Which caribou do the wolves target in Julie of the Wolves?

The wolves seem to single out the weakest of the caribou for their kill.  Instinctively, they seem to know that a reasonabley healthy caribou can outrun them, but if the wolves can just manage to catch the animal, they will be able to quickly bring it down.  Working as a team, they use their deadly teeth and claws to disable the caribou with "slashes and blood-letting bites".  When the unlucky beast is dead, the wolves tear it open and unceremoniously "(fall) to the feast".

Miyax has seen how swiftly the healthy caribou can run.  They are so confident in their ability to outrun their predators that the herds pass close by "their enemies the wolves" without a second thought.  She realizes that "the young and the healthy ones (do) not fear the wolves, and the sick and the old (are) doomed in winter".  This is the natural order of things, survival of the fittest.  Miyax remembers that she had been able to glean life-saving meat and hides from the last caribou which the wolves had brought down.  Upon examination of the animal, Miyax had discovered that that caribou had been "so infested with the larvae of nose flies it had not been able to eat...a weakling, it had become food to give strength both to her and to the wolves" (Part 1 - "Amaroq the Wolf").

What are the two caribou fighting over in Julie of the Wolves?

Because these are brute animals, there is no real way for us to know what the two caribou were fighting over, but there are two possibilities: food and/or a mate. During the Arctic winter, food is incredibly scarce. There are few lichens and grasses left for the caribou to feed upon. When food becomes scarce, less tolerable food (such as bark) is coveted. If a lone lichen or patch of grass is found, the entire herd of caribou will fight for that little bit of food. Further, it is traditional for all species of deer to use their antlers in order to show prowess and fight for a particular mate. Especially if there is only one mountable female caribou, two males (and sometimes more) will fight each other by knocking their antlers together violently in order to prove which one is the strongest. The winner will sow his seed and continue the species. There have even been instances where, during the fight, two deer have gotten their antlers permanently locked and, therefore, condemned themselves to death.