Take the Northern White Rhino. It is big enough that we know exactly how many are left: two females, neither of whom could carry a calf to term, no living male. It’s extinct, with the caveat that scientists MIGHT be able to produce an embryo from frozen sperm and eggs that MIGHT implant in a southern white rhino, and MAYBE carry to term. But for all intents and purposes, it’s gone.
Littler creatures can be deemed to be gone if X number of years go by and none have been reported, and it is known to have a limited range. We know for example that orangutans have a very small range, constantly being lost to palm plantations. There will still be a population in captivity when the last wild ones are gone, but probably not enough to provide adequate genetic diversity.
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