## Genetics in a species with three sex chromosomes

For the discussion of math. Duh.

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captHij
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### Genetics in a species with three sex chromosomes

My daughter is in middle school and is an aspiring writer. I came home last night, and she was trying to think through what would happen in a society with three genders. So, we started thinking about the gender ratios and started tinkering with the Medelian genetics of the situation. So, we came up with a basic set of properties and a few simple rules, and then we asked about the implications. (Hence the reason to put this in the math forum.)

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:

Code: Select all

F  M  V
64 64 24

The chromosome frequencies are given below:

Code: Select all

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:

Code: Select all

F  M  V
24 64 96

The chromosome frequencies are given below:

Code: Select all

X  Y  Z
X 24 24 24
Y 24 16 24
Z 24 24  0

Zohar
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### Re: A World With Three Genders

It's worth noting there's a lot more than two genders in the real world, and have been recognized as such for thousands of years. Incidentally, there are also a lot more than two possible sets of genes, and a lot more than two versions of reproductive systems, and none of those things have to fit together with someone's gender.
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captHij
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### Re: A World With Three Genders

Zohar wrote:It's worth noting there's a lot more than two genders in the real world, and have been recognized as such for thousands of years. Incidentally, there are also a lot more than two possible sets of genes, and a lot more than two versions of reproductive systems, and none of those things have to fit together with someone's gender.

I agree, and this is a good point. In terms of coming up with simple rules and asking about the implications this seems like an interesting start point to go back to the most basic scenario.

Zohar
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### Re: A World With Three Genders

It's maybe a fun way to talk with your daughter about statistics and analysis, but it's important to emphasize the basic scenario you're talking about doesn't actually occur in the world.
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Nicias
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### Re: A World With Three Genders

You are talking about sex no gender.

Also, there are a variety of sex determination systems used by sexually reproducing life.

https://en.wikipedia.org/wiki/Sex-determination_system

morriswalters
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### Re: A World With Three Genders

If she is interested in how it has been handled fictionally, she might want to look at the Ringworld books. Niven describes a species called Pierson's Puppeteers.
Biologically, Puppeteers are highly intelligent herbivores; a herd animal, Puppeteers prefer the company (and smell) of their own kind. Their cycle of reproduction is similar to that of Earth's digger wasps: the Puppeteers consider themselves to have three genders (two male, one female): the two "male" genders are the equivalent of human female and male (one has an ovipositor, the other produces sperm) and the "female" is a (non-sentient) parasitized host into which the ovum and spermatozoon are deposited.

PeteP
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### Re: A World With Three Genders

Hmm taking your distribution for the first (with y>x>z) (rounding a bit)

Code: Select all

yy:--
yz: 1/6=2/12
yx:1/6=2/12
xx:1/6=2/12
xz:1/4=3/12
zz:1/4=3/12

(assuming no bias) results in:

Code: Select all

yy:--
yz: 1/6=2/12 =>1/6*(2/8*(1/2 xy 1/2 xz) +3/8*(1/4 xy 1/4 xz 1/4 zz 1/4 zy) + 3/8(1/2 zy 1/2 zz) )
yx:1/6=2/12 =>1/6*(2/8*(1/2 xy 1/2 xx) +3/8*(1/4 xy 1/4 xz 1/4 xx 1/4 zy) + 3/8(1/2 zy 1/2 zx) )
xx:1/6=2/12 =>  1/6*3/7*xz
xz:1/4=3/12=>1/4*3/7*(1/2xz 1/2 zz)
zz:1/4=3/12

Code: Select all

yy:--
yz: 1/6*3/8*1/4+1/6*3/8*1/2+ 1/6*3/8*1/4+1/6*3/8*1/2=0.09375  =>(dividing by sum)0.212
yx: 1/6*2/8*1/2+1/6*3/8*1/4+1/6*2/8*1/2+1/6*3/8*1/4=0.0729=>0.165
xx:1/6*2/8*1/2+1/6*3/8*1/4=0.0365=>0.082
xz:1/6*2/8*1/2+1/6*3/8*1/4+1/6*3/8*1/4+1/6*3/8*1/2+1/6*3/7=0.15476=>0.35
zz:1/6*3/8*1/2+1/4*3/7*1/2=0.0848=>0.19
0.09375+0.0729+0.0365+0.15476+0.0848=0.44271

Did I mess up somewhere or is that no stable distribution?

doogly
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### Re: A World With Three Genders

Nicias wrote:You are talking about sex no gender.

Sure, but really, all of the problems with dualism when applied to male/female are again encountered with sex/gender.
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captHij
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### Re: A World With Three Genders

@Nicias
- yeah, I should have said sex and not gender. Sorry about that. As noted by doogly, though, it still has the same issues. The wiki link looks interesting. I will have to take a closer look.

@morriswalters
- Thank you! I will pass on the pointer, and I am sure she will appreciate it.

@PeteP
- I took a quick peak at your numbers and did not immediately see anything off. The script assumes everything is iid so it has to be stable. If not then it would imply my script is wrong.

PeteP
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### Re: A World With Three Genders

Ignore mine wrong proportions, since order doesn't actually matter I assumed xy and yx were the same entries but looking at the f/m/v numbers you have to add them together.

gmalivuk
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### Re: Genetics in a species with three sex chromosomes

Sex isn't the same as gender, sex chromosomes aren't the only way biological sex is determined, and not all humans have exactly two of each chromosome.

I've changed the thread title to be more specifically about the genetic implications of having three sex chromosomes.
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PeteP
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### Re: Genetics in a species with three sex chromosomes

Anyway one result (int the y>x>z case) is that if you isolated a subcommunity of F and V after one generation there would be no xx in the population and a high proportion of xz but that would quickly turn into 50/50 xz/zz. (Unless you start only with xx and zz then you only last one gen of course.)

