How does "The Beast" represent savagery in Lord of the Flies?

The "beast" in Lord of the Flies by William Golding is the major symbol in the story which represents the "evil inside all human beings."  The boys on the island begin to deal with the beast from the beginning of the novel when the "littluns" start screaming about the "beastie".  Everyone else, especially the older boys, tell them that the beastie is in their imagination, but in all seriousness, the beastie is deep inside all of us.  It symbolizes man's savage nature or evil side.  Golding constantly shows us this side of man through the boys' actions of joining in the hunt with Jack and killing the pig for food.  The titles of several chapters seem to also sum up the symbolism.  "The Beast from the Air" represents "the adult beast" or the fact that as people seem to get older, they become more savage through the environment, knowledge and survival. The Chapter titled, "Painted Faces and Long Hair" symbolizes the change in the boys from innocent students to savage animals who hunt, fight and kill to survive.  While preparing for the kill Jack gets the "littluns" all fired up, paints their faces, teaches them chants, and gets them into a fury before they all kill the pig.  This fury increases through the various fights on the island, Jack screaming and yelling at Ralph for allowing the fire to go out, and also in the death of Simon, who was going to reveal the inner beast to everyone, but then was killed before he could explain.  Even Ralph, the one boy who seemed to keep his inner beast at bay, fell to his inner nature at the end of the book when the boys were chasing him and democracy and compromise was no longer an option.  In essence, as the boys changed through the need for meat, killing, fighting, chanting, their savage grew and grew until ironically, they were saved by adults who in essence were soldiers whose job was more than not, to hunt, fight, and kill the enemy to win the war.