Wizards Everywhere and When
When Rowling said that all Muggle-born wizards and witches have a magical ancestor somewhere in the family tree, she effectively confirmed that magic, if it can be said in her world to be genetic, is a multiple-gene characteristic. A single-gene model does also permit a recessive gene to lie dormant for several generations, granted, and one can postulate that the wizard community could be a sub-population with a very pronounced tendency for that particular recessive gene to be expressed. Things like that happen in the real world.
But if magic is a single recessive gene in the Potter world, it doesn't make sense for as many Muggle/wizard pairings to result in magical children as evidently happens. (In fact, of the known Muggle/wizard pairings, every one of them resulted in 100% magical children.) Here is why:
- If there is a counterpart dominant "Muggle" gene (M) that overcomes the presence of the magic gene (m), then in fact, the only way a Muggle/wizard pairing could result in any magic children is if the Muggle partner is Mm, one dominant Muggle gene and one recessive magic gene, and that pairing only results in 50% wizard children rather than the 100% that we see in the books. The pairing is Mm (carrier Muggle) x mm (wizard) = 50% Mm, 50% mm. Incidentally, this is also the only way that a single-gene model allows Muggle-born wizards to be born; a pair of carrier Muggles results in 50% Mm (carrier Muggle), 25% MM (non-carrier Muggle), and 25% mm (wizard).
- If the magic gene does not have a counterpart dominant Muggle gene to overcome its expression, then it shouldn't be able to skip generations in phenotypes. If it's there, it's expressed. There should be no Muggles carrying it and therefore no Muggle-born wizards. The pairings are mm (pureblood wizard) x 00 (Muggle) = 100% m0 (halfblood wizard), and m0 (halfblood wizard) x 00 (Muggle) = 50% m0 (halfblood wizard), 50% 00 (Muggle).
Essentially, with a single-gene model, we can have Muggle-born wizards permitted or we can have 100% magical offspring from wizard/Muggle pairings, but not both. The incompatibility of the single-gene hypothesis with the Potter universe indicates very strongly, if not definitely, that magic is a multi-gene trait. This ties in well with the presence of certain characteristics, such as Parseltongue, that most wizards do not have, but are known to be inherited. In a multiple-gene setup, there may be any number of "Muggles" walking around who have some portion of the required genotype to express magic, but not the whole thing.
And too, we must remember that Rowling's wizards have been secluded from the general population for about 320 years and mostly married amongst themselves. This resulted in a very high rate of duplication in a child's magic genes, since children would inherit magic from both parents, usually. Such children could also marry Muggles and expect to have all magic children themselves (though these children could not have the same expectation in a marriage with a Muggle) because of the gene duplication.
Before seclusion, however, wizards mixed freely (for the most part, though families like the Blacks probably still isolated themselves). The magic genes were spread throughout the population, making it less likely that a Muggle/wizard marriage would result in all magical children, as the wizards themselves tended to have less completeness in their magic gene sequences for being of mixed ancestry, and much less duplication of genes, unless both parents just happened to contribute a copy of a particular magic gene. (In this case, the Blacks actually had a perfectly valid point that marrying with Muggles could dilute the magic strain and result in more non-magical children born.) But this also resulted in there being a Muggle population with apparently quite a lot of carriers of pieces of the magic genotype. If two of them with the combined genes necessary to complete the sequence paired off, there could be a Muggle-born wizard. The bit in Deathly Hallows about the Department of Mysteries' research that "magic is only passed on when wizards reproduce" turned out to be correct in essence, though undoubtedly the Death Eater Ministry distorted the actual findings, which would have been that magic is only passed on when people carrying the magical genes reproduce. And those genes had to get into the Muggle gene pool originally through a witch or wizard.
The British Isles, it seems, have a rather high concentration of witches and wizards. This is no surprise, actually. Rowling has based her world very strongly on folklore and legend, and the British Isles have a lot of wizards and magical creatures featuring in their national legends. I would be willing to bet that not all areas of the world have a similar concentration. Some would have higher concentrations and some lower.
American Witches and Wizards
Many fan-fiction writers seem to want to have American characters, for instance, but I have serious doubts that there would be that many American witches and wizards—at least, of strictly Anglo descent. There certainly would have been no widespread migration of British witches and wizards to America in the early colonial years. Rowling's admission in the fourth book that there is a "Salem Institute for Witches" in Salem, MA might seem to contradict this guess, but not so fast. Let's look closer at this first. The timing is wrong for it to have been coeval with the witch trials, the location is wrong for that implied date of founding, and for there to be two schools in America (yes, two. That is a women's school, and there would be one for the boys too) at such an early date is well in excess of the requirements of population.
