Probably indirectly at most, through effects such as wealth, educational background, culture, parenting approach, et cetera. But I doubt that it's very substantial, since I've met plenty of people who, for example, are highly skilled in pure mathematics at uni, yet their parents have absolutely no taste for anything remotely abstract of that nature.
Plus it's important to believe that your ability isn't determined. If you do believe it, then the implication is that it's a waste of time trying to improve your own ability, and hence that any motivation to improve yourself is ultimately worthless.