Lost and Shakespeare

So I was reading up on the Tempest for class (obviously my Shakespeare class), and I began to notice some similarities to my favorite TV show in the post-Arrested Development world. (I must say any life without Arrested Development is not worth living.)

People on a ship are drawn to a strange island by a freak storm. There they encounter many strange things, and someone gets abducted (Ferdinan).

Sounds a lot like Lost where some people in a plane crash on a strange island, and someone (Claire, then Walt) gets abducted.

Could the whole thing be a big allusion?