Species purposely introduced by humans would be considered artificial not 'natural' selection. If the cats swam over to the island of their own volition as a survival strategy though, that would blow my mind.
So, would ticks brought to a new prairie by bisons. So, would seed brough by the feces of migrant birds.
Yes, we can CHOOSE any moral framework, including one where we introduce this arbitrary notion of artificiality to treat the impact of homo sapiens as a distinct category. But let's not treat this as science. I wouldn't go so far to call it as a religion, but it is still on the realm of ethics and philosophy.
We can even have pragmatical reasons for choosing so, like the need for a particular eco-system to stay in a given state for our own confort, health and economic reasons. But it is still an arbitrary choice.
Species migrate by themselves in the nature, sometimes they play havoc on the existing biome they migrate themselves into. This was, it is, and it will be a significant driver of evolution long after we are gone from earth.
And on this particular case, it is not even like we are restoring the island to some idealized, pristine steady state. Cats are not the only species that piggyback on our civilization to spread, we also have the domestic mouse. If anything, completely eliminating the cat from those islands will serve only to ensure that the domestic mouse will be the dominant species there.
> So, would ticks brought to a new prairie by bisons
Ah, no. Nature is specifically what has unadulterated by humans. If humans are involved, it's not natural. I didn't make up the words, but that's exactly what it is. At least if you're talking about nature as being distinct from something else. If you're talking about nature writ large, then there is no distinction, but we're not talking cosmology here.
> we can CHOOSE any moral framework
I was only making clear the distinction between natural and unnatural.
But, to take on this argument, cats and mice are exotic pest species in many places. You might object to them being called pest, but their existence is usually at the extinction risk of native species. It's fair to say there'll be enough cats and mice around the world. You could say that we should just let whatever thrives to thrive, but I'd argue the world would be a more boring place without native species, and indeed ecosystems can collapse from the introduction of exotic species, potentially even causing existential risk to the introduced species (including us humans).
Sure, "we broke it so we should try to help maintain it" is entirely an ethical question and not a scientific one.
Are you satisfied now? Can we go back to talking about the problem instead of arguing about the definition of "natural"?
...but wait, you're the one that introduced the word "natural" to this conversation, using it as a reason to do nothing. That's ridiculous. If everything is natural, then your argument would say we should never do anything ever.
You can't have it both ways. If you want to use such a wide-reaching definition of natural, then you can't also use "natural" as a motivation to not intervene.