, such as Mumbai, creeping in alleys and such, “and the media plays those appearances up,” Jacobson said. Those stories create a “misconception that these big cats continue to thrive in the wild — when actually our study underlies the fact that they are increasingly threatened,” said Luke Dollar, co-author and program director of the National Geographic Society’s Big Cats Initiative.

The cats “are capable of surviving in human-dominated landscapes provided they have sufficient cover, access to wild prey and tolerance from local people,” the National Geographic announcement said. “In many areas, however, habitat is converted to farmland and native herbivores are replaced with livestock for growing human populations.”

The study was produced with the help of the National Geographic Society’s Big Cats Initiative, the Zoological Society of London, Panthera and the International Union for Conservation of Nature.

“A severe blind spot has existed in the conservation of the leopard,” said Philipp Henschel, co-author and Lion Program survey coordinator for Panthera. “In just the last 12 months, Panthera has discovered the status of the leopard in Southeast Asia is as perilous as the highly endangered tiger.”

Jacobson said the leopard’s stealth might have resulted in a lack of understanding “for how threatened it is,” because invisibility is their stock and trade. “No one had done this work before, so we didn’t have a good idea.”