Given that the OP did not provide any range parameters to his query, it really opened up the the responses to subjective interpretation of the question.
So, given that some respondents have shorter range limitations on the hunting that they do, some of the less powerful rounds being put forth can be just as effective as those of higher velocity and energy.
For example, the 375 Win loaded with 200 gr bullets at 2200 fps with 2150 ft-lbs of energy, will still be doing over 1800 fps and carrying almost right on 1500 ft-lbs of energy at 100 yards. So given these numbers and an experienced hunter/shooter who knows the limitations of his firearm, and the quarry faced at the given moment, this may be effective on the animals listed, at reasonable ranges for this weapon. I know how effective it has been on numerous bears,wolf, moose and caribou over the 24 years I have been using mine.
Admittedly, not my first choice for bison or grizzly bear, but if I didn't have another rifle in my hands at the time, and had the right opportunity present itself, I think I would find myself in a situation similar to what Bell must have found himself in with an elephant and a 6.5x55! LOL (Keeping in mind of course, the distances that Bell was using the 6.5 and 7x57 on elephants...)