The researchers were startled to find bears having to swim up to 60 miles across open sea to find food. They are being forced into the long voyages because the ice floes from which they feed are melting, becoming smaller and drifting farther apart.

Although polar bears are strong swimmers, they are adapted for swimming close to the shore. Their sea journeys leave them them vulnerable to exhaustion, hypothermia or being swamped by waves.

According to the new research, four bear carcases were found floating in one month in a single patch of sea off the north coast of Alaska, where average summer temperatures have increased by 2-3C degrees since 1950s.

The scientists believe such drownings are becoming widespread across the Arctic, an inevitable consequence of the doubling in the past 20 years of the proportion of polar bears having to swim in open seas.

“Mortalities due to offshore swimming may be a relatively important and unaccounted source of natural mortality given the energetic demands placed on individual bears engaged in long-distance swimming,” says the research led by Dr Charles Monnett, marine ecologist at the American government’s Minerals Management Service. “Drowning-related deaths of polar bears may increase in the future if the observed trend of regression of pack ice continues.”

The research, presented to a conference on marine mammals in San Diego, California, last week, comes amid evidence of a decline in numbers of the 22,000 polar bears that live in about 20 sites across the Arctic circle.

In Hudson Bay, Canada, the site of the most southerly polar bears, a study by the US Geological Survey (USGS) and the Canadian Wildlife Service to be published next year will show the population fell 22% from 1,194 in 1987 to 935 last year.

New evidence from field researchers working for the World Wildlife Fund in Yakutia, on the northeast coast of Russia, has also shown the region’s first evidence of cannibalism among bears competing for food supplies.

Polar bears live on ice all year round and use it as a platform from which to hunt food and rear their young. They hunt near the edge, where the ice is thinnest, catching seals when they make holes in the ice to breath. They typically eat one seal every four or five days and a single bear can consume 100lb of blubber at one sitting.

As the ice pack retreats north in the summer between June and October, the bears must travel between ice floes to continue hunting in areas such as the shallow water of the continental shelf off the Alaskan coast — one of the most food-rich areas in the Arctic.

However, last summer the ice cap receded about 200 miles further north than the average of two decades ago, forcing the bears to undertake far longer voyages between floes.

“We know short swims up to 15 miles are no problem, and we know that one or two may have swum up to 100 miles. But that is the extent of their ability, and if they are trying to make such a long swim and they encounter rough seas they could get into trouble,” said Steven Amstrup, a research wildlife biologist with the USGS.

The new study, carried out in part of the Beaufort Sea, shows that between 1986 and 2005 just 4% of the bears spotted off the north coast of Alaska were swimming in open waters. Not a single drowning had been documented in the area.

However, last September, when the ice cap had retreated a record 160 miles north of Alaska, 51 bears were spotted, of which 20% were seen in the open sea, swimming as far as 60 miles off shore.

The researchers returned to the vicinity a few days later after a fierce storm and found four dead bears floating in the water. “We estimate that of the order of 40 bears may have been swimming and that many of those probably drowned as a result of rough seas caused by high winds,” said the report.

In their search for food, polar bears are also having to roam further south, rummaging in the dustbins of Canadian homes. Sir Ranulph Fiennes, the explorer who has been to the North Pole seven times, said he had noticed a deterioration in the bears’ ice habitat since his first expedition in 1975.

“Each year there was more water than the time before,” he said. “We used amphibious sledges for the first time in 1986.”

His last expedition was in 2002, when he fell through the ice and lost some of his fingers to frostbite.