I vaguely recall reading something alongt those lines myself; a built-in "best-before" date in the genetic make-up of a species, leading to or at least contributing to its eventual decline and/or disappearance. I don't remember how or if they addressed the discrepancy with things like Horseshoe Crabs, sharks, etc. that have been successful in an essentially unchanged form since before the time of the dinosaurs.
In any case, Homo sapiens has been around for such a tiny blip of time on the cosmic or geological scale that it seems unlikely to be suffering from that type of species burnout. We won't be eliminated by nature, unless it's some cosmic fluke like an asteroid. We will do ourselves and each other in by much more straightforward means. Pollution, climate change, overpopulation, deforestation, famine and disease will kill off a sizeable fraction of the total. Our civilized lives will become more difficult to maintain, standards of living will decline, resources will dwindle and human nature will show its true face. The currently vocal do-gooders of the world will become silent when their homes are cold, their faucets run dry and their lights go out. Then the fighting starts...
To continue the Star Trek theme: we are just a bunch of big, noisy, aggressive tribbles...and the grain bin is getting empty...
...and pretty soon (cue Three Stooges theme song)...we'll all be victims of circumstance (or coicumstance)...
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