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The magic gene is a portion of human DNA that determines whether a person will have magical abilities. Those people born with the gene active are witches and wizards, while those who are not are Muggles or Squibs.

The magic gene is dominant^[1], and 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 magic gene occasionally resurfaces in later generations and produces a Muggle-born witch or wizard^[2].

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 9 & 3/4 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.^[3]
• According to J.K. Rowling, nobody knows where magic comes from.^[4]
• Despite the magic gene being dominant, that doesn't explain Squibs or Muggle-borns, or how muggle borns manifest their powers the same way as Half-bloods or Pure-bloods. It is therefore possible that magic is controlled by more than one gene or is only partially dominant.
• A paper has been submitted to J.K. Rowling explaining that it is in fact possible for the magic gene to be dominant: http://mypocketshurt90.tumblr.com/post/27495622491/i-sent-this-paper-to-jk-rowling-explaining-how-the

Appearances

• Harry Potter and the Half-Blood Prince (Indirectly)
• J. K. Rowling Official Site

Notes and references