THE polar bear population could plunge with climate change, according to a study that shows females are giving birth to fewer cubs due to the loss of sea ice.  Researchers at the University of alberta studied how melting sea ice in the 1990s affected breeding of the bears. The females hunt seals on the ice in spring and summer to build up energy for autumn and winter when they give birth.  The study found the early melting of the ice made it more difficult for the bears to hunt seals and build up energy.  In the early 1990s 28 per cent of pregnant polar bears in the Hudson Bay region failed to have even a single cub.  The study, published in Nature Communications, found that if spring comes one month earlier than in the 1990s, 40 to 73 per cent of pregnant female polar bears will not reproduce.  The polar bear population of western Hudson Bay is about 900, down from 1,200 in the previous decade.