(Though honestly from a story perspective details about chromosome distribution is one of the last interesting things. )

gmalivuk
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### Re: Genetics in a species with three sex chromosomes

It could be interesting background to have in a story that you want to retain appeal for the sorts of pedantic nitpickers most of us probably are, at least for certain subjects.

If something is described as having a genetic component, no matter how passingly, there will always be bionerd readers who try to figure out the dominant/recessive patterns and so forth. (And reproduction always has a genetic component, even if not described explicitly as such, so if a species in the story has more than two distinct reproductive sexes, people will also be interested in how that works, even if they don't need it laid out explicitly.)
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PeteP
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### Re: Genetics in a species with three sex chromosomes

Oh yeah it makes sense to think about it and make something that is consistent but it is not necessarily something you want to explain explicitly. And if you want to do something that doesn't quite fit the simple model there are plenty ways to justify it by declaring it to be more complex. You can have external factors during development that trigger an specific expression of the genes instead of it just depending on which you have. If you get further away from humans you can have life stages where the sex changes at some point. It could depend on multiple genes interacting. Etc.

Soupspoon
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### Re: Genetics in a species with three sex chromosomes

Or throw a 'curveball' with a ZW-like system, flipping the 'dominance/determination', and allowing for parthenogenic production of 'missing males'.

(Not sure how you'd do that (via diploidy) for three sexes, given a missing haploid from a pair would always be missing, but an artificially two-determinant population of various combinations might have a limited viability until an individual possessed of the missing 'flavour', whichever that might be, entered into the system. In social animals, could be quite the 'event' when a peripatetic invited/uninvited guest comes to stay and re-add that component (and others) into a stagnant gene pool.)

And can dominance be Rock/Paper/Scissors-like, perhaps? Then secondary characteristics of the three diploid pairings dictate the relative usefulness to the population (e.g. strength, intelligence and resilience) to twist the sexual-allelle frequencies, according to the type(s) of challenges (conflict, stagnation, famine?1) the population has need to survive.

But that looks too artificially balanced. Zexual dimorphism (above-mentioned Puppeteers, or an extension of the 'squid/coral' marriages of Stewart/Cohen's "Heaven" waterworld is much more typical of sexual dynamics than "equal but different", which seems to me to be a fragile pact of equality that would surely be competitively unbalanced by the first creature born that has a chance advantage over the other-sexes.

1 There's an old Universe Simulator project I was working on, years back that used a three-way RPS system of competition and cohabitation. I might be reviving it, so I'm trying to avoid the 'better' descriptors to avoid giving too much away should it ever finally see the light of day (fat chamce!). Though these weren't interbreeding populations, but separate civilisations each specialising (with options to slowly change, losing qualities to gain qualities) in a different aspect of the RPS-ish continuum.

arbiteroftruth
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### Re: Genetics in a species with three sex chromosomes

Things get interesting if you assume the genes are selfish in their sexual preferences. So that for example, an XY male would typically prefer an XX female over a ZZ V-male, because the XY male's X chromosome would contribute an instinct to propagate the X chromosome rather than the Z. Conversely, a YZ male would prefer ZZs as the best mates. An XX female would prefer XY males who share the X chromosome, rather than YZ males or ZZ V-males who don't. ZZs would prefer YZs and XZs about equally, and would be less pleased with XYs and XXs.

If we assume these tendencies are absolute across the population, then the species will diverge. XY males and XX females would have equal populations and mate almost exclusively with each other. YZ males and XZ females would have a combined population equal to the ZZ V-males, and YZs and XZs would each mate almost exclusively with ZZs and not with each other. The species would only be held together by relatively rare exceptions in which the populations interbreed, or in which YZs and XZs mate and create new XYs.

But overall, the species would tend to diverge into two subspecies. And within the XZ/YZ/ZZ species, the XZs and YZs will tend to be in competition for mates, so there's a good chance one or the other would die out, and you'd be left with two ordinary two-sex species, one consisting of XYs and XXs, and one consisting of ZZs and either XZs or YZs, but not both.

elasto
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### Re: Genetics in a species with three sex chromosomes

Your daughter may also be interested in reading Asimov's "The Gods Themselves", which he described as his favorite novel. About a third of it takes place in a parallel universe amongst an alien species with three sexes.

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### Re: Genetics in a species with three sex chromosomes

A biology caveat to what looks like a fun math problem:

There is no reason to assume for a fictional species that sex determination is chromosomal. For instance, for some species, sex is determined by incubation temperature.

All you need for N biological sexes in a fictional species is to posit that there are biological pathways that reliably split into N different directions. Split those pathways with different chromosomes if you want, but you don't need to.

Eebster the Great
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### Re: Genetics in a species with three sex chromosomes

An interesting question is about mammals with three sexes. There are apparently several, but one I am familiar with is the Andean muroid (mouselike rodent) genus Akodon. Akodons technically have just two sexual phenotypes: male and female, but the genetic story is considerably more complicated. There are many species of akodon, but in a typical example, there are three sex chromosomes, labelled X, Y, and Y*, resulting in XY males, XX females, and XY* heterozygous "sex-reversed" females. Because the Y*Y zygotes are nonviable, YY is impossible. To compensate for nonviable Y*Y zygotes, XY* females have superior sexual performance to XY females: so much so that in many populations, most females are sex reversed and males are comparatively rare. The Y and Y* chromosomes have the same shape but differ in C-banding patterns, and such a situation is possible due to the fragile nature of the SRY (sex-determining region of Y) gene, which is the primary sex-determiner in mammals and which may also be responsible for some of the complications in human sex-assignment.