Wow, a question like that is more loaded than what is the best knife! Definately isn't survival related as far as guns/calibers go so I will keep my thoughts to hunting. The rifle used in that hunt was a custom ultralight .300WSM but I just wanted to ensure it had a kill under its belt.
Here in AK you may be going hunting for one species but encounter another one. Most likely the season is open for several different species so be prepared. I don't worry about recoil because it normally takes one or two shots to finish an animal. I say more than one shot because these animals can get pretty big and are much more resilient than one could imagine. Furthermore, if the animal runs it may be into thick brush making it difficult and even dangerous to track or up and over a mountain that would require crampons or climbing ropes to get to.
That being said it has been proven that a 220 swift can kill a brown bear and indigineous natives use .223 for everything. Just because it works doesn't mean it will work all of the time.
I tend to use a larger bore so I can plant the animal in its tracks and so it bucks the wind for the longer shots. A .270 works great for most animals up here but there is always that chance encounter with a brown bear. Brown bears have so much blood flowing through them that they can have thier heart blown out and still run 9 seconds or more clocking speeds over 35mph. That is alot of distance closed fast. I have seen it happen after multiple well placed shots from multiple people. Exciting to say the least.
Any .30 caliber rifle with heavy rounds should do the trick. Practice makes perfect (consistency). I choose a .338 lapua but any .338 caliber is perfect for AK in my book. I have even used 45-70 depending what kind of terrain I am hunting in. The .338 has a wide variety of bullets with high b.c. I use either 300gr matchkings for long range and have a separate load of 250gr accubonds in the same rifle for close work under 300yds. (same rifle, two different aiming points). The matchkings work amazingly well past 300yds.
Three of the goats taken during that hunt were around 300lbs. Even with well placed shots using accubonds or partitions they still went a good ways.
So what if you are hunting and come upon predators you want to dispatch? The .338 worked well on the wolves I shot with holes that were easily sewn shut. Otherwise in my base camp I will have a pistol or a small sized .243,.223, .204 for coyotes and foxes (can never make up my mind). Backpack hunts is just a pistol in the .44 flavor or .45ACP+p+.
Long winded post hey, guns are fun to talk about. When I go to Georgia next year for six months I will be bringing my .338L, .243AI, and ar-15 for the deer and pigs. They seem to cover anything I have gone after in the states.
Sometime this christmas when I have time I will be posting on LRH a couple caribou hunts I did these last couple of years.