<p>I actually propose an alternative genetic theory, but It has a lot more complications in it;
</p><p>B = Dominant Bending Gene, b = Bending Carrying Gene, N = Nonbending, n = Nonbending (null effect*), x = Replacement Gene**
</p><p>Having a B makes you a bender.
</p><p>Having a b or a N makes you a nonbender, but doesn't rule out your children from being benders.
</p><p>Having an *n nulls all bending ability, even if you have a B
</p><p>Having an **x only occurs when you have bb or nn which then becomes b²/B or n²/N and you require something to fill the gap. x allows you to be a bender, but when passed on, it becomes two n's which does limit whether your children will be benders as well.
</p><p>An R represents Raava and is exclusive for the avatar and contains very bending element. it is not hereditary.
</p><p>In terms of which bending they inherited: ᶠ = Fire, ᵃ = Air, ᵚ = Water, ᵉ = Earth, and ᵊ = Energy (just for the Avatars since Aang).
</p><p>If for example all humans, back before any were benders, had Nn as their genetic code. If you were given bending via a lion turlte, your genes turn into Bb (except for airbenders as their spirituality gives them BB instead).
</p><p>Below is an example of what the genetic ratio by my theory, I'm using Aang and Katara because they are the best example of a multi-ratio result:
</p>
<table border="0" cellpadding="0" cellspacing="0" style="width: 320px; width: 240pt; border-collapse: collapse;"><tr style="height: 15pt;"><td style="height: 20px; width: 64px; border: 0px black; border-image: none; width: 48pt; height: 15pt;">
</td><td style="width: 64px; border: 0px black; border-image: none; width: 48pt;">
</td><td colspan="3" style="width: 192px; border: 0px black; border-image: none; width: 144pt;">Aang
</td></tr><tr style="height: 15pt;"><td rowspan="3" style="height: 60px; border: 0px black; border-image: none; height: 45pt;">Katara
</td><td style="border: 0px black; border-image: none;">
</td><td style="border: 0px black; border-image: none;">Bᵃ
</td><td style="border: 0px black; border-image: none;">Bᵃ
</td><td style="border: 0px black; border-image: none;">Rᶠᵃᵚᵉᵊ
</td></tr><tr style="height: 15pt;"><td style="height: 20px; border: 0px black; border-image: none; height: 15pt;">Bᵚ
</td><td style="border: 0px black; border-image: none;">BᵃBᵚ
</td><td style="border: 0px black; border-image: none;">BᵃBᵚ
</td><td style="border: 0px black; border-image: none;">
</td></tr><tr style="height: 15pt;"><td style="height: 20px; border: 0px black; border-image: none; height: 15pt;">x
</td><td style="border: 0px black; border-image: none;">Bᵃn
</td><td style="border: 0px black; border-image: none;">Bᵃn
</td><td style="border: 0px black; border-image: none;">
</td></tr></table><p>Aang is an Air Nomad, and all Nomads were benders as far as we know, so Aang = BᵃBᵃ (the ᵃ = Airbending). The R represents Raava and the Avatar Spirit which can hold all the elemnts, but is not a gene and cannot be passed down, it just represents Aangs ability to bend all the elements. Katara is a bender, while her brother and parents were not. This is complicated and below is what I think is possibility of her bending:
</p>
<table border="0" cellpadding="0" cellspacing="0" style="width: 256px; width: 192pt; border-collapse: collapse;"><tr style="height: 15pt;"><td style="height: 20px; width: 64px; border: 0px black; border-image: none; width: 48pt; height: 15pt;">
</td><td style="width: 64px; border: 0px black; border-image: none; width: 48pt;">
</td><td colspan="2" style="width: 128px; border: 0px black; border-image: none; width: 96pt;">Hakoda
</td></tr><tr style="height: 15pt;"><td rowspan="3" style="height: 60px; border: 0px black; border-image: none; height: 45pt;">Kya
</td><td style="border: 0px black; border-image: none;">
</td><td style="border: 0px black; border-image: none;">N
</td><td style="border: 0px black; border-image: none;">bᵚ
</td></tr><tr style="height: 15pt;"><td style="height: 20px; border: 0px black; border-image: none; height: 15pt;">N
</td><td style="border: 0px black; border-image: none;">NN
</td><td style="border: 0px black; border-image: none;">Nbᵚ
</td></tr><tr style="height: 15pt;"><td style="height: 20px; border: 0px black; border-image: none; height: 15pt;">bᵚ
</td><td style="border: 0px black; border-image: none;">Nbᵚ
</td><td style="border: 0px black; border-image: none;">Bᵚx
</td></tr></table><p>As you can see, there is definatly a greater chance that she could have been born a nonbender like her brother, Sokka. However, by my theory, bb = B (It doesn't make a lot of sense, but its the best that I can come up with), but with one B, she needs another letter to fill in. Because she was the daughter of two dominant nonbenders she is given an x, which when changes when inherited as a set of n's. This makes Sokka 3/4, and Katara 1/4.
