Gender Ratio Speculation: A Mathematical Approach · 12:38pm Jul 20th, 2014
For as long as this fandom has existed, arguments have raged on about the ratio of genders in Equestria; ponies have been counted on screenshots, numbers have been extrapolated, real-world equine populations have been used for comparison.
Alas, none of that will happen here. I'm too lazy for that sort and I simply do this of mathematical curiosity; and work with the tools of mathematics and probabilities I will.
So be warned, ye who abhors numbers and calculations, for those be ahead. You have been warned.
Now that all the neigh-sayers to mathematics and pointless academic thought experiment have left, the fun shall be begun.
This is my first assumption: In Equestrian society, mortality rates are indiscriminate of gender.
That means the birth rates of the respective genders can be assumed equivalent to their actual relative frequency in the entire population if the gender ratio is to be stable.
Let us secondly assume that the gender ratio in Equestria is indeed stable over time.
Further, I assume in the following that the gender of ponies is determined by their genetic make-up in the same way that of earthly mammals is and that the impact of abortion is negligible.
Now let us examine the most basic scenario: foals are born by a mare and sired by a stallion.
This is the simplest of scenarios: the gender ratio is necessarily 1:1 since the probability for a colt to be born is invariably the same as for a filly.
However, in many fan fictions and fan theories (such as, for example, Chengar Qordath's Winningverse) have argued that magic might enable couples of the sex same to have foals.
How would that affect the gender ratio, I ask?
Let x be the relative frequency of mares among the population of Equestria.
If we pick two ponies at random, they both are mares with a probability of x². Such a couple can, by the laws of genetics, only have female offspring.
With a probability of 2*x*(1 - x) = 2x – 2x², we get a mare and a stallion. Such a couple has female offspring in 50% of cases.
With (1 – x)² = 1 – 2x + x² probability, we get a couple of stallions. A foal would be female (XX) in 25%, male (XY) in 50% and undefined (and probably dead) (YY) in 25% of cases; the ratio between fillies and colt is 1:2, the probability of female offspring therefore 33.3% or ⅓.
As a result, the probability for a female pony from a random couple must be x² + ½ * (2x – 2x²) + ⅓ * (1 – x)².
If we set this relative birth rate equal to the relative frequency of mares, we get the lovely equation
x = x² + ½ * (2x – 2x²) + ⅓ * (1 – x)² which simplifies to
x = x + ⅓ * (1 – x)² and can be put as
0 = (1 – x)² and has the solution
x = 1
This means if monogendered couples can have children and ponies pick there mates at random, stallions will go extinct. As that has not happened, we can safely assume that ponies do not pick their mates at random, or rather, indiscriminate of gender. In other words, not everypony is bisexual.
To represent this, I will assume a certain percentage of couples to be composed of mare and stallion and the remaining to be of two ponies of same gender in relation to a certain relative frequency of heterosexual/homosexual orientation. In correlation to real-world figures and with some rounding, I will assume the percentage of homosexual couples in an assumed prosecution-free Equestria to be 10%.
Now we have the following probabilities for a randomly chosen couple:
x/10 for a female homosexual couple,
90% for a heterosexual couple,
and (1-x)/10 for a male homosexual couple.
The probability for a filly to be born from a random couple is therefore x/10 + ½ * 0.9 + ⅓ * (1-x)/10.
We, again, set this equal to x:
x = x/10 + ½ * 0.9 + ⅓ * (1-x)/10 which equates to
30x = 3x + 27/2 + 1 – x and
28x = 29/2 therefore
x = 29/56 or about 52%.
Therefore, the resulting gender ratio in a world where monogendered couples can have foal, the gender ratio should be about 52:48 in favour of the female population.
Huh? What's that? You're saying stallions having children with stallions is silly or even impossible?
Okay, if it makes you happy, here are the numbers if we are sexist and say only mares can have children:
In that case, x = 10/19 or about 53% and the gender ratio is 53:47. Doesn't really make that much of a difference, though. Are you happy now?
