How many individuals of any given species are required to create an entirely new population?

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That’s exactly what I mean. I need to know (of course it varies for every species) how many individuals are necessary, in an ideal environment, to create a healthy population. The modern population of cheetahs came from about fifteen to twenty individuals because the cheetah, as a species almost became extinct. They have a rather fragile gene pool because of this and are more likely to become extinct again. However, you are correct, it depends on which species one decides to ask this about, so I suppose it was a rather vague question. I guess what I wanted to know was, on average, what is the ideal number of individuals (for land animals, as insects are a whole other situation entirely) it needed to bring into existence, an entirely new population of that species? I know there is no certain answer to that question, but a few estimations would be helpful.

Depends on the species. And what do you mean by an entirely new population? Repopulation after the species has been depopulated due to death and disease? One bacterium is enough to create a lot of bacteria. One bunny rabbit is not enough to create anything. Pick a species and I can help.