Meta: The genetics of bending
May. 22nd, 2012 10:05 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
dhampyresaIn this post, I'm going to take a look at the genetics involved in the inheritance of Bending ability in Avatar: the Last Airbender (AtLA) and Avatar: the Legend of Korra (LoK).
First off, I I will be using several terms of varying technicality levels and will therefore define them.
Genotype: the actual genetic make-up of an individual (here, bending/non-bending genes).
Phenotype: any and all observable traits of an individual (here, bending ability or lack thereof).
Alleles: the different forms of a gene.
Recessive allele/gene: an allele that needs to be present twice to be expressed.
Dominant allele/gene: an allele that needs to be present only once to be expressed.
I will be holding these two things true throughout: the bending gene has 5 alleles (b (non-bender), A (airbender), E (earthbender/metalbender), F (firebender) and W (waterbender)) and only the Avatar can bend more than one element meaning that the genotypes AE, AF, AW, EF, EW and FW all have a non-bending phenotype.
This image shows the family tree of Katara and Sokka, going back one generation (Kya and Hakoda). Circles indicate women and squares men. Waterbenders are blue and non-benders (i.e. anyone who has not bended any element over the course of either AtLA or LoK) are grey.
This repartition (gene unexpressed in parents/expressed in child) classic for a recessive gene. This would make Katara's genotype WW, Hakoda and Kya's Wb and Sokka's either Wb or bb.
If we take the view that all bending alleles share the same property (dominant/recessive), this would mean that Aang's genotype is AA.
However, this would mean that all of their children's genotype would be AW and they would therefore have a non-bending genotype. We know this isn't the case: not only is Tenzin an Airbender in LoK but using this image we learn that they have a waterbender child (Kya), a non-bender child (Bumi) and an airbender child (Tenzin).
This configuration is only possible if we posit that both Katara and Aang are carriers of a non-bending allele (b), making their genotypes Wb and Ab respectively. As they are both benders, this would mean that bending is a dominant allele. As such, the genotypes would be: Katara (Wb), Aang (Ab), Kya (Wb), Bumi (either AW or bb), Tenzin (Ab) with Pema (bb) and all his kids being Ab.
For the record, each of Tenzin's children have a 50/50 chance of turning out to be an airbender, meaning that there is a 12,5% probability of all three of them being, which is reasonable.Another bending kid would strech my credibility a bit, though.
But hold on! If Bending is dominant and both Katara's mother and father are Wb, wouldn't that mean they are both waterbenders? Well, yes, it would, but this premise is flawed: they are only both Wb if bending is recessive. Since bending is dominant, it is entirely possible that the genotypes go Hakoda (bb), Kya (Wb), Sokka (bb) and Katara (Wb) instead.
Yes, this means that Katara's mom was a waterbend.
Why not her father? Because if he was a bender he would have used his bending over the AtLA series.
You could say the same about Kya! Contrary to Hakoda, Kya is only present in AtLA in flashbacks. What's more, she was killed for being a waterbender: I find it unlikely that elite Fire Nation troops wouldn't check before killing her that she was a waterbender, given that killing the waterbender was their mission.
Then why don't Katara and Sokka know their mother was a waterbender? Probably because she never waterbended, in an attempt to not draw the Fire Nation's attention to the South Pole.
I'm still not convinced. Fair enough, it's possible that for whatever reason, Kya's waterbending gene didn't express itself properly and she was unable to waterbend.
TL;DR Bending is a dominant gene and Katara's mom was a waterbender.
First off, I I will be using several terms of varying technicality levels and will therefore define them.
Genotype: the actual genetic make-up of an individual (here, bending/non-bending genes).
Phenotype: any and all observable traits of an individual (here, bending ability or lack thereof).
Alleles: the different forms of a gene.
Recessive allele/gene: an allele that needs to be present twice to be expressed.
Dominant allele/gene: an allele that needs to be present only once to be expressed.
I will be holding these two things true throughout: the bending gene has 5 alleles (b (non-bender), A (airbender), E (earthbender/metalbender), F (firebender) and W (waterbender)) and only the Avatar can bend more than one element meaning that the genotypes AE, AF, AW, EF, EW and FW all have a non-bending phenotype.
This image shows the family tree of Katara and Sokka, going back one generation (Kya and Hakoda). Circles indicate women and squares men. Waterbenders are blue and non-benders (i.e. anyone who has not bended any element over the course of either AtLA or LoK) are grey.
