One of the basic premises of the Potterverse is that Muggles are much, much more common than wizards. This is what in part necessitates the need for the Wizarding world to hide itself away because, despite their superior powers, they would be overwhelmed by the far more massive Muggle population should conflict break out.
However, we also know that wizards and witches have been around a long time. In Prisoner of Azkaban, Hermione's letter mentions:
I bet he’s learning loads, I’m really jealous – the ancient Egyptian wizards were fascinating.
Given that in one of Ron's letters, the Pyramids were mentioned as magical locations, this means that while we don't have a definitive date of when wizardry entered the world, we can definitively say that wizards and witches have been around since at least 2500 B.C. Most likely they have been around much longer than that.
I could not find any evidence that suggests that magical people reproduce any faster or slower than a Muggle. Furthermore, being born to magical parents almost always means the child will also be magical (Squibs are considered very rare). While I don't have statistical evidence, it seems that merely having only one magical parent is enough to make it likely that the child will have magical abilities - based on Severus Snape, Seamus Finnigan, and of course, Tom Marvolo Riddle. Finally, there are of course Muggle-Borns, which while they are certainly very rare as a percentage of the Muggle population, they seem quite common enough at Hogwarts.
Finally, it's fairly easy to make the argument that Wizards are more powerful than Muggles in ancient times, given the lack of Muggle technology. In the modern era, there are arguments that Muggle weapons have exceeded Wizarding power, though there is not total consensus on this. It would be hard to argue, however, that Muggles had superior power (via technology) than Wizards prior to the 20th century.
In summary:
- Magical people have been around for at least 4500 years, probably longer.
- Magical people reproduce at roughly the same rate as Muggles.
- For most of history, magical people have had superior power to Muggles.
The question:
Given these reasons, why is is it that the Wizarding population does not dominate the human population via natural selection?
In-universe answer only, please. I'm not looking for a "J.K. Rowling is bad at maths" kind of answer.
Answer
We don't need to argue about reproductive fitness to explain this.
Here in the real world, the fertility rate falls off as the standard of living increases. Until quite recently, the magical community has had a much higher standard of living than Muggles. (Arguably, they still do!) So we would expect their fertility rate, historically, to be similar to our modern rate.
The current British fertility rate is 1.87 births per woman. It was about 2.9 births per woman at one point in the 1960s; it was probably higher still earlier on, but let's take that as a reasonable number for Muggle fertility, and the current number as a proxy for Magical fertility. (It seems reasonable, perhaps even a little too high, based on what we know from the books.)
Suppose that on average one in every two magical people marry Muggles; that seems like a slightly high estimate to me, but let's go with it for now. That would increase the number of couples in the magical community by 50%, e.g., if the birth rate was exactly 2 the effective birth rate would be 3:
That makes the effective birth rate about 2.8, nearly but not quite keeping up with the nominal Muggle rate of 2.9.
Obviously this all depends on what numbers you choose. But it is plausible.
Addendum:
As PlasmaHH and Adam point out in the comments, fertility rate isn't really the best statistic to be using here, because it doesn't take into account the number of people dying before reaching reproductive age. However, I don't think this makes my argument implausible, just slightly more subtle: you have to take into consideration that fertility may be affected by both mortality rates and standard of living.
(In particular, I don't believe the mortality rate for children has changed enough since 1960 to explain more than a fraction of the drop in the fertility rate over the same period, so those figures are probably still good enough to establish plausibility.)
The effect of mortality rates on fertility can be expected to cancel itself out, leaving only the standard-of-living effect as relevant. It seems reasonable to suppose that the adjusted fertility rates (counting only children who survive to reproduce) might remain different enough to counteract the growth rate of the magical community due to Wizard-Muggle marriages.
References: this Google chart based on data from the World Bank.
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