Remember when I said I thought you guys were overanalyzing things? Well, now it's my turn. I was always really fascinated by genetics and inheritance, though never enough to get into the actual DNA structure and study it academically/professionally would require. I've actually thought about this in the past.
When it came to earth/fire/waterbending, it was a toss up. Nonbenders had bender children and vice-versa as we see with Bumi and Piandao.
The only one that's uncertain is airbenders. As far as we know, all Air Nomads were airbenders. If this is true, then two Airbending parents will always have airbending children.
With airbenders and non-benders, it seems the odds are greater that the children will be airbenders. As Tenzin and Pema's children are all airbenders; Jinora, Ikki, and Meelo are and Katara predicted Rohan would be as well.
But with airbenders and benders, it seems to vary. The only case we have to look at is of Aang and Katara. It seems that if an Airbender has children with a Water/earth/firebender, it's once again a toss-up like every other match-up. Kya was a waterbender, Bumi a non-bender, and Tenzin an airbender.
Here are some Punnet squares I made.
This first one looks at Aang and Katara and assumes bending is a sex-linked trait. Katara is Xx, possessing a bending (X) chromosome and non-bending (x) chromosome. Aang is XY, possessing two bending chromosomes. Now, I don't think bending is sex-linked. First, Kya is either case I (XX) or case II (xX), it would depend on her children. Bumi must be case IV (xY), which means an airbending Y chromosome is recessive to a nonbending x chromosome. Tenzin must then be case III with XY, which means an airbending Y chromosome is dominant to an X bending chromosome. Aang MUST be XY because otherwise Tenzin would not exist, all of Aang's sons with Katara would either be waterbenders or non-benders. Second, Tenzin's X chromosome must be waterbending and his Y chromosome airbending. Therefore, his daughters would either be waterbenders or non-benders which we know is not the case.
Because of this, I think bending is more likely an autosomal trait.
As you see looking at Aang and Katara, it's a bit easier to explain. Kya is either case I or case III, Tenzin is case II, and Bumi is case IV.
If Tenzin is Bb and Pema, a nonbender, is bb, then their children are either Bb or bb. So the chances of them having airbending children are 50%. They've done very well going 4-for-4 though.
/end_biology_lesson
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