Back in 1972, a sort of late mid-point in the Cold War, a theory called "punctuated equilibrium" introduced by evolutionary biologists Stephen Jay Gould and Niles Eldredge provided a wry kind of solace. The theory was designed to explain how it was that fossils of many species seemed unchanged over vast periods at the same time that fossils of new species seemed to pop out of nowhere. The idea was that rapid changes in a species' ecology cause it to evolve quickly (in geologic time, remember) into a new species.
The solace, unscientific as it was and as unintended by the authors, involved the forlorn hope that a nuclear war - changing the earth into a world filled with radiation and cloaked in nuclear winter - might at least spawn evolutionary changes that could allow the surviving remnant of humankind to adapt to the new conditions.
Recent studies made possible by advances in genetics are dashing such hopes. While it is true that such studies have shown, for instance, that humans who migrated to the Tibetan plateau adapted to the thin air by evolving a gene variant that bolstered red cell production over a mere 3,000 years, most such variation takes something like 50,000 years to spread through a population. Not exactly a big help in the event of a global catastrophe.
So, people worried about drastic climate change or the emergence of some incurable AIDS-like pandemic out of some rainforest can forget about people adapting. Better to rely on technology. As "big history" shows, species such as humans don't adapt. They just quietly go extinct.