Genetics in the wizarding world. Is wizarding a genetic or recessive trait?

[bookworm857158367]

No: HPFGUIDX 100425

First of all, this is really a neat forum. It's nice to find other 
adults who've read the books. I've been re-reading the Order of the 
Phoenix after seeing the latest movie. While all of the references 
to "pure-blood" and "half-blood" and "mudblood" wizards and Squibs 
is distressingly reminscent of Nazi Germany, it does make me wonder 
how the genes are passed down.

If Filch is a Squib who can't do magic, for instance, as noted in 
the book, how can he talk to his magical cat Mrs. Norris? Did I miss 
some reference in the book? Is he just a very weak wizard who didn't 
have enough talent to be trained at Hogwarts?

My working theory is that wizarding must be a recessive gene and the 
non-magic gene is dominant. The so called "pure blood" families, 
like the Weasleys or the Blacks, all have members who carry only 
wizarding genes. There's no taint of Muggle blood.

The Longbottoms must have done some intermarrying with Muggles, as 
they thought there was a real possibility that Neville could be a 
Squib, a Muggle born to wizards. But Neville is just as much a 
wizard as the "purebloods."

How to explain a wizard or witch born to a Muggle family, like Lily 
Evans or Hermione Granger, or the child of a Muggle and a wizard who 
turns out to be a wizard, like Seamus Finnegan? I think these Muggle 
families have to be descended from Squibs who originated in the 
wizarding world but settled among the Muggles. Maybe it was 100 
years in the past and the family has forgotten all about it, but 
their magical genes survived and combined to produce a magical child 
when two descendants of the Squib families married. That would 
probably mean that a Squib isn't actually a Muggle like other 
Muggles. They probably don't carry enough magical genes to give them 
wizarding powers, but enough to make them sensitive to the magical 
world. So Petunia Dursley and Dudley both have some magic in them, 
deny it though they might. It would serve Vernon and Petunia right 
to have a grandson or granddaughter who goes to Hogwarts!