Give me an example of a spontaneous improvement in a species that has occurred "all around us" at a DNA level.
Evolution is not about improvement. It is about differential reproductive success. If you want a clear example of a life form that has evolved in our lifetimes, there is one clear example, a colony of bacteria in Japan that eats nylon. Nylon does not exist except where humans have made it.
Transitional species in progress are exemlpified by ring species.