Jack challenges Ralph from the very beginning of the story and, just as the circumstances of the challenge change, Ralph's response changes as well.
At the first meeting when Jack challenges Ralph in the election of a chief, and Ralph manages to win despite Jack's obvious leadership qualities. Ralph immediately starts to try and organize the boys to build shelters and start a signal fire while Jack gets to be in charge of the hunters.
The next challenge Jack issues to Ralph is less direct but consists of him continuing to hunt when he and his hunters were supposed to be maintaining the fire. This one comes to a head when Ralph complains about it publicly but the rest of the boys are beginning to wonder who they should follow since Jack provides meat for them.
As time goes on, Jack eventually challenges Ralph more openly and more strongly as he tries to take control of the boys. He contends that they need to hunt the beast, that they should forget trying to be rescued and try to "have fun." Eventually Ralph's responses grow weaker and weaker until Jack wrests control of the boys from him and Ralph is left entirely isolated.