Polar bears have long been the poster children for global warming. The worry was that, as the Arctic got hotter, the floating sea ice used by polar bears to hunt and mate would vanish — and, eventually, so would the bears.

So how are polar bears doing these days? It depends where you look. Some regions have seen big losses in recent decades. In the South Beaufort Sea above Alaska, bear populations have fallen 40 percent between 2001 and 2010. But in a few other areas, like the Chukchi Sea, the polar bears have remained surprisingly resilient — at least for now:

The map above comes from a new report on polar bears by Dag Vongraven and Geoff York for the National Oceanic and Atmospheric Administration's Arctic Report Card 2014. It shows the changes for 19 different polar bear populations in 2013 — some declined, some stabilized, and one population actually increased. (In many regions, there simply wasn't enough data.)

But that's just a single year. The report also took stock of the broader picture over time. Some findings:

1) The Arctic keeps getting hotter and sea ice keeps vanishing. In 2014, the extent of Arctic sea ice during the summer was 23 percent below the average between 1981 and 2010. This is part of a clear long-term decline:

2) Vanishing sea ice is a problem for polar bears. The bears spend some time on land but mostly live on the ocean — using floating sea ice as a platform to hunt, mate, and raise their young. There are about 25,000 polar bears left in the world, and if sea ice keeps vanishing, they're expected to struggle — having to swim longer and further to find food.

In the western Hudson Bay, polar bears have seen a 32% decline since 1987

3) Some populations have seen large losses over time. Scientists have only been tracking a handful of Arctic bear populations consistently across several decades — but what data they have is disconcerting.

The polar bear population in the western Hudson Bay has shrunk from 1,194 in 1987 to 806 in 2011 — a 32 percent decline. In that region, the scientists note, male polar bears are largely unaffected by sea-ice conditions (they're more likely to be killed by humans). But the health of females very much depends on the availability of sea ice. When that ice dwindles, so does the population.

Likewise, in the Southern Beaufort Sea, north of Alaska, the polar bear population has declined 40 percent between 2001 and 2010 — and has stabilized at around 900 bears (for now). Not coincidentally, this region has seen a large increase in ice-free summer days over time.

4) But some populations are hanging on. Sea ice hasn't retreated equally in all parts of the Arctic, however, and some populations are still doing relatively better. In the McClintock channel in Canada, for instance, populations actually increased in 2013.

One noteworthy area is the Chukchi Sea, where polar bear populations appear to have remained stable between 1986 and 2011 (though there are sizable gaps in this dataset). The Chukchi is right next to the Southern Beaufort, which has seen large losses over that period. So what's the difference?

The scientists note that the continental shelf — that is, the land extending away from the shore under the water surface — is wider in the Chukchi Sea. That shelf helps support seal populations, a favorite food of polar bears, and has helped them better survive the ice decline. The Chukchi has also seen fewer ice-free days.

5) Hybrid bears are starting to appear. In Nautilus, Tim McDonnell has a fascinating piece about polar bears mating with grizzlies as the polar bears' habitat shrinks and they spend more time on land. The NOAA report adds to this, noting that over the last million years, polar bears have occasionally interbreeded with brown bears during past periods of ice decline.

The authors add that their observations are so far consistent with the idea that polar bears are heavily dependent on sea ice and that global warming will have a negative impact on their populations — although there's likely to be a lot of regional variation. And if the planet keeps warming up significantly, scientists tend to think that polar bears won't be able to adapt and survive.

From the summer: 35,000 walruses are swarming Alaska's shore — because their sea ice is vanishing