Genetics has been built into the show concept for Heroes from the beginning. Mohinder’s father was tracking a genetic marker, and it’s all about humans evolving powers (in response to what selection pressure, I don’t know, but it’s comic book science). So the question of what can be inherited is built into the show’s premise. And the potential for powers is clearly inheritable, though it’s not clear how.

We only have two examples of characters for whom both parents have powers—Claire and Micah—and both of them have powers themselves. In each case, the child’s powers are unrelated to either parent’s, though one can certainly see the advantage invulnerability might provide for someone living with a pyrokinetic.

We also have three cases of full siblings where neither parent appears to have powers:

• Nathan and Peter Petrelli both have unrelated powers.
• Hiro Nakamura has powers, but Kimiko Nakamura has not displayed any…that we know of. (She’s highly intelligent. Perhaps she’s very highly intelligent?)
• It’s been implied that Shanti Suresh had some sort of paranormal ability, and while Mohinder seems normal so far, the question had been raised. Is he on the list?

So in cases where powers spontaneously appear, it’s not clear whether the mutation occurs in the parents’ generation or in the generation that actually exhibits abilities.

Finally, we have two families where at least one parent has powers. Nathan’s wife hasn’t demonstrated any powers, nor have their two children. (Yet.) Last, there’s the family that was killed by Sylar when Matt discovered he could read minds. It’s clear at least the father had powers (since his brain was gone), and Sylar certainly seemed to think the daughter had powers as well (since Sylar went after her once she was in protective custody).

In summary:

• Two parents with powers will have a child with powers.
• One parent with powers and one without may have a child with powers.
• Two parents without powers may have children with powers, but they may not all have them.
• The nature of an individual’s power does not appear to be inherited