As glaciers melted and the seas rose after the most recent ice age, the last surviving woolly mammoths were crowded onto small, isolated northern islands, where they stayed for millennia before joining their mainland cousins in oblivion.

Now there is evidence that water problems — the lack of clean fresh water — is what finally killed off the remnant population of woolly mammoths that took refuge on a Bering Sea island off Western Alaska.

A new study published in the Proceedings of the National Academy of Sciences uses chemical analysis of sediment below a lake on St. Paul Island to reconstruct conditions that appear to have killed off some of the world's last woolly mammoths.

The animals survived on St. Paul until about 5,600 years ago, about 5,000 years after most of the world's mammoth populations disappeared from the grasslands of North America and Eurasia. But even on the isolated Bering Sea refuge, conditions for woolly mammoths were deteriorating. As seawater levels rose and shrank the island's size, the climate became warmer and drier. The island's freshwater resources shriveled and the remnant woolly mammoths suffered, the study found.

"Freshwater resources look like the smoking gun for what pushed them into this untenable situation," study co-author Matthew Wooller, director of the Alaska Stable Isotope Facility at the University of Alaska Fairbanks, said in a statement released by UAF.

The study, the work of a large international team, uses analysis of a sediment core taken in March 2013 from the bed of Lake Hill, one of St. Paul's few lakes. The analysis of magnetic qualities, oxygen isotopes and assemblages of the remains of tiny aquatic creatures that lived there showed how freshwater became scarce between 7,850 and 5,600 years ago. It also uses isotope analysis of mammoth bones and teeth that showed the animals were showing stress from progressively drier conditions.

Dehydration and heat stress likely finished off the island's mammoths, which could not move to better territory, said Russ Graham, a Penn State University paleontologist and the study's lead author. Modern elephants can consume more than 50 gallons a day, and mammoths also needed lots of water to cool their huge bodies, Graham said in an email. "This would have been particularly hard for woolly mammoths because they have evolved adaptations like specific hair types to keep them warm in the cold climates. This would have been a maladaptation for warmer climates," he said.

As lakes became shallower, the water in them became cloudier and dirtier — the types of water conditions that modern elephants dislike and avoid, the paper notes. Evaporation caused minerals to be more concentrated in the water that remained, Wooller said.

"In essence the lake water was becoming more saline — although not as a result of mixing with ocean water but rather as a result of concentrating of minerals in the lake as lake levels dropped," he said in an email.

The mammoths probably contributed to their own demise, the study says, by digging into the earth — in the manner of modern elephants that dig lakeside mini-wells — and stripping away plant cover edging the lakes and speeding up the erosion that was diminishing water quality.

The extinction of St. Paul's remnant woolly mammoth has long been a puzzle.

What ultimately killed them was probably not hunting, the authors of the new paper have concluded. There is no evidence than humans used St. Paul Island before the arrival of Russians in the late 18th century,

Predation from polar bears was not to blame either, as the oldest polar bear remains found on the island are at least 1,000 years more recent than the most recent mammoth remains, the study points out.

Increasing snowpack has been posed as a possible extinction driver, but that theory is "inconsistent" with the isotope analysis of the lakebed sediments. Volcanic eruptions are also ruled out. And it is unlikely that extinction came from shifts in the types of plants growing on the island because the vegetation types were stable during the Holocene epoch — the recent past by geologic measure — though analysis of pollen suggests that tundra productivity might have been declining, the study said.

By evidence and deduction, that leaves the scarcity of freshwater as the most likely culprit.

The St. Paul mammoths' fate sends some important messages about modern climate change, the authors said.

Island populations are especially vulnerable to environmental changes, even small ones, and the study "underscores the need to pay particular attention to islands in an environmentally changing world," Graham said.

Freshwater supplies on islands are also very vulnerable, he said. People living on some South Pacific islands are already facing some freshwater shortages. As the sea rises, the wedge of saltwater has been pressing up against the freshwater in the water table, restricting it, he said.

St. Paul was not the only island where woolly mammoths found refuge after most of their kind had been wiped out.

The world's last known surviving woolly mammoths lived on Russia's Wrangel Island, now a nature reserve. Mammoths lived there until about 3,700 years ago, according to paleontological evidence.