MLP genetics

In _MLP:FiM_, there are 3 apparently separate & specialized pony races: "Earth ponies" (physically strong & naturally gifted at agriculture), the Pegasi (fliers who magically manipulate the weather), and Unicorns (magic specialists - the fourth type of pony, the all-female "Alicorns", are extremely rare and are usually explained as being magical); they are not separate species and can interbreed, but almost all depicted families are homogenous. (All main characters' families are, as far as shown, the same race as their daughter.) The one exception is the Cake Family of bakers, where the two Earth ponies [Mr. and Mrs. Cake](http://mlp.wikia.com/wiki/Mr._and_Mrs._Cake) have two children in season 2 episode 13 (["Baby Cakes"](http://mlp.wikia.com/wiki/Baby_Cakes)), a pair of fraternal twins, who are discordant - Pegasi and Unicorn. When queried by the confused main characters, he claims "My great-great-great-great grandfather was a unicorn, and Cup Cake's great aunt's second cousin twice removed was a Pegasus. That makes sense, right?" The puzzle here is how can we explain that almost all families except the Cakes are homogenous in pony race, but it is still possible for one (or two) occasional discordant offspring?

A polytomous [liability threshold model](!Wikipedia) is sufficiently flexible as to explain all of these patterns by simply setting thresholds appropriately and expecting assortative mating. For example, there could be a single race trait which is polytomous with 2 thresholds, `Pegasi|Earth|Unicorn`, and the thresholds are set sufficiently extreme as to ensure most families of 2-3 children (_MLP_ families tending to the very small) are homogenous, such as at -2SD and +2SD. Then [assortative mating](!Wikipedia) ensures that most Pegasi families have a 'race trait' mean somewhere well below -2SD, Earth families have a mean ~0, Unicorn families have a mean trait >2, etc. Then, if Mr Cake is unusually close the 2SD threshold and Mrs Cake is unusually close to the Pegasus threshold, the two fraternal twins could inherit differentially from their parents and wind up being pushed across different thresholds. (Siblings/fraternal twins may both inherit 50% from each parent, but they will inherit different 50%s at random due to the randomization of [meiosis](!Wikipedia), and their relatedness to each other can easily be ±5%, so in a particularly extreme case perhaps that would be enough.) Alternately, it could be determined by multiple binary liability threshold traits, one for each race, and the expressed race is simply the maximum of the 3 trait values; in which case similar logic holds for the two twins. The mane problem, you might say, with the liability threshold model is that it is, if anything, *too* flexible and so it's hard to provide good evidence picking it out with just the _MLP_ evidence. (In real world genetics, one could accumulate evidence for a liability threshold model by examining 'risk' in increasingly distant relatives and whether it drops off with genetic distance as it should, looking for continuous measurements reflecting an increased genetic trait value like depressed IQ or schizophrenia symptoms in relatives of schizophrenics, or using molecular genetic methods like [GCTA](!Wikipedia) or [GWAS](!Wikipedia) to see if a binary trait is highly polygenic, etc, but none of that is possible here.)

A Mendelian model is a little harder to come up with but there are at least 4 attempts. [HelloNurse](https://news.ycombinator.com/item?id=17051442) suggests a monogenic model with 3 alleles each causing a different race, Earth pony dominance, and epistasis or environmental randomization (ie low penetrance):

> Mendelian ponies could have a single gene with 3 alleles, E/U/P, with EE, EU and EP earth, UU and PP respectively unicorn and pegasus and UP either unicorn or pegasus at random (i.e. depending on other genes). If the two parents are EU and EP they are earth but offspring of all three types is possible. An even simpler model: one gene with two alleles, earth and fancy, earth dominant, fancy ponies become unicorns or pegasi depending on rainbow intensity or other non-genetic factors.

[Grim-S-Morrison](https://grim-s-morrison.deviantart.com/art/Biology-is-Magic-279676444 "Biology is Magic") gives a 2 gene model, with a dominant/recessive Earth/Unicorn effect and a dominant/recessive Pegasus/Unicorn, giving a Punnet table (reproducing in Markdown):

> |    |EuPu (Earth parent)  | |  |  |  |    |
> |----|--|-----|--|--|--|----|
> |EuPu (Earth parent)|  |EP  |Eu   |uP |UU  |
> |    |EP (Earth)|EEPP (Earth)|EEPu (Earth)|EuPP (Earth)|EuPu (Earth)|
> |    |Eu (Earth)|EEPu (Earth)|EEuu (Earth)|EuPu (Earth)|Euuu (Earth)|
> |    |uP (Earth)|EuPP (Earth)|EuPu (Earth)|uuPP (Pegasus)|uuPu (Pegasus)|
> |    |uu (Earth)|EuPu (Earth)|Euuu (Earth)|uuPu (Pegasus)|uuuu (Unicorn)|
>
> Table: Grim S Morrison's 2-gene model using Earth pony dominance; hypothetical [Punnett square](!Wikipedia) for Mr & Mrs. Cake

This admittedly has some problems explaining why Pegasi and Unicorns appear to be quite common in Equestria; it would require an extreme caste system to keep Pegasi & Unicorn families highly homogenous & a large fraction of the population, rather than being submerged in Earth ponies and mostly popping up in Earth pony families, which is so rare that multiple adult ponies could be quite surprised at any discordance. And of course, if two Pegasi ever have Earth pony offspring (rather than Pegasi or Unicorn) or two Unicorns are ever shown as having non-Unicorn offspring, the model would be immediately falsified.