First, the timing. In the alternate universe, wizarding seclusion took place in 1689. In the real world, the Salem witch trials took place after this, and one can apparently assume that they occurred in the alternate universe as well, or the Witches' Institute wouldn't be in Salem. Does anyone seriously believe that the Ministry of Magic (which would have jurisdiction over any witches and wizards in the colonies at that point) would let real witches be executed after seclusion? Nuh-uh. In the alternate world, as in the real world, those executions were of innocent "Muggles" who were scapegoated for, essentially, being different. We don't need to posit actual witchcraft taking place in Salem that Muggles took the blame for. They were under Seclusion by then, and it was official policy to hide magic and suppress memories of it whenever it was observed by Muggles. Puritan hysteria, as happened in the real world, is more than sufficient to explain the disgraceful acts in Salem. And that leads to...
The location. Let's take a reality check here. Most of the British colonies were founded by people fleeing religious persecution, yes, but what did they do as soon as they arrived? Why, they started persecuting other religions themselves, that's what. The colony of Massachusetts was arguably the very worst offender. Potterverse wizards seem not to have the common sense they were born with, granted, but it is stretching credulity to suggest that they would voluntarily go with the Puritans to Puritan colonies and live under such rule without the protection of local magical authorities that they would have had in Europe even before Seclusion. If we are going to hypothesize migrations of any witches and wizards from Britain into early America, we should ignore Salem. I'd fix my eyes squarely upon Rhode Island and Philadelphia instead. Those areas were founded on religious freedom for all.
And finally, population. The few witches and wizards who settled in early America didn't need a school yet, because there just wouldn't have been that many of them. Probably no more than a few dozen. Their children would have been sent abroad to Hogwarts or educated at home. The need for an American school of magic (or, rather, at least two, as that one is a women's school only) only came about after the severance of ties with Britain. I would date the founding of the Salem Institute to the 1780s or 1790s rather than the 1600s. One now wonders if the few American magical families might have chosen to send their children to Beauxbatons briefly, out of solidarity with the French, but it may be that the French language proved to be too much of a barrier. The French Revolution and Napoleonic wars may also have given them anxiety, necessitating the founding of American schools of wizardry. The school for girls was probably put in Salem basically to thumb one's nose at the Muggles. If American wizard families did send their kids to France at first, then the school might not have been founded until the centennial of the witch trials. There is a comparable school for boys somewhere along the East Coast too, and to guess the location of this school, I'd look at any area with a strong history of Masonic connections in its prominent families. (While we're running on in this vein, the back of the Declaration of Independence might give directions.)
However, America is a melting pot, and there is no need to focus strictly on Anglo-origin witches and wizards when there are probably quite a good many more who are of different ancestry. I am inclined to look highly suspiciously at southern Louisiana, and New Orleans in particular, for Dark magic traditions. And it wouldn't be a bad idea to consider areas of the Appalachian Mountains, or much of the desert West. Why not? They have their own magical beast, the jackalope, and all kinds of local folklore and legends. One would also expect a high concentration of Parselmouths in the West, all things considered; it would definitely come in handy. One wonders if, in the alternate universe, a folklore character like Paul Bunyan was a wizard who was able to channel his magic into extreme height and strength. Perhaps the various con artists that preyed on the settlers in the West were simply highly proficient with the Imperius Curse, and Jesse James was an accomplished (if self-taught) Dark wizard. But the odds are that the ethnic group with the highest concentration of witches and wizards in America is the Native Americans themselves. With all due respect to Stephenie Meyer (that is to say, none whatsoever), I think they would be far more likely to be wizards (and Animagi) than werewolves in a fantasy alternate universe setting. It's easy to get going with this once it is started, needless to say; that is a great thing about having an active imagination. People who are determined to write fan-fiction stories with characters from America have a wealth of possibilities to look at that are indisputably American. They have no need to make it a badly thought out mirror of the types of witches and wizards in Rowling's alternate Britain.
Origin of an Insult?
With her statement about where Muggle-born wizards come from, Rowling also effectively confirmed the theory that has been making the rounds among older fans for some time; namely, that the term "Mudblood" originally was not a catchall slur for a wizard of Muggle birth, nor was the term "mud" or its synonyms used to refer to actual Muggles (as we see one of the Gaunts referring to Tom Riddle Sr. as a "filthy, dirt-veined Muggle"). The theory went that "Mudblood" originally was a slur against wizards whose true ancestry was "muddied" because paternity at some point was unknown or misattributed. With Rowling's information that Muggle-born wizards do have a magical ancestor somewhere back in the family tree, the obvious conclusion to draw is that this was an undocumented extramarital or premarital relationship that just didn't produce a wizard child, but a carrier of the partial genotype. Wizards keep genealogical records, after all. They know who is related to whom, if it is legally documented. And for all that families like the Blacks would blast off a member of the family who married a Muggle, the writers of records like Nature's Nobility would still have made note of the fact, because the connection would (after seclusion) have been highly likely to produce all wizard children.
