Life is a movie. Currently we are in the early stages of Idiocracy, to be followed by a short period of WALL-E. The Children of Men will be the ultimate finale.
Assuming the birthrate does manage to exceed 1.0 in the next few centuries, I can see historians of the 25th century scratching their heads about the cause of the downfall of 21st century civilization in much the same way as we contemplate the demise of the Phoenicians and Egyptians. They will wonder aghast as to why a society that became so wealthy could disappear suddenly within a few decades.
Just ask Julius Ceaser.