In 2012, the federal government, fearing that extreme weather or an infectious disease could wipe out the species, came up with a backup plan to designate private land in Louisiana as “critical habitat” for the frogs’ survival. The frogs do not live there now, and the designation could limit the ability of the owners to develop the land, by one account potentially costing them about $33 million.

The landowners sued, and they lost in the lower courts. A divided three-judge panel of the United States Court of Appeals for the Fifth Circuit, in New Orleans, said the government’s designation was entitled to judicial deference.

The Endangered Species Act requires the Fish and Wildlife Service to identify species in peril and to designate their “critical habitat,” meaning places they live now or places “essential for their conservation.” The service designated the land in Louisiana as the second sort of place.

It found that the land included the ponds crucial to the frogs’ survival. But it acknowledged that the frogs needed more, including an open forest canopy, while the Louisiana land had a closed canopy. The service said it would not take an unreasonable effort to thin the canopy.

Chief Justice Roberts said the case turned on the meaning “critical habitat.”

“According to the ordinary understanding of how adjectives work, ‘critical habitat’ must also be ‘habitat,’ ” he wrote. “Adjectives modify nouns — they pick out a subset of a category that possesses a certain quality. It follows that ‘critical habitat’ is the subset of ‘habitat’ that is ‘critical’ to the conservation of an endangered species.”