Is the narrator a developing/dynamic character?

The protagonist, whose real name never appears; he's referred to only as "Brother" by Doodle. The narrator has Doodle's best intentions in mind, but he allows his pride and determination to get in the way, which ultimately results in tragedy. We never really find out if the narrator changes but I suspect his brother's death is traumatic enough to cause change. At the end of the story, the narrator lifts Doodle's head and it falls back down, limp; he sees that Doodle had been bleeding from the mouth and is now covered in red. The narrator shakes him and calls his name, but he doesn't move. He observes that Doodle's neck has never looked so long, thin, and fragile. Screaming, the narrator collapses over his brother's body, "sheltering [his] scarlet ibis from the heresy of rain."