I understand that the minimum number of people needed to repopulate after a worldwide catastrophe is around 160. If that is the case, how is the human race still here?
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There have not been worldwide catastrophes within human history, but if we stick to natural events, there have been many plagues with huge death-tolls. Fortunately for our species, we had become sufficiently numerous and diffused for there to be very many survivors.
If any catastrophe is facing the human race in the future, it is its own over-population plus depletion of resources.