As this is the probably most offensive thing I have ever written, I think I ought to clarify a few things.
If you are homosexual, bisexual, heterosexual, polysexual, pansexual, rainbowsexual, in some other way sexual or even completely asexual, it was never my intention to offend you, and I'm sorry if you feel offended.
If you have a genetic composition outside that which is considered 'normal', I also didn't intend to offend you and I'm sorry if you are.
If you are a bigot, a hypocrite, humourless or vanilla ice cream, it probably was my intention to offend you, and if you are offended, tell me so I can gloat.
If you are me, you should be ashamed of yourself (and myself), because you are a bad person and should feel bad.
Lastly, I used only a very approximate model in my calculations and haven't really taken anything but what I said into account. Remember that if you want to file any complaints.
I also made this mainly for my own amusement.
Have a nice day.
However, the observed ratio is actually much lower.
I was just rewatching Return of Harmony. In Cheerilee's class, there are the CMC, the two bullies, Twist, Snips, and Snails. So the ratio of fillies to colts is 6:2, or 75%/25%.
Unless Equestria has a prejudice against boys getting an education, and therefore they are underrepresented in the school population, this implies either a lot of female/female pairings... or a lot of male fetuses miscarrying.
Explanations for the dearth of adult males can include "stallions frequently go into the military, so the Royal Guard is all stallions and that means the stallions aren't at home." But this doesn't work for children. Now maybe it's a one-off and other schools (and classes) aren't like this, but the ratio among the children is consistent with the ratio seen among the adults.
My theory is that stallions, in the wild, are significantly more violent than mares. So the Tree of Harmony is actually causing a significant percentage of male conceptions to miscarry at the embryonic stage, possibly before the mare even knows she's pregnant, because a society that is heavily dominated by mares will be able to put enormous cultural pressure on stallions to conform to mare cultural values.
In almost every species on Earth, males are more violent than females; this may in fact be the only biologically based personality difference, because it's the only one that consistently shows up in all primates and all cultures of humanity. This doesn't make females necessarily pacifistic, but it does imply that if you really, really, really want a harmonious society and are willing to do awful things to get one, aborting half the unborn boys might be a strategy to achieve it. I can't see the ponies willingly doing this -- they do not exhibit the misandry that would be necessary to get mothers to cooperate with sex-based abortion. So something's doing it to them. What do we know that's very powerful, viewed almost unequivocally as benevolent, and really cares a lot about Harmony?
It's kinder to imagine that the ratio of female homosexuality is actually much, much higher than it is on Earth, and that female homosexuals can reproduce together with magic, but that male homosexuals cannot. (This is not as sexist as it sounds. Females actually have all the necessary equipment to gestate a pregnancy; all the magic would need to do is get the DNA of the other mare into a form that it could inseminate the mother. Males would need to actually grow an entire reproductive apparatus and start making eggs; you could teleport the nucleus of an egg into another egg and thus get away without sperm, but you can't combine two sperm and have them behave like an egg.) There's an understandable mechanism behind this, based on your ratio:
Ponies are not all bisexual. However, most ponies are sexual -- they do seek romantic love and sexual conjugation from a partner. And sexual beings who are deprived of their preferred partner type are well known to be able to switch if they have to, thus male/male relationships on ships and in prisons.
If the rate of female homosexuality started out at 10%, producing 53% mares, then 6% of the mare population has no stallion to partner with them. Since male homosexuality is also 10%, the gays drop out of the equation, as for every happy lesbian couple there's a pair of happy gay stallions and thus the shortage for the hetero mares remains constant. Some of those mares will seek romance with each other, even though that is not their preference, because ponies appear to be monogamous, despite the prevalence of stallions having harems in the animal kingdom. Say that 2% of the mares remain unpartnered and 4% partner with each other; this drives up the homosexual pairing ratio for females to 14%, but males stay at 10%.
