Basically, when we don’t see any members of the species for a while. They could be extinct, or they could be good at hiding. The Zanzibar leopard is an example that is or was thought to be extinct, but there is some evidence to suggest they may still be alive and just really good at living around humans without being seen.
I know that when you’re investigating how many different species there are in an enviroment, you can use [rarefaction](https://en.m.wikipedia.org/wiki/Rarefaction_(ecology)) in order to determine whether or not you have sampled enough of the enviroment to get an accurate look of that area’s richness. I’m not an expert, but I would imagine that a similar thing can be done with a specific species in order to tell how likely it is to be extinct
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