This repartition (gene unexpressed in parents/expressed in child) classic for a recessive gene. This would make Katara's genotype WW, Hakoda and Kya's Wb and Sokka's either Wb or bb.
If we take the view that all bending alleles share the same property (dominant/recessive), this would mean that Aang's genotype is AA.
However, this would mean that all of their children's genotype would be AW and they would therefore have a non-bending genotype. We know this isn't the case: not only is Tenzin an Airbender in LoK but using this image we learn that they have a waterbender child (Kya), a non-bender child (Bumi) and an airbender child (Tenzin).
This configuration is only possible if we posit that both Katara and Aang are carriers of a non-bending allele (b), making their genotypes Wb and Ab respectively. As they are both benders, this would mean that bending is a dominant allele. As such, the genotypes would be: Katara (Wb), Aang (Ab), Kya (Wb), Bumi (either AW or bb), Tenzin (Ab) with Pema (bb) and all his kids being Ab.
For the record, each of Tenzin's children have a 50/50 chance of turning out to be an airbender, meaning that there is a 12,5% probability of all three of them being, which is reasonable.Another bending kid would strech my credibility a bit, though.
But hold on! If Bending is dominant and both Katara's mother and father are Wb, wouldn't that mean they are both waterbenders? Well, yes, it would, but this premise is flawed: they are only both Wb if bending is recessive. Since bending is dominant, it is entirely possible that the genotypes go Hakoda (bb), Kya (Wb), Sokka (bb) and Katara (Wb) instead.
Yes, this means that Katara's mom was a waterbend.
Why not her father? Because if he was a bender he would have used his bending over the AtLA series.
You could say the same about Kya! Contrary to Hakoda, Kya is only present in AtLA in flashbacks. What's more, she was killed for being a waterbender: I find it unlikely that elite Fire Nation troops wouldn't check before killing her that she was a waterbender, given that killing the waterbender was their mission.
Then why don't Katara and Sokka know their mother was a waterbender? Probably because she never waterbended, in an attempt to not draw the Fire Nation's attention to the South Pole.
I'm still not convinced. Fair enough, it's possible that for whatever reason, Kya's waterbending gene didn't express itself properly and she was unable to waterbend.
TL;DR Bending is a dominant gene and Katara's mom was a waterbender.
(no subject)
Date: 2012-05-22 09:59 pm (UTC)That way the young Kya, Bumi, and Tenzin could all have the AW genotype, in which some other factor determines whether A or W or neither gets expressed.
Granted, it only works if Pema is a mixed-type nonbender, rather than a bb-type nonbender, so that her kids would all be mixed-type Airbenders. We'll have to wait on her backstory for that...
Knowing Mako and Bolin's history would help too. If bending is recessive, they're FF and EE, and their parents must both have been FE (meaning their grandparents must have been in two mixed-nation marriages). If bending is dominant and mixed genotypes are nonbending, they're Fb and Eb, and their parents were either Fb and Eb (both benders), or FE and bb (both nonbenders, one set of mixed-nation grandparents). And if nonbending is dominant and mixed genotypes express in various ways, they're both FE, and their parents were Fb and Eb (both nonbenders, no earlier mixed marriages). The last one is the backstory I would have guessed for them, if nothing else.
I do feel like, if bending is a simple dominant trait, there should be a lot more benders than there are.
...ooh! What if there's a "nonbending" allele that's dominant (B) as well as the recessive "eh, do what you want" allele (b)? That way you could have Kya as BW, and Hakoda as Bb, WB, or bb, leaving Katara as WW or Wb (and Sokka as BB, Bb, or BW)...and I'm going to cut myself off here before I start trying to draw up according squares for everyone like some kind of demented bendy Sudoku.
tl;dr This was an interesting post, thank you for making it :D
(no subject)
Date: 2012-05-23 07:40 pm (UTC)The bending gene having 6 alleles is good idea and not one I'd thought of. I had originally gone with two genes: 1) B/b that allowed bending or not and 2) A/E/F/W/N that determined what, if anything, someone could bend. If Pema was AA/Bb and Tenzin AN/BB, their kids could be AA/BB, AA/Bb, AN/BB and AN/BB.
If the non-bender allele dominant for gene 1 and gene 2 being heterozygous means non-bending and non-bending being recessive, we'd get a 25% x 48% = 12% bending rate. If we assume recessive non-bending for gene one we get 75% x 48% = 36% which is closer to the rate in the series, I think.