This is partially a followup to my question on ancestral guidance.
Suppose you have a species, or a subset of a species, that has a particularly interesting mechanic, like the above mentioned ancestral guidance or several other mechanics from super-powers. You need an Applied Phlebotinum (warning: TV tropes link) to explain why this superpower is real. However, due to the setting and type of story you're trying to tell, you want to avoid anything to do with magic (because it doesn't fit the sci-fi theme), evolution (because it's such an easy cop-out) or interference from ancient aliens (because it's such a tired cliché that's been used so often you'd rather not use it).
How can you explain the superpowers in your story in a (semi-)scientific way? With semi-scientific, I mean that it can include hypotheses that aren't fully proven yet, but might have scientific merit.