In Hatchet, how did Brian's relationship with nature change?

Gary Paulsen's Hatchet is one of the great survival stories in literary history, and arguably the most famous featuring a young adult protagonist. The novel tells the story of 13-year-old Brian Robeson, who is on a flight to northern Canada when his plane crashes down, forcing him to survive for 54 days in the Canadian wilderness with nothing but a hatchet. 
This type of literary conflict is classically referred to as "Man vs. Wild," distinguished from the other standard conflicts of "Man vs. Man," "Man vs. Society," and "Man vs. Self." In some ways, this is the simplest type of conflict; a hero tries to survive amidst a chaotic and unfeeling natural world that has the potential to kill them. 
Hatchet follows familiar plot points in this world. First, the hero adjusts to his completely alien environment (Brian takes in the utter and total silence of the woods, something that never existed back home). Next, the wilderness begins to throw challenges at the hero as they struggle to achieve their basic needs for water, food, and shelter. After some embarrassing and/or painful mishaps, the hero begins to learn the lay of the land and achieve calm mastery over their environment. 
Though Brian is in the woods for less than two months, his mastery is undeniable as he successfully creates shelter, hunts small animals, makes fire, etc., strengthened by the fact that he goes on to star in four more novels with similar settings. And as he learns to navigate the "Wild," we see his relationship move from fear to respect, from fumbling to grace, and from anxiety to calmness. Their is a spiritual transformation that often takes place in any "Man vs. Wild" narrative, in which the hero comes to inadvertently love the land that he battles, and to create victory through symbiosis.