Chapter 23:

If Harry is correct about how magic is inherited, this idea can bring some interesting issues in future chapters. Short resume of Harry's idea: there are recessive magic gene (M) and dominant non-magic gene (N). Magic users have two magic genes (MM), and pair of them are needed to work with magic. Squibs have one magic gene (MN) and muggles have two non-magic genes (NN) all of them can't do magic.

First, how squibs appears? Actually people with MN genes can live between muggles because muggle-borg wizards and witches are born from parents with MN genes. But let's just do not call them squibs. Real squibs are born from couples of witch and wizard and both parents have MM genes. N gene can appear here as a result of mutation only.

Second, half-breeds exist. Magic-users can have children from giants, goblins, veela and, possibly, some other creatures. These half-breed can use magic, and there are two possibilities: they have MM genes or they have some m gene. m gene should be recessive gene, when appears with M gene, because according to HP wiki all known half-breeds can use magic. So half-breeds have MM or Mm genes.

What can Harry do with all these things? He can come with some eugenic proposal how to increase number of wizards, this may even help to make relationship with Lucius better. He can just find this M gene and connect it to the source of magic. But I'm not sure, that Harry will have time for all these, he may have more important goals. I hope he can delegate some of these studies to somebody else, for example, to Draco.

By the way, can Polyjuiced person become pregnant and give birth?