Professor van Oppen is collaborating with Dr. Gates, who heads the Hawaii Institute of Marine Biology on a small island in Kaneohe Bay, off Oahu. Their joint project is partially funded by the family foundation of Mr. Allen, the billionaire philanthropist.

On a recent day at the lab, a manager, Jen Davidson, meticulously examined coral colonies growing in indoor tanks under artificial lights.

Starting with hardy coral polyps that survived past environmental assaults in Kaneohe Bay, the Gates lab is trying to make them even hardier, crossbreeding the corals and testing offspring in water treated to mimic the hotter, more acidic conditions likely to prevail in a future ocean.

Under normal conditions the animals grow and build their reefs only slowly, one of the factors that is stymying the effort to save them. “We can do all this work here, but can we scale it up enough to make an impact?” Ms. Davidson asked.

Researchers in Florida may be closest to answering that question. At the Mote laboratory in Sarasota, a researcher named David Vaughan has perfected a technique in which coral samples are broken into tiny fragments; the polyps grow much faster than normal as they attempt to re-establish a colony.

“It used to take us six years to produce 600 corals,” Dr. Vaughan said in an interview. “Now we can produce 600 corals in an afternoon, and be ready in a few months to plant them.”

Florida’s reefs have been badly damaged over the years, not just by climate change but by more direct human assaults, like overfishing that disturbs the ecological balance. Yet the Mote lab and other centers have already replanted thousands of small coral colonies.