A little background about the world of wizardry:
In a rebuttal to that paper the following month (Nature Vol 437, 318, 2005), doctors at the University of Cambridge (might as well be from Hogwarts) posed some of the same concerns as me and my fellow graduate students. Hermione is born of muggle parents but is a wizard herself. By assuming that being a wizard is a recessive trait then both of Hermione’s parent would have to be carriers of the wizard gene, or heterozygous for wizarding, to allow her to get both recessive alleles. With both of her parents being heterozygous, odds are there was a wizard in the family somewhere along the line on both sides. It is possible, however, Hermione didn't know of her families potential wizarding past because it’s been many generations since there was a wizard or they kept their powers a secret.
They were also skeptical about the idea of incomplete penetrance being the culprit for Neville’s reduced wizarding abilities in comparison to his comrades because incomplete penetrance is associated with dominant alleles and this phenotype is determined by having none.
I think wizarding ability is greatly affected by level of intelligence, the environment and other non-wizard factors and is also not determined simply by one gene. I propose that there is some form of epistasis happening where multiple genes are interacting along a pathway to determine the phenotype. Multiple genotypes can then produce the same phenotype and there can be possible variants of said phenotype based on which genotype you receive, accounting for varying levels of wizarding ability.
In the rebuttal they state that “it is not possible, from the evidence presented so far, to conclude that wizarding is a heritable trait.” I, however, think with a little time with the series and creativity, the mode of inheritance can be determined (but ain't nobody got time for that).