The observed fossil transitions that inform our knowledge of Polar Bear speciation are very well documented. Bear fossils change through time: generally, when examining the fossil record, successively deeper levels of sediments or sedimentary rocks yield successively older fossils. For some transitions from one species to another, one can find a well-characterized series of transitional specimens leading the observer across the species "boundaries" (Kurten, 1976).
Sometime during the mid-Pleistocene period (roughly 100,000 to 250,000 years ago), a number of brown(same as grizzly) bears (Ursos arctos) probably became isolated by glaciers. Many probably perished on the ice; however, they apparently did not all disappear. Some survived due to the fact that "organisms vary" (Gould, 1977); that is, every litter of grizzlies has a variation in coat thickness, coat color, etc., which imparted a slight evolutionary advantage to some individuals of each litter. Successive, successful individuals repeated this simple process, yielding a rapid series of evolutionary changes (driven, presumably, by the combination of small population, and extreme selection pressure) in order to survive. Note that these new variants were not necessarily "better" in any absolute sense, or on any absolute "bear" scale of perfection: they were simply more in keeping with their new environment than their immediate ancestors or their more unfortunate siblings. Today, polar bears are adapted to their harsh northern environment.
Hecht (in Chaline, 1983) describes polar bear evolution: the first "polar bear", Ursus maritimus tyrannus, was essentially a brown bear subspecies, with brown bear dimensions and brown bear teeth. Over the next 20,000 years, body size reduced and the skull elongated. As late as 10,000 years ago, polar bears still had a high frequency of brown-bear-type molars. Only recently have they developed polar-bear-type teeth.
Kurten (1976) describes bear