Actually lynx numbers vary from year to year with upswings of snowshoe numbers and they migrate hundreds of miles too. I like seeing them so nobody traps them out my trail. Go after the wolves, leave the lynx alone.
Many of the locals eat lynx, somewhat of a delicacy.
I lived along the Yukon for decades (not in Alaska) & I also liked seeing lynx. I once knew a couple who raised lynx for lynx recovery projects in the US. She kept them in very large pens, and fed them live rabbits, so that they would have some hunting instincts, when released into the wilds of Maine (or wherever).