In MLP:FiM, the 3 pony races sometimes bear offspring of other pony races; I review 4 complicated Mendelian models attempting to explain this, and note that a standard polygenic liability-threshold model can fit it parsimoniously.
(For background on My Little Pony: Friendship is Magic, see my review of My Little Pony.)
Another fictional universe with genetic mechanisms is My Little Pony: Friendship Is Magic, where there are 3 pony races which are heritable. One outlier family which has all 3 races represented challenges simple Mendelian interpretations of MLP races. I review 4 attempts to reconcile the outlier with Mendelian mechanisms, and propose another interpretation, drawing on polygenic mechanisms, treating race as a polytomous liability threshold trait, which is flexible enough to explain all observations in-universe (at least for the first few seasons of MLP).
In My Little Pony: Friendship Is Magic, 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 can be considered breeds/races: almost all depicted families are homogenous & have offspring of the same race, they are clearly distinct, distantly related (eg. Pinkie Pie & the Apples/Pears), typically reproduce within their own race, and tend to cluster geographically (with the noted exception of Ponyville).
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 2 Earth ponies Mr. and Mrs. Cake have 2 children in season 2 episode 13 (“Baby Cakes”), a pair of fraternal twins, who are discordant—Pegasi and Unicorn. When queried by the confused main characters, Mr Cake appeals to a vague genetic explanation, claiming “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 2) occasional discordant offspring?
Mendelian
Most fans are familiar with Mendelian genetics, and start there. A Mendelian model justifying the observations is hard to come up with, but there are at least 4 attempts.
HelloNurse
HelloNurse 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 (ie. depending on other genes). If the 2 parents are EU and EP they are earth but offspring of all 3 types is possible. An even simpler model: one gene with 2 alleles, earth and fancy, earth dominant, fancy ponies become unicorns or pegasi depending on rainbow intensity or other non-genetic factors.
Grim-S-Morrison
Grim-S-Morrison 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):
Grim-S-Morrison’s 2-gene model using Earth pony dominance; hypothetical Punnett square for Mr. & Mrs. Cake
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)
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 2 Pegasi ever have Earth pony offspring (rather than Pegasi or Unicorn) or 2 Unicorns are ever shown as having non-Unicorn offspring, the model would be immediately falsified.
Stone/Aleksi
Finally, Tad Stone & Soryu Aleksi take as a starting point that Earth ponies are much more common, and Unicorns rare; they don’t try to explain Alicorns. They also go with a blocking method:
Going from here, the ponies would have 2 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:
Tad Stone & Soryu Aleksi 2-gene model, racial types
Race
Possible allele combinations
Earth pony
PPUU, PpUU, PPUu, PpUu
Pegasus
ppUU, ppUu, ppuu
Unicorn
PPuu, Ppuu
This would make Mr and Mrs Cake’s children possible if both parents are PpUu:
Tad Stone & Soryu Aleksi 2-gene model, Punnett square
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)
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 2 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.
Miscellaneous
There are some further theories which I think are inconsistent with the evidence:
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CocoaNutCakery 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 (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).
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theaceofspadez’s “The Genetics of the Pony: The Nelson Theory for Pony Inheritance” founders on attempting to explain too much and making Alicorns far too frequent, and also postulating “Alicorn Earth/Pegasus/Unicorn” variants too.
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Tacticalrainboom’s environmental determination theory 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 locations throughout Equestria are all Earth ponies), what environment Manehattan & Ponyville have in common causing Earth ponies but which the capital city of 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).
Conspiracy Theories
But wait—there are more possible explanations! Could Mrs. Cake have been cheating on Mr. Cake or they did a threesome, 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? Or could the twins have been affected prenatally by Discord at the beginning of season 2? Or perhaps ponies are not even diploid (so all the Mendelian explanations are fundamentally wrong), but polyploid, in which case just about any kind of inheritance is possible?
Polygenic Models
As noted in my similar discussion of the wacky implied genetics in Frank Herbert’s Dune universe, as important as Mendelian genetics is, simple monogenic Mendelian models describe few traits in the real-world—rare medical diseases, the occasional low-level trait like coloration, that sort of thing. Almost all traits (even ones often described as Mendelian) turn out to be highly polygenic: influenced by thousands of different mutations, and adding up for the most part. Because of this, in modern genetics, or animal/plant breeding, or medicine, the default is to assume polygenic models rather than Mendelian models.
While a polygenic model is easy enough to imagine for a trait like height (lots of little Mendelian genes each worth a fraction of a centimeter, which sum up to give a total height), it’s less clear how this works for a trait which takes on several discrete values, like, say, pony races. It still can be done! Instead of imagining the thousands of genes adding up and that’s that, we imagine that this sum is some sort of ‘tendency’ or ‘liability’ and that there are thresholds, on either side of which one topples over into that particular discrete value: a liability threshold model. So if ponies were either Unicorn or Earth but could not be any kind of hybrid, there might be a ‘Unicorn-ness’ variable, and if one has enough Unicorn-increasing mutations, a critical threshold will be passed and one will develop as a Unicorn; and if not, one defaults to Earth. (An analogy might be bee larvae: if they are fed enough royal jelly, a new developmental process kickstarts to try to turn them into a queen; or in human sex development, the ‘default’ is to be female, and only if the Y chromosome & hormones kick in appropriately does the ‘male’ program activate and masculinize a fetus—should the program go awry, such as in XY gonadal dysgenesis, then they may look like a normal female.) This can be generalized to multiple thresholds, possibly in an order.
A polytomous liability threshold model is the natural sufficiently flexible as to explain all of these pony patterns by simply setting thresholds appropriately and expecting assortative mating. For example, there could be a single race trait which is polytomous with 2 independent 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 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 2 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, 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 2 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 or GWAS to see if a binary trait is highly polygenic, etc, but none of that is possible here.)
That said, reviewing the theories, I think my polygenic threshold models or Tad Stone’s 2-gene model fit the best overall.