“The results predict five times more warming than we’ve seen in the last 15, 20 years,” Bruno told me. In some areas, up to 10 times more warming is forecast.

“Given the effects we’ve already seen of 0.7 [degrees Celsius] of warming—corals being wiped out, species dying, seabirds being affected—it’s staggering to imagine what will happen in the places that will see 10 times that much warming. It’s frightening,” he said.

Bruno and his colleagues find that most tropical MPAs will exceed their “community thermal-safety margin”—a scientific term for the amount of heat that makes an entire ecosystem unsustainable—just three decades from now. MPAs in more temperate areas will not exceed that margin, on average, until 2150.

The study examined a specific climate scenario called RCP 8.5, which assumes humanity will continue to emit more and more heat-trapping carbon pollution through the end of the century. It’s unclear if that projection will come to pass—and, of course, it all depends on how the world’s richest governments (and their citizens) act. Global carbon emissions rose in 2017, an ominous sign, after remaining flat for several years.

Andrew King, a climate researcher at the University of Melbourne who was not involved in the study, said the MPA study was “interesting and very important”: “It adds to the evidence that it is difficult to protect marine species in particular” from the ravages of climate change, he told me in an email. “Compared to land-based ecosystems, [marine species] have evolved to adapt to a narrower range of temperatures, so any warming becomes a problem more quickly.”

The new paper also raises two problems for conservationists—one new and one old. First, the team’s models suggest that the parts of the oceans that don’t warm will suffer the worst of another environmental problem. Scientists predict that vast swaths of the ocean will lose their oxygen content as the century wears on, creating denuded “dead zones.” Bruno and his colleagues modeled this effect—and they found many of the areas that are most vulnerable to deoxygenation are the same ones where warming is least likely.

“It’s almost an impossible trade-off,” said Bruno. “The global pattern for deoxygenation is almost the opposite of the warming pattern. You can put [an MPA] in a place that won’t warm, but then there’s going to be less oxygen there, which is at least as big a problem as climate change.”

The second problem is a human problem, not a natural one. It’s also more familiar to conservationists. For the last two decades, scientists have aimed to protect parts of the ocean that will resist global warming—to find so-called refugia from warming. “There’s a huge effort to figure out where warming isn’t happening as fast and to move MPAs there, or put new MPAs there,” Bruno said. “We’re clearly not doing that.”