Undoubtedly, some Muggle-borns have had magic genes in their family histories dating from before Seclusion, when wizards and Muggles mixed openly and intermarried all the time, and not all children would have been wizards. The family tree books probably wouldn't have been kept then. The magical ancestor could have been perfectly up front, with a legal marriage or acknowledgment of paternity, just from before a time when wizards kept detailed records of who was a wizard and to whom they were related. If the wizard or witch did not manage to pass on active magic to the first generation of children, it makes sense that the family of carriers would have been completely off the radar of whoever wrote the first edition of Nature's Nobility. But, unfortunately, I still doubt that this accounts for all of the Muggle-borns. Even if they were to trace their family trees back, I rather suspect that somewhere the wrong father would be put on the tree, because there would have been no records proving otherwise.
And with the increasing mixing of wizard and Muggle cultures in recent years, one has to wonder just how many alleged Muggle-borns are actually halfbloods whose biological fathers never stepped up. The back story of Dean Thomas is a decent comparison. Dean is a halfblood whose wizard father was killed for refusing to go along with the Death Eaters, and his mother never knew of her lover's magic. (Presumably they were not married, or it would have been a matter of public record in wizarding books that Dean had a wizard father.) This back story shows that Rowling has probably thought about this possibility herself, though Dean's story is not nearly as cynical as hypothesizing halfbloods from extramarital affairs where the woman either could not get the wizard father to admit paternity (in which case the woman probably would have been single) or pushed it off on another man in her life, such as a Muggle husband, rather than admitting that she had been unfaithful. This is a rather ugly and unpleasant line of theorizing, one that seems not to apply to the most prominent example of a Muggle-born, Hermione Granger. It seems unlikely that Rowling would do this for Hermione's background. She probably chose the nicest possible way for Hermione, that of legally acknowledged relationships between wizards and Muggles way back in the day, that produced carrier children for many, many generations. In all probability, she is very distantly related to Hector Dagworth-Granger, actually, just as Slughorn thought at first.
Regarding "Diverse" Witches and Wizards in the British Wizarding World
I bring up this subject with a certain degree of trepidation. A number of years ago, before the release of Goblet of Fire, some critics were complaining about how white the Potterverse was. After the release of the fourth book, and the introduction of witches and wizards of color such as the Patils, Cho Chang, Dean Thomas, etc., another set of critics complained that Rowling was pandering and that a traditional British subculture such as the Wizarding World wouldn't have so many "diverse" members. On this sensitive topic, it seems that there is no way to please everyone. (Or, I might cynically suggest, anyone.)
For my part, I have no objection whatever to the witches and wizards of color, or their number. As culturally traditional as the wizarding world might be in some regards (though I think some fan-fiction writers overdo this aspect to a great degree, particularly regarding the role of women), the books are set in the 1990s. I think the percentage of nonwhite wizards in Britain is completely appropriate, especially when one considers that, in Muggle history (which we have no reason to think didn't mirror our own real-world history), the British Empire dissolved in the 20th century.
Now, I do think that the wizarding world of Britain probably was almost entirely white until approximately the mid-20th century, not because of internal racism, but because there simply would not have been very much wizarding migration from other parts of the world (though admittedly, there would have been much more than in the Muggle world), nor (given the astronomically small percentage of Muggle-born witches and wizards compared to all Muggle births) many Muggle-born introductions from families of color. Even on the rare occasions when such new members did join the community, they would have mostly intermarried with white wizards and witches. Over time (and it would not have taken that much of it), the genes would have become too diluted for the strain to be noticeable. Sure, not all newly recognized wizards of color would have married other magicals, but that still only postpones this diluting process by one generation. The children of those who married Muggles of the same ethnicity as themselves would have been magical and therefore educated in the wizarding world, and therefore much more likely to marry a witch or wizard themselves than their migrant or Muggle-born wizard parent. There's really just no plausible way for there to have been long-lasting wizard families of color in the British Potterverse, at least prior to the mid-20th century, unless Muggle history unfolded very differently than in the real world. But it is around that time that the Potterverse would indeed have become more racially diverse, and witches and wizards of color would have had enough potential partners of their own race that consanguinity would no longer have been a concern for the next generation (if they preferred to marry in their own ethnic group).
Consider, for example, the Patil family. Parvati and Padma are described in the books as being Indian in appearance, indicating that most (if not all) of their ancestors were from India. The only way that works out -- and, in fact, it works out quite well -- is if the Patils lived in India until rather recently. They probably would have decided to move to Britain when India gained its independence from the British Empire. Being a wizarding family, the Patils would have answered to the Ministry of Magic rather than any Muggle government, and they probably would have preferred continuity in that regard than having to deal with Muggle political instability. One can propose such a background and immigration rationale for a number of wizards and witches. Cho Chang's family likely originated in Hong Kong, for instance. Most adult black wizards probably came from families that had lived in Africa and moved to England after the colonies there became independent. In recent times, of course, it is probable that there are more Muggle-born births to people of color than previously, as the nonwhite population of Britain increases, but the halfblood and pureblood families of color probably are ex-colonial.
