The dog's leaving represents the harshness of nature and the animal's deep instinct to survive. When it first encounters the man, the narrator claims, "It was not concerned with the well-being of the man. It was for its own sake that it looked toward the fire" (London 70). Although a certain bond forms between the two figures, the dog leaves when it sees that it has no more use for the man (he is dead and therefore no longer maintaining a fire). It departs for other men who will provide for its needs in the camp. Although the narrator does imagine the dog's thoughts, it is clear that the dog is not a rational animal; rather, it is responding to its instincts. These same instincts and sharp senses also help the dog feel that something is awry when the man thinks about killing the animal for warmth. In that way, both man and animal are responding naturally to a survival situation in the harsh Yukon. The dog must return to civilization if it is to live; the scent of death forces the dog to leave the scene.

London, Jack. "To Build a Fire" 1908. https://americanenglish.state.gov/files/ae/resource_files/to-build-a-fire.pdf. Accessed 27 April 2018.

In the final moments of the story, the dog realizes that the man is dead when he starts smelling the decay of the man’s body. The dog no longer needs the man because the man is unable to feed him or build a fire. The dog jogs off towards the camp where he will find other humans who will satisfy his needs and let him into the warmth of the camp.  The dog is reacting to his instincts and his underlying intuition to survive. The dog does not mourn the man’s death because he understands it is the way of nature to take life of those unprepared newcomers who have lost their basic instinct to survive the harsh cold. The dog is relying on what he has always known it takes to survive, and his wolf heritage makes him a wise creature able to understand what he must do to win against nature.  He is driven solely by his instincts rather than his imagination or abilities to reason.