Do you have some models you're looking at that cause you to believe with such certainty that this is what the future holds? I have not seen, nor can I even really fathom, a scenario in which declining birth rates leads in of itself to extinction (unless the birth rates drop to basically zero for some reason), but certainly this could be due to a failure of imagination. A declining population would certainly look different, but I don't see it causing the end of civilization, much less the species.