Question: Element Benders can pass on their abilities genetically. I'm wondering is an avatar that has access to more elements than usual is able to pass on more than their native bending talent. We haven't, to my knowledge much to go on but this family tree.

![enter image description here](https://i.stack.imgur.com/I76q1.jpg)

I doubt we'll see any hard evidence soon (i.e. proof by contradiction), but if there is something I've missed theory wise, it would help answer.

I see two lines of thought on this:

1. Being an avatar is if not hereditary, some how genetic. Some portion of gene could be passed on unlocking non-native bending.
2. Being an avatar is purely spiritual, and cannot be 'passed on' as with normal bending genes. This may imply however that non-avatars can become avatars if they contemplate their navels thoroughly enough...

Which one is correct, or is there a third option?

Answer: 
I think that from was shown in the shows, being an Avatar is completely spiritual thing. And there is always exactly one Avatar, a reincarnation of the previous Avatars.

Based on that:

1. Being Avatar is not hereditary and Avatar's children can't inherit any of the “extra” powers.
2. You also can't become Avatar through navel-gazing, you have to be born as one and there is only one (living) Avatar at any given time.

All of this is also connected to the origins of bending and possibly energybending, which wasn't explained yet.
No, the avatar can only pass on their native elements to their children. Hope that helps. :)