OF GENETIC DOMINANCE OR RECESSION
theory suggested by Houkiboshi that will attempt to compare the genetics of an Uchiha-Hyuga offspring and an Uchiha- -x- offspring.
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Mendel's Law of Segregation
A pair of alleles compose a gene; a gene codes for a trait. A gene coding for a trait is the same for all individuals; its the variation of alleles that accounts for the differences from one individual to another.
In Naruto, for example, a specific gene(s) codes for a bloodline limit; the variations in allele combinations allows for the coding of different types of bloodline limit.
An offspring will inherit one allele from each parent, a segregation that only occurs during conception.
When the combination is heterozygous (dissimilar alleles, example: Ss, Bb, Nn), one allele will be dominant than the other; whichever will be a matter of chance. This dominant allele will code for a dominant trait which will be expressed by the offspring. The recessive allele, however, will be unaltered and may be passed on the next generation for another equal chance of dominating in somebody else's lifetime. This dominant-recessive relationship is also called simple dominance.
Mendel's Law of Independent Assortment
This law states that the inheritance of one trait is independent of another.
Theory assumptions and their explanations
(1) One gene is sufficient to code for a bloodline limit.
In reality, one or more genes may code for one trait but in this theory, one gene coding for a bloodline limit is assumed for easier understanding.
(2) Bloodline limit alleles are more dominant than non-expressing alleles.
So far, it has been shown that the offspring of clans with bloodline limits or perform family-exclusive specialized jutsus have all manifested such traits. Thus, alleles responsible for these may be naturally dominant.
(3.) Sharingan is more dominant than byakugan.
The question of which is more dominant between two bloodline limits is yet to be officially answered.
It was stated that the Uchiha came from Hyuga. Consider that had byakugan been more dominant, there would have been no Uchiha branching out in the first place.
Natural Selection by Darwinian Evolution
Sharingan may also be caused by germline mutation, a type of genetic mutation that can be passed on to descendants. Mutation of the byakugan, by itself or in combination with another bloodline, may have created a change in genetic alleles leading to the evolution of the sharingan. By natural selection, the less favorable mutations are removed and the favorable ones will persist. If so, sharingan was then more favorable than byakugan.
Even in the first few years of the Uchiha clan, there might have been an equal chance of byakugan resurfacing (based on Mendel's Law of Segregation). This didn't seem to happen since the Uchiha clan progressed.
(4.) To take into consideration the possibility that clans may marry inside and outside their families, Sasuke, Hinata and -x- are given two possible allele combinations.
Sasuke's alleles are represented by SS or Ss ; where S = sharingan allele , s = non-sharingan allele
Hinata's alleles are represented by BB or Bb ; where B = byakugan allele , b = non-byakugan allele
-x- alleles are represented by NN, nn or Nn ; where N and n = non-bloodline limit alleles
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The following are probabilities of allele combinations of an offspring of Sasuke and Hinata using the Punnett Square (Mendelian Genetics) and the assumptions stated (sharingan > byakugan > non-bloodline limit alleles).
Probability 1 - Parents' alleles are homozygous
SS + BB = SB
The offspring have: Mendelian Genetics 50% chance of inheriting sharingan ; 50% chance of inheriting byakugan Assumptions 100% chance of inheriting sharingan
Probability 2 - One parent's alleles are heterozygous
SS + Bb = SB , Sb
The offspring have:
Mendelian Genetics First combination - 50% chance of inheriting sharingan ; 50% chance of inheriting byakugan Second combination - 50% chance of inheriting sharingan ; 50% chance of inheriting no bloodline limit
Assumptions 100% chance of inheriting sharingan for both combinations
Or
Ss + BB = SB , sB
The offspring have:
Mendelian Genetics First combination - 50% chance of inheriting sharingan ; 50% chance of inheriting byakugan Second combination - 50% chance of inheriting byakugan ; 50% chance of inheriting no bloodline limit
Assumptions First combination - 100% chance of inheriting sharingan Second combination - 100% chance of inheriting byakugan
Probability 3 - Parents' alleles are heterozygous
Ss + Bb = SB , Sb , sB , sb
The offspring have:
Mendelian Genetics First combination - 50% chance of inheriting sharingan ; 50% chance of inheriting byakugan Second combination - 50% chance of inheriting sharingan ; 50% chance of inheriting no bloodline limit Third combination - 50% chance of inheriting byakugan ; 50% chance of inheriting no bloodline limit Fourth combination - 100% chance of inheriting no bloodline limit
Assumptions First combination - 100% chance of inheriting sharingan Second combination - 100% chance of inheriting sharingan Third combination - 100% chance of inheriting byakugan Fourth combination - 100% chance of inheriting no bloodline limit.
