It's a bit of a roundabout way of getting there, but here's the breakdown:
* Species originally referred to a kind or sort of thing, a distinct group within a larger category.
* Over time, the word special developed from species, meaning "of a particular kind" or "distinctive."
* Specialize then arose from special, meaning "to make something special" or "to focus on a particular area."
So while "species" isn't directly within "specialize," it's the source of the word's meaning.