If wolves (or foxes) are fitter than rabbits, why rabbits have not become extinct?

If wolves (or foxes) are fitter than rabbits, why rabbits have not become extinct?

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I do not pretend to "demolish" the Darwinian theory of biological evolution and the "survival of the fittest", that's far from my intention. I have this doubt because of the fact that humanity, as Homo sapiens sapiens, extinguished the Homo sapiens neanderthalensis because we were fitter to survive.

Please consider this question as if the humanity hadn't appeared yet (because we have domesticated rabbits).

Thanks in advance.

Edit: I have assumed that wolves and rabbits (or hares, maybe) live in the same ecosystem.

Simple: wolves and foxes are not fitter than rabbits. If they were, rabbits would be extinct.

This question is like asking "If Gary Kasparov is better than Michael Jordan, why hasn't he won a chess championship against him?"

And the answers are the same: - "what do you mean, 'better'? Better how? At what?" - "either way, they've never played in a chess championship against each other, so… "

"Fitter" in evolutionary theory means "better at something"; in general it will be "better at surviving", but better at surviving under what circumstances? There isn't a single "fit" or "fitter". Maybe you thought that wolves are better at surviving than rabbits because wolves kill rabbits and not vice-versa, but I could as easily argue that rabbits are better at surviving than wolves because rabbits would survive fine without wolves, but wolves would go extinct without rabbits (not completely true because they have other prey, but you get the idea). The truth is, as far as we can tell wolves and rabbits are equally good at surviving because both have survived.

So you can only talk about fitness if you focus on one specific circumstance to be fit in. But then there is the other implied idea in your question, which is that fitter species drive less-fit ones to extinction. This is true only if the species are in competition. Two species (or individuals, or anything) are in competition when if one species does badly, the other will do well as a result, and vice-versa. For example, maybe they eat the same food, and there is only so much to go around, so every additional bit of food A gets is less food for B, and vice-versa. In that case it is clear that one species being better at surviving than another is bad for the other species, and can (and, according to theory, will) drive it to extinction. Like fitness however two species can be in competition in some ways but not others. For example, two species might compete for food, but have a mutually-beneficial relationship with respect to predators, where if there is more of A the predators will go for them which is good for B, and vice-versa.

Wolves and rabbits are clearly not competitors: things that lead to more wolves will indeed lead to fewer rabbits, but things that lead to more rabbits will also lead to more wolves. As such, even if one were measurably fitter than the other by some metric, it would not necessarily lead the other to extinction. For example rabbits being better against the cold than wolves could promote the existence of wolves in cold places, because a lot of them might freeze but the abundance of food might make it worth it.

This does involve an interesting ecological paradox, which is that according to theoretical models, if you have X species in perfect competition, all but one will eventually go extinct. There is a lot of research in how and why our world's massive biodiversity exists despite this. A big factor is that as I have pointed out, perfect competition is extremely rare in nature. Most species aren't competitors at all, and those that do compete usually don't compete on everything, everywhere and at all times. But when they do or close enough, yes, one should drive the other to extinction. Whether this is why the Neanderthals went extinct is another question

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