The next generation, the number of fillies is higher, because female-female pairings don't produce males. (I won't bother doing the math to figure out how much higher.) So increment by increment, generation over generation, the percentage of mares in homosexual pairings because there are not enough stallions increases, thus causing the percentage of fillies to colts to increase. If the trend continues indefinitely, stallions will go extinct, but presumably the spell to permit female-female couplings to have children was invented recently enough that that hasn't happened yet.
So. Either something's killing the boys before they're even born, or converting them to girls (the observed ratio would actually be consistent with half the XY conceptions spontaneously transforming into physiological females; that might be more the Tree of Harmony's speed than abortion); or stallions are slowly going extinct because female-female pairings can produce female offspring and mares prefer to have a mare all to themselves than to share a stallion with another mare, even if their true preference would have been to have a stallion if one had been available.
2393308
I'm not touching that. No, brain, shut up. I'm not going to tell the nice lady about the beautiful beautiful thoughts I have on that tree... not yet...
And that's also the point where my equations stop making the slightest bit of sense. They tell me that 75% mares equates to about 67% homosexual couples...
I know.
I was just being silly on that part.
It was just that the maths were a bit simpler if I let stallions have kids.
If everypony takes a partner and has foals, of course.
I have looked down this road of iteration. The maths get quite complicated quite quickly and I'm too lazy. This is why I assumed a stable gender ratio.
The unstable stuff usually ends up with a monogendered population of mares.
Or something happens directly during conception. That would be a lot more energy efficient. And maybe ethically less questionable.
2393308
I apologize for the greentext arrows, as I do not have a know-how on breaking up a quote like Capacitor here does.
The observed ratio is unreliable as long as the bulk of that observed ratio is made up of background pony crowds, which are clone infested, inconsistent, and copy-pasted, to put it as bluntly as possible. The vast majority of the total number of ponies we see in the show are contained in these background pony crowds, and given how odd they can be, they aren't really what I'd call outright proof for anything.
>Explanations for the dearth of adult males can include "stallions frequently go into the military, so the Royal Guard is all stallions and that means the stallions aren't at home."
Reducing the population that significantly would require an exceptionally massive draft of some form, or massive casualties, either of which but especially the latter are pretty dark.
>So the Tree of Harmony is actually causing a significant percentage of male conceptions to miscarry
This whole part about this 'theory' of yours is very disturbing and carries some terribly grim implications. I don't know exactly how to put it, but I don't like it at all. I could say more negative things about it than that, and with greater levels of detail, but honestly I don't know how to properly word it, and it would take a long time to make it satisfactory anyway, so we'll leave it simple I suppose.
>because a society that is heavily dominated by mares
By sheer numbers, or by social/economic power? Because the latter is seemingly wrong from what we can observe, and the former relies on the very headcanon this blog post is discussing. Equestria has a matriarchal government technically, given that all current alicorns are female, but I don't think they really have a matriarchal society, because ponies of both genders in the show have plenty of good careers and positions on an equal-scale, and there's no indication of discrimination. The notion that their society is matriarchal is popular fanon, and while it's certainly not impossible, there's not really as much in the way of directly observable proof for it in the show itself as some people seem to believe.
My current standpoint/theory or whatever is that the background pony crowds are merely inaccurate and the gender ratio is in fact equal. And that Equestria is relatively egalitarian, and lacks matriarchal or patriarchal elements in any significant form. The fact that the ponies are primarily monogamous is more evidence for an equal ratio, unless you also want to pile on the headcanon that they're using some form of mass same-sex reproduction to compensate for a potential imbalance.
But nobody knows for sure about any of this stuff. What information you can pull from the show about stuff like Equestria's society or other statistics, is in the end very limited. With that in mind, it's ultimately uncertain, and we are pretty much just making theories or whatever, with such limited information. Something like that, I don't know.