Katniss and Gale's relationship changes as their lives change.
Katniss and Peeta build thier relationship in an ever changing environment.
How does the relationship between Gale and Katniss evolve from its begining to the end of the book?
How does the relationship between Peeta and Katniss evolve from its begining to the end of the book?
In the beginning, Katniss sees Gale as simply a friend. I don't think she wants to see him as anything more. She doesn't want their relationship to change. The same can't be said for Gale. We are given hints that Gale might just harbor something more than friendship for Katniss. It isn't until Katniss's relationship with Peeta starts to change that she realizes she may have other feelings for Gale as well. Only then is she able to admit that Gale may have other feelings for her. Her guilt at being with Peeta and knowing that Gale will see them together shows us how her relationship with him is starting to change. Just because Gale isn't necessarily around physically doesn't mean her relationship with him cannot change. Katniss will return a different person and Gale will be different as well. Of course, it isn't until book 2 that we really see proof of their changed relationship, but we do catch a glimpse of what is to come in book one.
Peeta and Katniss's relationship changes in more noticable ways. Katniss doesn't really know Peeta in the beginning. She feels indebted to him from long ago but certainly hasn't harbored the same feeling Peeta has. During training, Katniss isn't even sure if she trusts Peeta. She is clearly drawn to him in friendship even though she tries to sort of whether or not he can be trusted. Once they are thrown together in the arena, everything changes rapidly. Peeta's love for Katniss develops into something real while Katniss tries to convince herself it is all for the cameras. Clearly, she has feelings for Peeta as well. The question is what those feelings really are and how deeply they really go. Katniss leaves book one confused and uncertain in both of her relationships.
In some ways it doesn't feel like there is much evolution in the relationship between Katniss and Peeta from his perspective. On the surface, they actually begin to speak to each other and, of course, they develop a bond during the games. With that being said, their relationship in the beginning was Peeta protecting Katniss despite the consequences (his mom hitting him for burning the bread), and in the end he is still sacrificing himself to protect her.
From Katniss's perspective there is an evolution since in the beginning of the book she was not aware of his feelings and no relationship existed on her end. By the end of the book, she has developed a bond with him and taken the job of protecting him as well.
It seems to me that the relationship between Katniss and Gale fades away as the book goes on. We don't see Gale, of course. Katniss thinks about him some, but she is forced to start to grow more of a relationship with Peeta. By the end of the book, we are unsure as to what will happen next. Her relationship with Peeta has grown from zero to something potentially big while her relationship with Gale has become (seemingly) less important.