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Some magical abilities are determined by genes rather than by practice and knowledge.

For example, Parseltongue is granted simply by having the right genes, not by learning it. (Harry Potter knew Parseltongue because of his connection to Voldemort, and he lost the ability after Voldemort's connection to him was destroyed.)

Knowing Parseltongue isn’t quite the same as learning Spanish. Firstly, you don’t so much learn it, as just innately know it. The language is incredibly rare, as Harry is told countless times. The only place it isn’t rare, is within the bloodline of Salazar Slytherin himself – and as such, is usually hereditary.

The author herself as said that magical abilities are based on genetics.

Rowling: "Muggle-borns will have a witch or wizard somewhere on their family tree, in some cases many, many generations back. The gene resurfaces in some unexpected places."

Could a Muggle get a gene transplant at a young age and as the gene expressed itself as the child grew up, the person would become magical?

Note: The quotes above come from Reddit.

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We don't know

There is nothing in the source material, not the books nor the films nor Pottermore that gives any clue what the effects of such a transplant would be.

Magic is magic

"Oh dear, maths."
JKR

As evidenced by the quote, maths aren't JKR's strong point. I think it's not unreasonable to extend that to other sciences, such as biology. Much of her system of "magical blood" was drawn in an analogy to the Nazi's ideas of blood purity, even more than she had expected:

Section: F.A.Q.

Why are some people in the wizarding world (e.g., Harry) called 'half-blood' even though both their parents were magical?

The expressions 'pure-blood', 'half-blood' and 'Muggle-born' have been coined by people to whom these distinctions matter, and express their originators' prejudices. As far as somebody like Lucius Malfoy is concerned, for instance, a Muggle-born is as 'bad' as a Muggle. Therefore Harry would be considered only 'half' wizard, because of his mother's grandparents.

If you think this is far-fetched, look at some of the real charts the Nazis used to show what constituted 'Aryan' or 'Jewish' blood. I saw one in the Holocaust Museum in Washington when I had already devised the 'pure-blood', 'half-blood' and 'Muggle-born' definitions, and was chilled to see that the Nazis used precisely the same warped logic as the Death Eaters. A single Jewish grandparent 'polluted' the blood, according to their propaganda.

— JKR, in the FAQ on her old website (emphasis mine)

Neither JKR's ideas of magic blood nor the (partial) inspiration for it were scientifically sound ideas. Most of her ideas about magic are, well, magic. As with many other ideas in Harry Potter, they just serve the narrative without having been developed beyond that. Many of the questions on this Stack unearth the inconsistencies and contradictions that follow from that position.

Should there ever be a story in the Harry Potter universe that features a gene transplant, it will grant the receiver of the transplant as much magic as the story demands.

Until that story is written, no-one knows.

  • You won me over with the math quote. – Slacklord the Terrible Apr 6 '17 at 18:46
  • 1
    @TerribleFan "You had me at 'maths'"? – SQB Apr 6 '17 at 19:09
  • @RichS anything else I could add to make this answer acceptable? – SQB Jul 21 '17 at 11:54

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