To be magical, one must have an allele pair of mm. So if two pure bloods are marrying, the test-cross of alleles would be mm x mm. This would have a 100% rate of having a magical offspring, proving how pure-blooded families like the Malfoy’s always have a magical child. This is why wizards will often marry between themselves, forcing their offspring to hold magic.

As for a half-blood, there are a few possibilities. One parent must be a witch or wizard, making their allele pair mm. As for the other parent, they must be a muggle, making their MM or Mm. Because we are assuming absolute dominance, a muggle can have a Mm allele pair and will still be a muggle because the M covers up the m. So the cross would have to be either mm x MM or mm x Mm. In the case of mm x MM, the offspring will either be a muggle or a squib. To quickly touch on a squib, this would be a Mm pair but would not assume absolute dominance. Because they are not assuming absolute dominance, they would still have some magical power, but not as much as an absolute dominant wizard or witch. If it is mm x Mm, the offspring can either be a muggle, squib, or magical. That just comes down to whether the pair is Mm (squib or muggle) or mm (magical), assuming absolute dominance.

As for a muggle born, this is where it gets interesting. If both parents are muggles, then the allele pairs must be MM or Mm. Even if it is a squib, that does not affect the situation. If either parent is MM, then the offspring cannot be a magical being. However, if both parents are Mm, then there is a 25% chance that the offspring will hold magic. There is also a 50% chance that that match will have an Mm offspring, which can lead to more muggle-born wizards.

So for those who believe muggles are useless, here is a whole article on how they are not. This may be confusing to some of you who have not yet studied biology, but I may write a series of articles explaining this in more depth. This is a very surface-level article without diving into the depths of genetic variations or more, but I tried to keep it simple. This is a very complex theory that has now been revealed, and I am coining the Magical-Genetic Theorem.

Written by Michael Issarles, and proof-read by Eleanor Raven