I'm not sure any ungulates rate being on a Big Whatever list, if one looks at the African model there is only the buffalo (and he rates inclusion because he can and will kill the hunters who make less than optimum shots) in their Big Five even though they have some of the most impressive ungulates on the planet, Lord Derby Eland as example or Giant Sable both of these could well have replaced the leopard. While big and beautiful and extremely difficult to obtain they are none-the-less not part of the big Five because they pose no danger to man........And I know, a good case could be made that leopard doesn't really either, nor does the cape buff if left alone without some sport putting holes in his hide. However in the days of old both these critters did do in a fair number of sports and so earned their inclusion in the Big Five of Africa.
Now if this is to be carried across the pond to NA then it only follows that our most dangerous animals are the only ones who qualify..........Polar bear, Grizzly, Bison, Wolf and cougar are really the only animals we have that could be considered a threat or at least were at one time. Not sure about the cougar, which through out history has probably only accounted for 1 or 2 kids, and I would have a lot of difficulty including it in a list of NA Dangerous big five. The wolf in days of old did a fair bit of preying on man and still occasionally gets credit for the odd kill. So he has, shall we say, earned his place as a people killer and therefore somewhat dangerous game. I would be open to a different animal than the cougar, but not moose or sheep (like I said before sheep already have their own club...The Grand Slam) or elk, as none of these animals are considered dangerous to man at all under normal circumstances, or normal hunting circumstances. I rate black bear the same, however a case could be made for him as he does hold the record for the number of kills, but then so do crocs and hippos and they aren't included in the African count, so..........
And Mig is right where as it isn't just a species either, it must be a fully mature male to qualify..........lioness do not make Africas list the same as a 2 year old grizzly sow won't make NA list, or cow buffalo either side of the pond, don't count.........now leopard and wolf don't seem to matter, males and females are equally dangerous and must be included if they are fully mature. Some say cow elephant don't count either, even though they are by far the more dangerous ### of that species, if it ain't a bull it ain't big five, now rhino again doesn't matter either cow or bull makes the list, and I think probably polar bear would be treated the same as long as fully mature.
There is just too much to consider.........I'm getting a headache.........