The Amur tiger is without a doubt the apex predator of the Siberian wilderness. If they become extinct that will be such a tragic loss! They share their environment with the Russian grizzly which is the direct ancestor of American grizzly bears. Ussuri brown bear, horse bear, or black grizzly. A typical alpha male weighs roughly 580 pounds. Tigers occasionally hunt bears. They prey mostly upon juveniles or sub-adult bears and occasionally an adult she-bear. Normally bears within the 300 pound range or less. With good reason. The tiger is seeking a meal, not a fight.
The grizzly will kill tiger cubs or young tigers if the opportunity presents itself. Grizzly bears are not great hunters, as are tigers. While the huge bear will hunt and kill on occasion, he acquires the majority of his red meat from scavenging or usurping the kill of another predator. Contrary to my earlier posts, I have partaken of crow and admit that I was wrong ( unless news proves things otherwise ). A grizzly bear will usurp a kill from sub-adult or female tigers; giving the bear a huge size advantage. Same reasoning, the bear is seeking a meal, not a fight.
When fully adult male tigers and male grizzly bears do fight, most often it is a shatun bear; weak from starvation and perhaps half his normal weight, but desperate.