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European Eel

Yeah, those farmers aren't actually breeding the eels. They're capturing baby eels off the Atlantic coasts of Europe, and then rearing those into adulthood in a protected environment. This is also mentioned in the link you provided, in a handy diagram.

And so far, neither conservation nor food production breeding efforts have yielded any captive-bred baby eels that survived into adulthood. So it's not that they have yet to achieve great success, they have yet to achieve any success at all.

I added breeding as an option because the species is farmed in Europe (http://www.fao.org/fishery/culturedspecies/Anguilla_anguilla/en) . But you are right that conservation breeding efforts have yet to receive great success.

It's important to note that in real-life the eels die after breeding. I tried to replicate this by having an obscenely long breeding period.

Honestly, I feel like any sort of in-game breeding for this species is just unrealistic, since in real life, no captive breeding effort has resulted in a second generation of adult eel yet.