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Taking mosquitos as an example: a female mosquito can lay ~100 eggs each time it feeds, and those eggs take < 10 days to mature into adults. Assuming each female only lays one batch of eggs (conservative), A single female mosquito can spawn over 125,000 other females per month.

I'm not sure that every single bug is like that, but the exponential growth is pretty crazy. As your parent said, the carrying capacity of the environment is all that really matters. If a population can multiple 125,000x per month, it is basically guaranteed to fill the environment's carrying capacity no matter how many you kill.

https://www.cdc.gov/dengue/resources/factSheets/MosquitoLife...




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