I will post some of our results below, but I was wondering if this has come up here before. It seems like a Randallian thing to do. I tried searching the forum, but it would seem that the word "gender" comes up in nearly every thread here.

Anyway, here is what we got. We assumed three chromosomes, X, Y, and Z. There are three genders, M, F, and V. (Her name for the third gender started with V.) Each person has a diploid (two chromosomes) that determines gender. Two people can reproduce if their genders differ. The M gender does not give birth.

This morning I made up a quick and dirty code in R to sort things out. You can find it at http://pastebin.com/ZFNf5crs I did it while half asleep this morning so it is likely wrong. */disclaimer* (Change line 45 to change the dominant/recessive relationship that is used.)

We looked at two different dominant/recessive relationships. The first is Y is dominant to X, and X is dominant to Z. So if any chromosome is Y the result is an M gender. Otherwise, if any chromosome is X the result is an F gender. Everybody else is a V gender. In this case the numbers of peoples of different genders is given below:

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` F M V `

64 64 24

The chromosome frequencies are given below:

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` `

X Y Z

X 16 16 24

Y 16 0 16

Z 24 16 24

The other relationship we looked at is Z is dominant to Y, and Y is dominant to X. So if any chromosome is Z the result is gender V. Otherwise, if any chromosome is Y the result is M, and otherwise the result is F. The interesting thing here is that it is possible to get a person with YY diploid. (We decided that Manly Dan Corduroy from the show Gravity Falls is YY.) In this case the gender frequencies are the following:

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` F M V `

24 64 96

The chromosome frequencies are given below:

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` X Y Z`

X 24 24 24

Y 24 16 24

Z 24 24 0