According to Brian, what was the "great, single driving influence in nature?"
To put it simply, food. Food is the thing that drives every single action in all of nature. All the animals he encounters, even the plants are all focused on getting food.
It took him a rather traumatic moment to realize all of this though. He had found the turtle eggs and was rather pleased about it as it represented a big step up from the berries he'd been depending on. He buried them close to him and then woke up to find a skunk digging for the eggs.
His first thought was to laugh but then he tried to shoo the skunk away and the skunk quickly retaliated. The skunk sprayed him and shattered his feeling of success and made him realize that he had to begin to change the way he was going about "living" in the wilderness. It spurred him to find a way to protect his food from other animals, and to find more ways to diversify his food supply so that one adverse event wouldn't leave him starving.