Depends on how many women and the ages. So lets see. All your kids are half siblings but if your kid has a kid with a unique woman then I think we are on the level of first cousins so one more should be not to bad although technically they could probably marry. If some of the women where babies and could have kids for 30 years your figure you can get 3 distinct generations. I think with the one male extinction is avoidable. Now if we are talking 3 females and one male then yeah we gone as a species. EDITED - going to make another point with one man and many women. women carry unique mitochondria which the man does not play a part in. So that is sorta another bood to that situation as far as diversity outside of the main genetic code.
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