Tsuki no Sango

The story takes place in approximately the year 3000, when humankind arrived at the peak of its civilization, but is losing its will to keep living. It follows a girl, called "princess" by those around her, who lives on a small island with a fifty-person colony and a shining coral reef. She is a descendant of the Moon people, and the story focuses on how her ancestors supposedly came to Earth.

(Source: myanimelist.net)