In Harry Potter and the Chamber of Secrets Hagrid makes an interesting comment. He says
"Most wizards these days are half-blood anyway. If we hadn’t married Muggles we’d’ve died out."
This comment got me thinking about the genetics and population dynamics of the Harry Potter universe. This topic prompted a lot of questions.
Why is the magic population so small relative to the non-magic population?
Hagrid's comment implies that there is something inherent in magic users that puts downward pressure on their population. There are a few possible explanations:
- A genetic effect associated with the same genes that allow magic use also reduces fertility.
- Certain magic users face cultural pressure not to have children (for example, witches might face pressure not to have children, resulting in more magic using men choosing non-magical partners).
- Hagrid could be referring to a specific event, rather than a general trend (for example, say there was a catastrophic event in the past which eliminated a critical mass of magic users).
Size of the Magical Population
The size of the magical population is hard to gauge, but it is clearly fairly small. Let's work out an estimate. We know that Hogwarts is the only school of magic in the UK, and that attendance at Hogwarts of another school of magic is (effectively) mandatory for magic users. Based on the size of the great hall, which ostensibly contains all of the students and staff at once, Hogwarts likely has about 200 students ages 11 - 18.
According to the UK office of statistics, people ages 11-18 made up about 10% of the total population in 1998 (about 5.9m out of 58m people). We know that witches and wizards can live longer than regular people, so let's generously assume people 11-18 make up 5% of the magic population. Based on these assumptions, the total magical population is the UK in 1998 was approximately 4,000 people, or about 0.007% of the total UK population. The UK accounted for approximately 1% of the global population in 1998. This implies a global wizarding population of about 400,000.
The quidditch world cup is said to have 100,000 attendees in Harry Potter and the Goblet of Fire. The 2002 Football World Cup had about 2,700,000 attendees (27x as many) . The world population in 2002 was 6.2 billion , meaning 0.04% of the world population attended the Football World Cup. One could extrapolate that the global wizarding population is 100,000 / 0.0004 = 250,000,000. However, I believe the ease of transportation in the wizarding world means a much higher percentage of the world population attends the quidditich world cup, likely as high as 25%, based on a a global wizarding population of 400,000.
This population estimate aligns nicely with the apparent scale of the magic economy: magic users in the UK are effectively a small town. The ease of transportation enabled by magic (apparition, flue powder) means that the population can be geographically distributed over a large area without losing the cultural cohesion of a small community. A variety of observations seem consistent with the magical population existing as a distributed small town (or perhaps small nation-state):
- They have their own currency.
- They have a small number of businesses (one bank, several restaurants, several specialized stores).
- They have a single government.
- Most Magic users seem to prefer (or are limited to?) magic-specific occupations. It is implied that this is a cultural preference, rather than law.
Magical Ability Propagation
There's general consensus in the literature that magical ability is inherited, though it's unclear whether the trait is expressed on a single gene or multiple, or whether it is dominant or recessive.  . This is consistent with the potential for non-magic users to have magical children (e.g., Hermione) and the ability for magic users to have non-magical children (squibs, like Mr. Filch).
Birth Rates Among Magic Users
- Weasleys - 7 Children
- Dumbledores - 3 Children
- Hagrid's Parents - 1 Child (his half brother is not a magic user and does not count)
- Potters - 1 Child
- Malfoys - 1 Child
- Lovegoods - 1 Child
- Longbottoms - 1 Child
- McGonogal - 0 Children
Education and Autonomy
There is a lot of research yet to be done. Some ideas:
- Set up population simulation to try to determine approximate rates for the wizarding world.
- Analyze the supply chains for magic users - how do they differ from those of non-magic users?
- Is in-breeding a problem among magic users? The preference for "wizard blood" among some users could lead to such situations.
 Live Science
 Muggle Net