This amazing small island with it's own cloud !

This is amazingly common anywhere with a lot of islands it seems. Oftentimes it’s originated from a time when people needed (or stole) the resources on land and so livestock was driven across the water (sometimes swam - literally one person gets in and swims with the head steer and the herd follows. People in a boat will make sure there are no strays. The herd can live quietly eating the nutritious salty grass for the summer and no one is stealing your cattle (or sheep) without a good deal of hard work and a high chance of getting caught. That also leaves the workable land around you to be farmed or utilized in a way that better aids you and your family. Keep in mind we are talking about little more than substance farming here, not a commercial enterprise.

Islands end up with native animals in all sorts of bizarre ways. Name any of the tiny ass islands in the pacific for example, and almost all of them have a couple wonky, found-nowhere-else-in-the-world species that have branched off from some larger local-ish branch.
So, during the neolithic period, people were inventing tools and domesticating animals. Which means if, say, my village drops sheep off on the island, and then a disease wipes us out or you raid our village and kill all of us, well, my sheep just became feral sheep. Animals can also cover shockingly large distances of water if you're willing to drown enough animals trying - which it turns out, nature is fine with. Storms might knock animals into the ocean and then coincidentally drop them off on another island - all it takes is one pregnant sheep to suddenly have a new offshoot of feral sheep. 100 generations of inbreeding later you have a "unique species" which is true in the most literal sense but in a practical sense it's just 500 years of iteration on "shitty brown sheep that's really fucking hard to drown".