Which have an effect on fertility and death rate. There is literally nothing that matters to population dynamics other than fertility and death rate.
We have extensive experience on that now: Technological and social development drives fertility to at or below replacement levels rapidly. This is the main factor. Importantly though, _this is not a prediction_. This reduction has already happened. So the bulk of the prediction is just playing out the consequences of developments we've already seen.
Of course major events like climate change have the potential to invalidate this prediction. But that doesn't mean this prediction is useless. And this is would not be due to "sensitivity to initial inputs".