</p><p>Whe you pull this back to Aang and Katara; Bumi is 1/2 and Kya and Tenzin are both 1/2 also. But seeing as Tenzin inherited more from Aang, his Bᵚ translates into Bᵃ as humans can only hold one set of bending, and Kya likewise inherited more from Katara, and vice versa.
</p><p>Tenzin is like Aang and has BᵃBᵃ, Pema is a nonbender, and for this sake I will just say tha she is NN without any real evidence to prove otherwise:
</p>
<table border="0" cellpadding="0" cellspacing="0" style="width: 256px; width: 192pt; border-collapse: collapse;"><tr style="height: 15pt;"><td style="height: 20px; width: 64px; border: 0px black; border-image: none; width: 48pt; height: 15pt;">
</td><td style="width: 64px; border: 0px black; border-image: none; width: 48pt;">
</td><td colspan="2" style="width: 128px; border: 0px black; border-image: none; width: 96pt;">Tenzin
</td></tr><tr style="height: 15pt;"><td rowspan="3" style="height: 60px; border: 0px black; border-image: none; height: 45pt;">Pema
</td><td style="border: 0px black; border-image: none;">
</td><td style="border: 0px black; border-image: none;">Bᵃ
</td><td style="border: 0px black; border-image: none;">Bᵃ
</td></tr><tr style="height: 15pt;"><td style="height: 20px; border: 0px black; border-image: none; height: 15pt;">N
</td><td style="border: 0px black; border-image: none;">BᵃN
</td><td style="border: 0px black; border-image: none;">BᵃN
</td></tr><tr style="height: 15pt;"><td style="height: 20px; border: 0px black; border-image: none; height: 15pt;">N
</td><td style="border: 0px black; border-image: none;">BᵃN
</td><td style="border: 0px black; border-image: none;">BᵃN
</td></tr></table><p>
This large probability says that all of Tenzin's and Pema's children will be benders, but it does open the possibility that Jinora, Ikki, Meelo and Rohan will have nonbending children depending on the results. This is only a rough idea as Rohan hasnt been confirmed as an Airbender and it may change because of it. But for now i am guessing that it was a 100% chance that all the chidren wold be airbenders.
</p><p>For another example of multi-benders is Mako and Bolin:
</p>
<table border="0" cellpadding="0" cellspacing="0" style="width: 256px; width: 192pt; border-collapse: collapse;"><tr style="height: 15pt;"><td style="height: 20px; width: 64px; border: 0px black; border-image: none; width: 48pt; height: 15pt;">
</td><td style="width: 64px; border: 0px black; border-image: none; width: 48pt;">
</td><td colspan="2" style="width: 128px; border: 0px black; border-image: none; width: 96pt;">Firebending Dad
</td></tr><tr style="height: 15pt;"><td rowspan="3" style="height: 60px; border: 0px black; border-image: none; height: 45pt;">Earthbending Mum
</td><td style="border: 0px black; border-image: none;">
</td><td style="border: 0px black; border-image: none;">Bᶠ
</td><td style="border: 0px black; border-image: none;">bᶠ
</td></tr><tr style="height: 15pt;"><td style="height: 20px; border: 0px black; border-image: none; height: 15pt;">Bᵉ
</td><td style="border: 0px black; border-image: none;">BᶠBᵉ
</td><td style="border: 0px black; border-image: none;">Bᵉbᶠ
</td></tr><tr style="height: 15pt;"><td style="height: 20px; border: 0px black; border-image: none; height: 15pt;">bᵉ
</td><td style="border: 0px black; border-image: none;">Bᶠbᵉ
</td><td style="border: 0px black; border-image: none;">bᶠbᵉ/Bᶠᵉx
</td></tr></table><p>I am making a guess that their father was a Firebender as Mako's red scarf came from him and it is generally accepted that fire is associated with red as earth is to green. The odds are prety much 50/50 between Mako and Bolin. Depending on which parent they inherited more from also determines which of the equal bending genes the belong to. The example is the BᶠBᵉ, If they inherited more from their dad, then they would be a firebender, but an earthbender is from their mum, in the same sort of way as Tenzin and Kya.
