Consider the title, The Long Valley for a moment. What does that have to do with these stories? It is their setting, of course, but it is also something else. The real Valley in question is the valley of life, in which these characters move from blindly accepting the cultural narratives in a state of innocence, through corruption, disaster, horror, and shame, toward death. This movement is described in many of the stories.
The first story is no exception. "The White Quail" shows a wife with a garden that is sacred to her, because she feels it is a part of her own soul. When she is visited by the beautiful, strange looking bird, the white quail, she realizes something about the value of her garden. She feels that she has become one with nature or something. Then her husband kills the bird and buries it shamefully. He never tells her. This is a symbol for innocence lost.
In other story, "The Snake," someone wants to watch a mouse die, to be eaten by a snake, but Dr. Phillips is concerned about this. Why should anyone want to watch something die? He has his scientific process, but he is convinced that he isn't intrigued by animal death in the fetishistic way that the woman is. And yet, he does show her. These uses of animal life are not the only instances of death, either. In "The Murder," there is a murder, and throughout the stories, people die, typically wives.