Over-all , an offspring of Sasuke and Hinata have:
Mendelian Genetics 33.33% chance of inheriting sharingan 33.33% chance of inheriting byakugan 33.33% chance of inheriting no bloodline limit
Assumptions 66.67% chance of inheriting sharingan 22.22% chance of inheriting byakugan 11.11% chance of inheriting no bloodline limit
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The following are probabilities of allele combinations of an offspring of Sasuke and -x- using the Punnett Square (Mendelian Genetics) and the assumptions stated (sharingan > byakugan > non-bloodline limit alleles).
Probability 1 - Parents' alleles are homozygous
SS + NN (nn) = SN (Sn)
The offspring have: Mendelian Genetics 50% chance of inheriting sharingan ; 50% chance of inheriting no bloodline limit Assumptions 100% chance of inheriting sharingan
Probability 2 - One parent's alleles are heterozygous
SS + Nn = SN , Sn
The offspring have: Mendelian Genetics First combination - 50% chance of inheriting sharingan ; 50% chance of inheriting no bloodline limit Second combination - 50% chance of inheriting sharingan ; 50% chance of inheriting no bloodline limit Assumptions 100% chance of inheriting sharingan for both combinations
Or
Ss + NN = SN , sN
The offspring have: Mendelian Genetics First combination - 50% chance of inheriting sharingan ; 50% chance of inheriting no bloodline limit Second combination - 100% chance of inheriting no bloodline limit Assumptions First possible combination - 100% chance of inheriting sharingan; Second possible combination - 100% chance of inheriting no bloodline limit
Probability 3 - Parents' alleles are heterozygous
Ss + Nn = SN , Sn , sN , sn
The offspring have: Mendelian Genetics First combination - 50% chance of inheriting sharingan ; 50% chance of no bloodline limit Second combination - 50% chance of inheriting sharingan ; 50% chance of inheriting no bloodline limit Third combination - 100% chance of inheriting no bloodline limit Fourth combination - 100% chance of inheriting no bloodline limit Assumptions First combination - 100% chance of inheriting sharingan Second combination - 100% chance of inheriting sharingan Third combination - 100% chance of inheriting no bloodline limit Fourth combination - 100% chance of inheriting no bloodline limit
Over-all , an offspring of Sasuke and -x- have: Mendelian Genetics 33.33% chance of inheriting sharingan 66.67% chance of inheriting no bloodline limit Assumptions 66.67% chance of inheriting sharingan 33.33% chance of inheriting no bloodline limit
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Based on simple dominance and on the assumptions, an offspring of Sasuke and Hinata will have equal chances of inheriting sharingan compared with an offspring of Sasuke and -x-. Nevertheless, because Hinata has the byakugan, an offspring of Sasuke and -x- will have higher chances of not inheriting any bloodline limit.
Inheritance, however, do not always follow simple dominance.
One exception is incomplete dominance, where when two heterozygous alleles are inherited, an intermediate may also be created.
An offspring of Sasuke and Hinata may inherit certain elements of the sharingan and the byakugan; An offspring of Sasuke and -x- may only inherit certain elements of the sharingan.
Another exception is codominance, which states that when two heterozygous alleles are inherited, both traits may be expressed.
If this occurs, an offspring of Sasuke and Hinata may inherit both the sharingan and the byakugan; An offspring of Sasuke and -x- may simply inherit the sharingan.
Based on Mendel's Law of Independent Assortment, do note that an offspring who inherits a bloodline limit must also inherit the ability to control it. An example is Kakashi's sharingan, which he seems unable to deactivate likely because of his non-Uchiha traits.
Moreover, having inherited the trait to use the sharingan do not necessarily mean an offspring may be able to readily use it. The user may need to fulfill certain prerequisites to manifest it; in this case, a user needs to experience a life-threatening circumstance.
Generally, if Sasuke would want to revive a clan, a partnership with Hinata has its advantages against someone with no bloodline limit. That is, if Sasuke would want to retain the sharingan or allow its evolution. There is still the possibility that he may want otherwise. Or whatever Kishimoto rules out of it.