“If the genetic mix of brown bear & polar bear produces fertile offspring, doesn’t that mean they belong to the same species?”
Not necessarily. Species can also be defined by geographic distribution, if there is/was some sort of geographic reason (i.e. physical barrier) that prevented different populations from interbreeding. If this was the reason that polar bears and other bears separated into distinct breeding populations, and the barrier is removed, there is no reason the hybrids cannot be fertile (if it happens that they actually are fertile).
Think about coyotes and wolves. Both are defined as separate species, but able to interbreed with fertile offspring. It doesn’t mean that the resultant hybrids will result in a merging of the species; but that the occurrence of hybrids will mostly be where the populations bump up against each other. In most cases, such hybrids don’t have any special advantage over either species (and might actually have a disadvantage in breeding) and thus never become a significant percentage of the breeding population of either species. The only time the populations would merge would be when the hybrids have a distinct survival advantage, with hybrids rapidly becoming dominate in both populations. Most generally, the populations will stay separated, unless other factors intervene making one population more viable, replacing the less viable population, with the inclusion of some percentage of hybrid breeding hybrid stock.
Explains those dog breeds that are advertised as half-wolf but said to be as hazardous as a full blooded wolf.
Interesting discussion on this thread. Thanks!