Aaron Nowack wrote:

As an aside, I remember a discussion on the genetic
inheritance of Bloodline Limits once sprung up on a
web-forum. They figured that since only a few of the
Uchiha clan were able to manifest the Sharingan, and
we'd only seen male Sharingan users, the necessary
traits would mostly likely be on the Y chromosome -
i.e. a patrilineal inheritance. 

Well, we've only seen male Sharingan users, but we've only seen two
female Uchiha that I'm aware of, neither of which in a situation where
they'd use the Sharingan.  For what it's worth, it certainly seems that
Sasuke and Itachi inherited their eyes from their mother, so I'd be
inclined to say that both genders can use the Sharingan.  (Also, it
apparently evvolved from the Byakugan, which we know is gender-neutral.)

However, a matrilineal inheritance makes for much more
comedic effect, at the expense of Sasuke and/or
Itachi. ^_^

I seem to remember reading at least one fairly amusing fic involving a
matrilineal Sharingan inheritance, a drunken Sasuke, Naruto, and Oiroke
no Jutsu.  :)

So do I.

There is a way to mostly make it work with basic mendelian genetics. If 
the Sharingan is a simple recessive mutation of the X chromosome (X'), 
Males are much more likely to have  the sharingan than females, but are 
unable to pass the trait to their sons. Any female sharingan user must 
be X'X', and so all of her sons will be sharingan users.

In this case, Sasuke would be unable to sire a sharingan using Uchiha in 
less than two generations (if his kids are willing to interbreed) unless 
he can find a hybrid XX' female. The Uchiha clan was large, so it might 
be possible, but any bastard children are almost certainly unaware or in 
hiding.

On the other hand, if a sharingan user is female, she'd be X'X'. All of 
her female kids would be XX' hybrids, with a 50% chance of their own 
male kids having the sharingan, and all of her male kids would be X'Y 
sharingan users. This would obviously make any female sharingan user 
much more valuable than a male as breeding stock to anyone interested in 
that bloodline.

Sometimes I put way too much thought into some things.

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