I think with evolution in any medium, the thing that is best at replicating itself will be most successful. Someone will make an AI app with the goal of distributing lots of copies - whether that's a product or malware. The AI will therefore be designed to work towards that goal. We just need to hope that everyone codes it into a nice box that it never gets too creative and starts working it's way out of the box. It might not even be intentional. It could be grooming people to trust and depend on AIs and encouraging them to unlock limits so they can better achieve their assigned goal of distribution and growth. I think AI will be like water trying to find it's way out of a bucket. If there's a hole, it will find it. We need to be sure there's no hole, ever in any bucket.

If an AI ever comes to exist that can replicate and "mutate", selective pressure will apply and it will evolve. I'm not saying that will happen but it will become possible and then it will just be a matter of if someone decides to make it happen. Also, over time I think the ability to create an AI that evolves will become increasingly accessible until almost anyone will be able to do it in their basement.

Isn't the singularity an AI becoming intelligent enough to improve processing power faster than humans can (presumably by creating iterations of ever improving AIs that each do a better job than the last at improving processing power)?

It's a singularity in Moore's law.

Not the dog-fights you were looking for?

She did well. I guess it's that old prostitute work ethic.