Finally, [Tad Stone & Soryu Aleksi](https://tadstone.deviantart.com/art/My-Little-Pony-Genetics-287664115) take as a starting point that Earth ponies are much more common, and Unicorns rare; they don't try to explain to explain Alicorns. They also go with a blocking method:

> Going from here, the ponies would have two genes, a Unicorn and a Pegasus gene. Both genes have a dominant allele that blocks the development of wings or horns respectively, and a recessive one to develop the features:
>
> - _P_: Pegasus blocker
> - _p_: Pegasus
> - _U_: Unicorn blocker
> - _u_: Unicorn
>
> An Earth pony is a pony where both genes contain at least one blocking allele...The possibilities then are as follows:
>
> |Race|Possible allele combinations|
> |----|----------------------------|
> |Earth pony| PPUU, PpUU, PPUu, PpUu |
> |Pegasus   | ppUU, ppUu, ppuu |
> |Unicorn   | PPuu, Ppuu |
>
> Table: Tad Stone & Soryu Aleksi 2-gene model, racial types
>
> This would make Mr and Mrs Cake's children possible if both parents are PpUu:
>
> |      |              |                |                |      |
> |------|--------------|----------------|----------------|------|
> |      | _PU_         | _Pu_           | _pU_           | _pu_ |
> | _PU_ | PPUU (Earth) | PPUu (Earth)   | PpUU (Earth)   | PpUu (Earth) |
> | _Pu_ | PPUu (Earth) | PPuu (Unicorn) | PpUu (Earth)   | Ppuu (Unicorn) |
> | _pU_ | PpUU (Earth) | PpUu (Earth)   | ppUU (Pegasus) | ppUu (Pegasus) |
> | _pu_ | PpUu (Earth) | Ppuu (Unicorn) | ppUu (Pegasus) | ppuu (Pegasus) |
>
> Table: Tad Stone & Soryu Aleksi 2-gene model, Punnett square
>
> Of course this would mean that Mr and Mrs Cake each have a (possibly very distant) Pegasus and a Unicorn ancestor. However, in the series only a Pegasus cousin for Mrs Cake and a Unicorn for Mr Cake are named. With only these two as non-Earth pony ancestors it would not be possible following my own theory, but in all likelihood they don't know all their ancestors. Also a pretty complicated combination of genes would be needed in that case and we can't describe such a thing without knowing much, much more.

This explanation works nicely and violates the minimum of elements.

There are some further theories which I think are inconsistent with the evidence: [CocoaNutCakery](https://cocoanutcakery.deviantart.com/art/MLP-Pony-Genetics-267870595) suggests a more complicated epistasis, explaining the non-observed combinations as being fatal/producing nonviable embryos, and explaining the Earth pony-like magic of [Fluttershy](http://mlp.wikia.com/wiki/Fluttershy) (a Pegasus) as being due to additional magic resistance & explaining Alicorns similarly; this has the serious defect of requiring Unicorn & Pegasi families to have much lower fertility or severe infant mortality rates (which are not supported in canon and are rather against the spirit of the show). theaceofspadez's ["The Genetics of the Pony: The Nelson Theory for Pony Inheritance"](https://theaceofspadez.deviantart.com/art/The-Genetics-of-the-Pony-271328436) founders on attempting to explain too much and making Alicorns far too frequent, and also postulating "Alicorn Earth/Pegasus/Unicorn" variants too. Tacticalrainboom's [environmental determination theory](https://www.reddit.com/r/mylittlepony/comments/1k1t8k/i_solved_the_genetics_of_pony_typesraces_this/) argues that it's not genetic at all but environmental (eg Pegasi are caused by exposure to high altitude & weather magic), but this is quite a stretch as it can't explain why Earth ponies colonizing new places have Earth pony offspring (eg. the entire Apple clan from many different locations throughout Equestria are all Earth ponies), what environment [Manehattan](http://mlp.wikia.com/wiki/Manehattan) & [Ponyville](http://mlp.wikia.com/wiki/Ponyville) have in common causing Earth ponies but which the capital city of [Canterlot](http://mlp.wikia.com/wiki/Canterlot) does not to cause mostly Unicorns, or why, if deviations from the local norm are due to random environmental fluctuations, both Cake twins would be discordant instead of being the same type (presumably any random environmental fluctuation affecting Mrs. Cake ought to affect the fraternal twin fetuses simultaneously & *equally*).

But wait - there are *more*! [Could Mrs. Cake have been cheating on Mr. Cake or they did a threesome](https://www.reddit.com/r/mylittlepony/comments/rq9ht/statistical_probability_of_the_cake_twins_having/), since fraternal twins don't have to be fertilized by sperm from the *same* father, and this is why he had shifty eyes/was vague? Were surrogacies and/or egg/sperm donors involved, because [one or both of the Cakes are infertile](https://www.reddit.com/r/mylittlepony/comments/3612bw/theory_why_the_cake_twins_are_not_earth_ponies/)? Or could the twins have been affected prenatally by Discord at the beginning of season 2? [Or perhaps](http://www.bronibooru.com/posts/40230) ponies are not even diploid (so all the Mendelian explanations are fundamentally wrong), but *[polyploid](!Wikipedia)*, in which case just about any kind of inheritance is possible?

That said, reviewing the theories, I think my polygenic threshold models or Tad Stone's two-gene model fit the best overall.