Polar bears have been present in the series since the first season, but where did they come from? I believe they were used by Dharma to turn the wheel at the Orchid Station.
In one of the episodes, it is shown that a fossil of a polar bear is found in the desert, right where everyone who turns the wheel and moves the island is teleported. Perhaps Dharma used these animals because they are the only ones smart and strong enough to turn it, and that they would also survive the "teleportation".
Perhaps the cages that Sawyer and Kate are locked in when they are kidnapped were made for the bears. When Sawyer manages to complete the "puzzle" of the cage, one of the others says: "Congratulations, a polar bear did it in 5 minutes", or something like that. Perhaps the puzzles were to train the bears.
Therefore, the bears found in the forest on the island during the series probably escaped from the cages, and the one that was found in the desert moved the island.
Forgive me if there is any English mistake, I'm from Brazil and just want to contribuct with the LostPedia