Title: A dissertation on the hypothetical genetics of the Cake family
There has been dissension among the ranks of bronies as to whether the Cake parents, who are Earth ponies, could produce a pair of fraternal twins with one being a pegasus and the other a unicorn, given only one distant ancestor carried a single representative phenotype of each on either side.
I have developed a plausible pattern of inheritance to explain this seeming incongruity.
Let's say that pegasi and unicorns were genetically designed, using earth pony as the genetic base, by the alicorns playing god on the mythical continent of Atlantis. The easiest way to add the genes to the earth ponies would be to design an artificial chromosome carrying all the needed genes. Then this chromosome's expression could be triggered by a special transcription factor integrated elsewhere in the genome, likely tied via a promoter to other developmental genes. My bet is the BMP-Bcat-Wnt signalling system, since horns and wings both require skeletal augmentation and early patterning.
But, you wouldn't normally want a pony to end up with both, so one could also include suppressors on each of the types of artificial chromosomes, such that if any pony ended up with both types of chromosomes and promoter elements, the supressors would shut down the expression and the offspring would be an earth pony carrier of both traits. Also, if out-breeding with Earth ponies occurred, the different chromosomes and promoters could become separated (aka Au=unicorn artificial chromosome, Pu=unicorn-specific promoter element. Unicorn genotype-phenotype correlation= AuPu. Earth pony base: B=base chromosome Q=null carrier for artificial chromosome. Earth Pony genotype=BQ. Assuming they are homozygous for each trait and crossing, you end up with an F1 genotype Au/Q Pu/B.
Successive generations would further dilute this background. Assume also the same rules apply for Pegasi Ap/Ap Pp/Pp homozygous genomes: F1 earth pony cross yields Ap/Q Pp/B.
We can add in the assumption that at some point, any one of the Cake's direct relatives might have reproduced with another Earth pony carrying a promoter or artificial chromosome from the opposing genome. Now, taking into account that each type of artificial chromosome carries the suppressor for the other trait AND that the promoters are specific to each artificial chromosome, we can end up with these diploid genotypes in Mr and Mrs Cake without their developing any pegasi or unicorn traits: Ap/Q Pu/B and Au/Q Pp/B.
Following gametogenesis, these 8 haplotypes can be generated: Parent 1: ApB, ApPu, QPu, QB Parent 2: AuPp, AuB, QPp, QB.
As you can see, with such combinations available, there is the chance for the twins (being fraternal rather than identical) to end up with the correct combinations to allow expression of either unicorn or pegasus: ApB/QPp= heterozygous pegasus, QPu/AuB= heterozygous unicorn. The raw statistical probability of each genotype is 1/4 x 1/4 = 1/16, which is actually not at all unlikely.
In my genetics lab, we've done mating with mutant mice for 3 genes with a probability of 1/32, and still end up with some of the combined mutant genotype in roughly every other litter of mouse pups, averaging 8-10 pups/litter. So, in conclusion, should the genotype function as described in this paper, it is entirely possible for the Cake foals to exhibit the unicorn and pegasus phenotypes despite having earth pony parents.
Soooo, Celestia... is this enough for my PhD in Pony Genetics? ;3