</p><p>For a bender to have a nonbender child, but then have a bender in later generations. Roku to Zuko is the best I can think of:
</p>
<table border="0" cellpadding="0" cellspacing="0" style="width: 320px; width: 240pt; border-collapse: collapse;"><tr style="height: 15pt;"><td style="height: 20px; width: 64px; border: 0px black; border-image: none; width: 48pt; height: 15pt;">
</td><td style="width: 64px; border: 0px black; border-image: none; width: 48pt;">
</td><td colspan="3" style="width: 192px; border: 0px black; border-image: none; width: 144pt;">Roku
</td></tr><tr style="height: 15pt;"><td rowspan="3" style="height: 60px; border: 0px black; border-image: none; height: 45pt;">Ta Min
</td><td style="border: 0px black; border-image: none;">
</td><td style="border: 0px black; border-image: none;">Bᶠ
</td><td style="border: 0px black; border-image: none;">bᶠ
</td><td style="border: 0px black; border-image: none;">Rᶠᵃᵚᵉ
</td></tr><tr style="height: 15pt;"><td style="height: 20px; border: 0px black; border-image: none; height: 15pt;">N
</td><td style="border: 0px black; border-image: none;">BᶠN
</td><td style="border: 0px black; border-image: none;">Nbᶠ
</td><td style="border: 0px black; border-image: none;">
</td></tr><tr style="height: 15pt;"><td style="height: 20px; border: 0px black; border-image: none; height: 15pt;">n
</td><td style="border: 0px black; border-image: none;">Bᶠn
</td><td style="border: 0px black; border-image: none;">bᶠn
</td><td style="border: 0px black; border-image: none;">
</td></tr></table><p>Roku is obviously another Avatar, and thus has Raava as a source for the rest of bending (excluding ᵊ/Energy), but is again not inheritable. But we can guess that he is an average Bᶠbᶠ. Ta Min his wife is a nonbender presumably and so is Rina their daughter. Rina and Jinzuk had Ursa and she was also a nonbender, but in order for Zuko and Azula to both be firebenders with the highest probability, she has to at least carry the firebending gene, so Rina is for this argument the Nbᶠ, and likewise the same Nbᶠ will be in Ursa:
</p>
<table border="0" cellpadding="0" cellspacing="0" style="width: 256px; width: 192pt; border-collapse: collapse;"><tr style="height: 15pt;"><td style="height: 20px; width: 64px; border: 0px black; border-image: none; width: 48pt; height: 15pt;">
</td><td style="width: 64px; border: 0px black; border-image: none; width: 48pt;">
</td><td colspan="2" style="width: 128px; border: 0px black; border-image: none; width: 96pt;">Ozai
</td></tr><tr style="height: 15pt;"><td rowspan="3" style="height: 60px; border: 0px black; border-image: none; height: 45pt;">Ursa
</td><td style="border: 0px black; border-image: none;">
</td><td style="border: 0px black; border-image: none;">Bᶠ
</td><td style="border: 0px black; border-image: none;">bᶠ
</td></tr><tr style="height: 15pt;"><td style="height: 20px; border: 0px black; border-image: none; height: 15pt;">N
</td><td style="border: 0px black; border-image: none;">BᶠN
</td><td style="border: 0px black; border-image: none;">Nbᶠ
</td></tr><tr style="height: 15pt;"><td style="height: 20px; border: 0px black; border-image: none; height: 15pt;">bᶠ
</td><td style="border: 0px black; border-image: none;">Bᶠbᶠ
</td><td style="border: 0px black; border-image: none;">Bᶠx
</td></tr></table><p>
Ozai is part of the royal family who are notoriuos firebenders so he is Bᶠbᶠ at an average. This gives Zuko and Azula 3/4 chance that they would be firebenders.
</p><p>This logic proves a lot of things that are canon in terms of known benders and nonbenders, but is just a theory, using a lot of guess work and assumptions to prove them correct. and I bet someone has made one that makes a lot more sense than this one, as well as explaining all the things in genetics better than I made.
</p><p>If anyone can think of something better than what I tried to make, then I encourage you to put forward something else to this.
</p>