The mourning dove is Michigan's state bird of peace. It therefore has deep symbolic significance in the story despite its relatively brief appearance. Byron tells Kenny that nothing can shake up a mourning bird, and to prove his point, starts throwing cookies at it as it sits on a telephone wire. Initially, the bird doesn't move, but when Byron throws his fourth cookie, it lands smack in the middle of the bird's chest, causing it to crash to the ground, dead.
Byron is crestfallen at what he's just done. His immediate reaction to the sight of the dead bird is to throw up. For the first time in the story, we get to see his sensitive side, something we never knew existed. After killing the bird, Byron suddenly stops acting like a tough guy. He now realizes just how precious each individual life is, whether it's a human life or an animal life. The killing of the mourning bird, a symbol of peace, will be paralleled later in the story by the fatal fire-bombing of the 16th Street Baptist Church in Birmingham by white supremacists, which will cause the deaths of innocent people, including children.