I think an awful lot of people mistakenly refer to a, "desert island," when they really mean a, "deserted island."
And due to a quirk in the English language, neither "desert" nor "deserted" (both words that describe areas void of anything important) imply the other. Desert things aren't necessarily deserted things, and vice versa. So for instance, when someone asks me what music I'd like to have if I were stuck on a desert island, I'd probably say whatever the natives like so I could barter with them for shelter or sunblock—both of which would probably be important on a sandy and treeless island.
So, get it right, people. A place devoid of people is "deserted." Deserted islands are often deserts, but you probably mean to specify the former, and not the latter.
P.S. Merriam-Webster disagrees. They're wrong, too.

What they really mean is a desserted island, with tasty treats everywhere.
Precisely the irony in the title.
I'll take mine with gumdrop trees, chocolate coconuts, and beaches made of peppermint bark. Oh yes, and diabetic natives.
--Dan