|"Are you a wizard or not?"
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Magic genes are portions of human DNA that determine whether a person will have magical abilities. Those people born with the genes active are witches and wizards, while those who are not are Muggles or Squibs.
Magic genes are described as being "dominant and resilient", with a powerful effect on the person, but not in the Mendelian sense. Any child born to a wizarding family will have some degree of magical ability, or at least magical awareness. Squibs, while unable to use magic, are still able to function within the wizarding world to a limited degree. The descendants of squibs who instead integrate into the Muggle world and marry will usually be Muggles, although the magical abilities occasionally resurface in later generations producing a Muggle-born witch or wizard.
It is not clear how the expression of the genes (or lack of it) produces Squibs or Muggles, or how Muggle-borns manifest their abilities the same way as Half-bloods or Pure-bloods. It is unknown how many genes are involved in the ability to perform magic - only the existance of an on/off switch can be inferred from available data.
However, while Rowling herself calls the magic gene "dominant", it is likely that she either has a poor understanding of genetics or is using the term in a non-Mendelian sense, since as a matter of fact, based upon its manifestation in the books, it is almost certainly recessive. If it was dominant, the laws of Mendelian genetics would require that one out of every four children of two wizard parents who both carried the regular non-magic gene would be Squibs -- and due to the rarity of wizards in general, most wizards would carry the non-magic gene -- and Muggle-born wizards would be rare and produced by random gene recombination or mutation without requiring any wizard ancestry. But if it was recessive, wizards would produce Squibs only on rare occasions due to gene shuffling, but Muggle-born wizards would occur whenever two Muggles who carried the magic gene, which would be inherited from a wizard ancestor, happened to marry, in which case one-quarter of their children would be wizards.
And in fact, the actual situation in the books makes the theory that it is recessive overwhelmingly more tenable than that it is dominant. The strongest arguments in favour of a recessive magic gene, of course, are the rarity of Squibs, together with the fact that they occur randomly even in Pureblood families (such as the case of Marius Black); as well as the fact that Rowling herself has stated that Muggle-born wizards inherit their magic ability from distant wizard ancestors. But there are other hints such as the case of the Creevey brothers, where two Muggle-born wizards occur in the same family, which would have a 1/16 chance of happening if magic was recessive, but would require the already very unlikely magic mutation to happen twice in the same family if it was dominant.
The ability of Squibs and Muggle parents of wizard children to function within the magical world to a limited degree may be an effect of their possessing the recessive magic allele as a carrier (Mm), with pure Muggles being MM and all wizards being mm. Ironically, a recessive magic allele would also discredit the Purebloods' dismissal of Half-bloods or Muggle-borns as inferior wizards as pure pseudoscience, since all wizards would technically be "Purebloods".
This would also give us the ability to determine the frequency of the magic allele in Britain. If there are 10,000 wizards in Britain (based upon the assumption that they all spend 1/10 of their lives as students at Hogwarts, which according to Rowling has a student body of about 1,000) and 60 million people overall, the frequency would have a possible maximum of 1.3%, which would be the case if wizards mixed freely with Muggles and the majority of wizards were Muggle-born. Since there is a large amount of endogamy among wizards, the true figure is significantly lower than that, most likely in the 0.4-0.7% range.
Behind the scenes
- J.K. Rowling stated that she had considered having Dudley Dursley have a magical child in the epilogue, and see them off to Hogwarts at Platform 9¾ at the same time as Harry and his family. She decided against this, however, stating that any latent wizarding genes would never survive contact with Uncle Vernon's DNA.
- According to J.K. Rowling, nobody knows where magic comes from.