In chapter one, Jack gives the impression that he is a tough and forceful leader due to the fact that he organized his choir and he has the confidence to declare that he ought to be chief. However, his harsh manner and his temper basically stop him from getting elected. The reader also sees a touch of vulnerability when Jack fails to actually kill the pig that the boys find on their exploration.
In chapter two, Jack's character does not change significantly, but he suggests that the appropriate response to the idea of a "beastie" is to hunt it and kill it. Basically, he is saying that only through violence and savagery will they survive on the island. Jack also does not seem significantly bothered by the death of the boy with the mulberry colored birthmark.
In chapter three, Jack becomes more and more preoccupied with hunting and he begins to neglect other responsibilities in order to continue his hunting. He is still unsuccessful, but is coming closer and relishing his role as a hunter. This is the point where Jack is clearly getting closer to actually being able to be a killer.
In chapter four, Jack finally kills a pig and the boys relish the meat and their feeling of power over their situation. Jack uses charcoal to give himself a mask and behind the mask he begins to completely embrace his role as a hunter and killer. He also demonstrates that he cares not at all about rescue or the fire. At this point, the split between Jack and Ralph grows ever wider.
In chapter five, Jack's power is further established as he basically declares that the rules are dead and they can survive and have fun by hunting, killing and eating meat. He uses the fear the boys have of a beastie to get them to buy into the idea of hunting as it can help control their fear.