The Single Coconut Tree Desert Island is a common visual trope in many forms of cartoon media, used to denote an isolated location in the middle of the ocean. Its most prominent use might have been in Gary Larson's The Far Side, where it was perhaps the most used setting. It is also a mainstay of The New Yorker's cartoons.

The Single Coconut Tree Desert Island is usually shown as being very small, less than 10 feet in circumference, and being less than a few feet above sea level. It has, as mentioned, a single coconut tree growing on it, and is usually inhabited by a castaway who reached the island in a shipwreck.

I had always taken the picture to be a type of visual shorthand, but I was interested in investigating whether such an island could actually exist. Apparently, a coconut palm is tolerant enough of salinity that it can indeed grow within a few feet of salt water, and could live on an island where its roots were immersed in salt water. A simple google image search has revealed to me that islands about ten feet across with a single palm tree growing on them do, indeed, exist. Since these seem to be stock photos with no authentication or information about location, I can't vouch for their veracity, but it seems likely that they do exist.

The biggest problem with the image of a small desert island is not botanical but geological. Most small ocean islands come in three varieties: islands that are part of a continent, where the intervening water only goes over the continental shelf, volcanic islands, where the island is part of mid-ocean volcanic ridge, and coral atolls, where submerged volcanic islands are covered with coral reefs and low, sandy beaches. The first two island categories are usually rocky, with the Single Coconut Tree Desert Island appearing to be in the third category. But islands and islets in coral atolls rarely come by themselves: they are usually part of a ring. If someone were stranded on one, it is most likely that there would be other islands within a few miles, if not within a few hundred feet. Of course, even these small distances could be a hindrance to a person who couldn't swim, but the idea that an island of only a few dozen square feet could exist in the open ocean is fairly improbable.

So the island, as depicted, could and probably does exist, but the wider context in which it exists, as a place of total isolation, is probably not a real phenomenon. However, given the fact that it is merely used as a visual shorthand to establish isolation and separation, it is realistic enough.