Pretty much.

New research shows that people with blue eyes have a single, common ancestor. A team at the University of Copenhagen have tracked down a genetic mutation which took place 6-10,000 years ago and is the cause of the eye colour of all blue-eyed humans alive on the planet today…

This part makes me happy to be a unique creature of this earth:

…The mutation of brown eyes to blue represents neither a positive nor a negative mutation. It is one of several mutations such as hair colour, baldness, freckles and beauty spots, which neither increases nor reduces a human’s chance of survival. As Professor Eiberg says, “it simply shows that nature is constantly shuffling the human genome, creating a genetic cocktail of human chromosomes and trying out different changes as it does so.”

via The Existence