In a world I am building, a race of humans exists on a tropical archipelago with a very hot climate. Their skin, naturally, is very dark, but I want to have their eyes [most, if not all of their eyes] be light grey. Is this possible?
Yes. Blue eyes are actually made by a lack of melanin in the iris and other colours a variation on this. (Blue is caused by the refraction of light around the iris, same reason the sky is blue).
We do, in fact get black people with blue eyes in humans. They are a minority but still do exist.
So yes, grey eyes are also possible for your humans.
Very dark skin with very light eyes is maybe genetically possible but extremely unlikely.
Brown eyes have dark melanin. Blue-eyed people lack this melanin and their eye tissue is colorless (the blue is a result of light scattering, same reason the sky looks blue)…. It's not a coincidence that people who lack melanin in their eyes would also lack it in their skin, hence blue eyes are most common in Northern Europe among very light skinned people.
Grey eyes occur in North Africa, the Middle East, and Asia. According to this website the exact genes are unknown but probably a similar combo to the blue-eye genes. Again these are not "very dark" people. Think of the famous "Afghan Girl" from the magazine cover Her eyes are green but very light:
To get around this, you'd need a genetic combo that codes for lots of melanin, but with a defect so the melanin is blocked locally in the cells of the eyes. It's possible, but then you'd need to replicate that gene defect through the entire island population.
One way to achieve this is by selective breeding. It could be that evolution resulted in your people having dark eyes, but then one small group had a mutated gene which gave them grey eyes. For some reason this gene tends to be dominant.
Over time (thousands of years), people preferred grey eyes, and tended to choose grey-eyed partners. This is selective breeding, in which male and female are selected (or select each other) in order to produce offspring with certain traits. We do this with animals today.
So just make it that grey eyes are more desirable, and as a result of years of selective breeding, the majority now has grey eyes. Those with dark eyes still occur, but are the minority.
No, or at least unlikely.
There is no evolutionary advantage in having blue, green or grey eyes. Pale skin, yes, in the north, but eye and hair colour are only a secondary effect of that.
If your islanders are really human, it's improbable. No melanin production in the eye would be the result of a genetic defect. That would usually only proliferate thoughout a whole population if it had some secondary advantage, for example resistance to an endemic infection, even if it was otherwise completely harmless. A dominant genetic variation occuring spontaneously is something rather rare, i believe.
In a manner of speaking, yes.
Recently, we have found evidence that the blue eye gene stemmed from the random mutation of one individual. Random mutation is the key to the bulk of ethnic geodiversity here. Contrary to popular belief, for example, it was agriculture, not latitude, that created the Caucasian and Mongoloid paleness. If it were latitude, the evidence would have shown us a case of human whitewashing far older than eight thousand years. The reason for the more likely connection between whitewashing and agriculture is that plant foods don't have much of the vitamin D that a dark skin needs.