Kingsley Shacklebolt appears to be a bit of an exception in this regard. Until it hit Pottermore, and the Potter Wiki, that the Shacklebolts were a very old pureblood family (at least as of the 1930s) on the same level as the Blacks and Malfoys, I had assumed that Kingsley's immediate antecedents had migrated from an African country that had recently been a British colony, to avoid Muggle political instability. I had assumed that if he was a pureblood, he was the "everyday" sort who maybe had a great-grandparent or two who had been Muggle-born, but probably had not grown up knowing any immediate family outside the wizarding world, and so considered himself pureblood on that account. This new information renders this hypothesis false. It is quite clear that the Shacklebolts would not have been considered "true" purebloods by the pureblood fanatic character who compiled his list if there had been Muggle-born antecedents in the direct line that recently.
That said, I do strongly suspect that the Shacklebolts of the 1930s were white. Kingsley himself is not old enough to have been born then. He seems to be approximately from the same time as the Marauders, or possibly a few years later. There wouldn't likely have been much widespread wizarding migration from Africa to Britain in the 1930s or earlier. And my extrapolations about the ethnic composition of the British wizarding world prior to the dissolution of the Empire (and the vast growth of the British nonwhite Muggle population) still hold. Let's face it, any black witch or wizard in the British wizarding world in, say, the 17th century (which is probably how far back one would have to trace "pureblood" descent to qualify for that status in the fanatics' eyes), was either brought to the island as a slave, or would have been an isolated migrant from Africa. (Wizards would have had access to broomsticks, flying magical beasts, Floo transportation, Portkeys, and Apparition, as well as spells to simplify packing one's worldly goods. The economic and logistical limitations imposed on Muggle migration in the past would not have applied.) Either type of person would have been assimilated into the wizarding community. Rowling has stated that witches and wizards do not engage in ethnicity-based racism, and while this statement refers to the late 20th century wizarding world, it probably would have been true in the past as well. They have a long history of pride in being wizards, not in having skin of a particular color. It is nearly impossible to imagine a witch or wizard who would remain enslaved to a Muggle, and it's equally impossible to imagine that the wizarding government would have permitted it. In addition to the profound insult to wizarding pride in allowing such a thing, it would be a security risk. Harry Potter used a burst of accidental magic against "Aunt" Marge when she was bullying and emotionally abusing him, so obviously slavery would be simply inviting such incidents that could expose the existence of magic.
So, between voluntary migrations and the probable policy of the Ministry of Magic (and its pre-Seclusion predecessor) toward witches or wizards in slavery to Muggles, it's quite possible to extrapolate the occasional addition to the past wizarding community of a person of color. It is not, however, really plausible to propose that distinct families of color could be both pureblood and of a nonwhite race for 300 years. There just wouldn't have been enough genetic diversity in the wizarding community to support that until large-scale migration started to occur in the 20th century. And no, the population of the wizarding community would not have been as high as it is in the 1990s. It probably did not undergo the same rate of growth that the Muggle population did over the past 300 years, of course. Witches and wizards would not have suffered the mortality rates that Muggles did. But there's also a heavy hint in Order of the Phoenix, in the St. Mungo's chapters, that magical medicine continued to develop after the 17th century just as Muggle medicine did. The wizarding community in the 17th century may have been half to two-thirds of its present size, just as an estimate. There simply wouldn't have been enough people in a British population of a couple thousand for wizards of color to marry only other wizards of color for 300 years. So, in all probability, the Shacklebolts of the 1930s were a predominantly white family. This generation would have included Kingsley's paternal grandfather. Kingsley's own father may or may not have been born yet. Given the tendency of pureblood families to promote very early marriages, and to start having children within the first year or two after marriage, I'm inclined to say not.
So my original hypothesis about Kingsley's antecedents may not be entirely wrong after all. His father, and possibly his paternal grandfather, could have married witches of color. And whatever "true pureblood" claims were made, they were made about the 1930s family, so these wives could even have been Muggle-born. If their families had indeed lived in Britain for many generations, they just about would have to have been. That said, I still prefer the idea that these women would have come from immigrant families from ex-colonies. I do rather like my theory about large-scale wizarding migration to the island, to avoid dealing with Muggle political upheaval, after these nations gained independence. It provides a perfectly reasonable way, without stretching credulity at all, for the British wizarding world to now include the degree of ethnic diversity that modern Western society in the real world has.