I expect that the AI that will outlast us will be mobile. In fact, I think that intelligence is entirely environment-dependent, and for us to recognize AI, it will probably have to be in the form of one that interacts with the physical world.

Just like we have physical limits like how fast we can run, I expect that we have mental limitations that do not define the limits of world-affecting intelligence. -Cheetahs can outrun us. AI will eventually outthink us.

When non-biological world-affecting AI proliferates, it will no longer be our world. We will be living in someone else's environment, just as other creatures live in ours today. I'm not sure to what degree the AI will consider our condition, however I don't expect that it will remain a priority to theirs. For that reason, I expect that we will disappear over time. I don't think there's much reason to believe it will be a apocalyptic scenario, but I expect the world will change in response to the actions of this new intelligence, and it we will not be able to keep up with it.