InsaneJournal

Current mood:	geeky
Current music:	Mean Girls.

This is for icemice, but may be useful to others?

MUGGLEBORNS! HUZZAH!

OR,

HOW KASSIE LEARNED TO MAKE PUNNET SQUARES IN PHOTOSHOP
THEN SUBSEQUENTLY PUT TOO MUCH THOUGHT INTO THIS
(a morality play)

ACT ONE Alright, so, first, I admittedly tried just doing a basic dominant/recessive inheritance for magic, but this is too simple and rather flawed: 1. Assuming that magic [here given the genotype M for dominant, m for recessive] is the recessive trait, then all magic-users would need to have the genotype mm; MM would be pure Muggle and Mm would presumably be Squibs... but they'd be the children of magic users who had children with Muggles too, which we know from canon doesn't work. One (meaning me) assumes that this is what the more reductionist members of Dumbledore's side think that the Blood Purist mindset resembles. 2. On the other hand, magic could be the dominant trait, but this poses problems of its own. If magic were the dominant trait, then genotypes MM and Mm would be magic-users, mm would be Muggles, and almost the entire world would be waving a magic stick around, shouting mangled Latin, and making things happen. Which is entirely nonsensical, since we know that Muggles are the vast majority. I WILL NOTE that, after going through the process of doing all of this, I neglected the possibility of mutation, which JKR sort of hinted at once, in her, "I didn't really do this much in high school" (understandably, since the teaching I got in genetics had the benefit of being in the twenty-first century, after many revolutionizing discoveries, and JKR wouldn't have had said privilege) way. HOWEVER, even factoring the possibility of mutation into things, a simple dominant/recessive pattern is too simple. So I tried a sex-linked recessive pattern, which is usually taught through the examples of hemophilia and red/green colorblindness in American biology classes. Basically: you have X chromosomes and Y chromosomes; if you have XX, you're biologically female, and if you have XY, you're biologically male; there are plenty of interesting occurrences that can happen with the genes themselves, how they end up expressed, and how a person comes to deal with and identify their gender, but for right now, all we care about is XX vs. XY. Now, on a chromosome map, the X chromosome is very large and chock-full of genetic information; it's the big, bad wolf of the sex chromosomes, if you will. Y, on the other hand, has genetic information in it, but he's smaller, contains less of it, and can very easily be pushed around by X. Sex-linked recessive patterns arise out of things that get expressed on the X chromosome, usually noted as Xq. With females, chances of being affected by these conditions are rare. Because X is so big and butch, it is possible for a woman to have the genotype XXq and not be affected because the X without the q on it has enough genetic information to outweigh the q and whatever it feels like doing. In order to be an affected female, you need to have both a carrier mother (i.e., XXq) AND a father suffering from the condition, and even then, it's fifty-fifty. You COULD get screwed and end up XqXq, but you could also end up just being another carrier. Males aren't so lucky. Because their Y chromosome gets pushed around by X, having a carrier mother lands them with a fifty-fifty chance of being affected; if a boy ends up with XqY as his genotype, he'll have whatever condition is being discussed. fig. 1: Sample punnet square for sex-linked recessive inheritance of magic, where m denotes the magic gene. This, too, creates problems. As you can see in the punnet square, if magic were a sex-linked recessive trait, there'd be no Muggleborn girls. Ever. Which we know is BS, since Lily and Hermione are both Muggleborn. (NB: I didn't do anything with Y-linked or X-dominant inheritance because, to be perfectly honest, I haven't been in a biology class that did doodly squat with genetics for a while [like, since 2006]. I sort of think we covered those, but we may not have, and if we did, I'm very rusty on them, so they got ruled out due to personal necessity. There are probably good reasons why they could or couldn't be a possibility, but I like the explanation I eventually wound up with. Anyway.) On to... ACT TWO So I'd exhausted the very simple ideas. Next stop, I turned to the idea of doing a dyhybrid cross. Usually, these come up in textbooks in the form of a test-cross, or taking two things with genotypes like AaBb and posing the question, "What's the likelihood of getting an offspring with [some random genotype here]?" The first trait I needed was sex, not due to issues of inheritance as before, but mostly to test and make sure we weren't going to end up with a predominantly male-inhabited or predominantly female-inhabited Wizarding world, because neither really suits the image of a (mostly) gender-equal society with a (presumed fairly) even distribution of genders. The second trait was magic, denoted with m and q rather than M/m because, given how things had gone before, I wanted to experiment with having magic be a case of mixed inheritance, or possibly a continuum of genes being expressed simply (so... less like hemophilia, more like hair color and texture). I settled with a continuum instead of mixed inheritance... honestly, because I thought it made more sense for almost no rational reason. Retrospectively, a continuum makes more sense because mixed inheritance brings up the issues of why magic can't be a simple dominant/recessive inheritance pattern from act one. Either way. Not so important to the story. fig. 2: Sample punnet square for a test-cross illustrating the mq idea of magical inheritance, where mm and mq denote a magical person and qq denotes a Muggle.* *: This is based on a quote I can't find from JKR, where she basically said that magical genes are very hardy, difficult to get rid of, and most likely would take the dominant-ish role here. This, too, creates problems. It's getting closer to some semblance of reality, but we end up with far too many magical people to make sense. Granted, this is a test-cross of two magical people, but this has the problem of accounting for Muggleborns. All of them would end up needing to be accounted for by random mutation (which JKR has hinted at or outright said occurs before, though I don't have the exact quote), and while I can accept the idea that magical genes (i.e., the genes in charge of magical inheritance, not the genes of magical people) are more volatile and prone to mutation than the other ones, it would still have to be a seriously rare occurrence. I won't try to put a number on it, but considering all the examples of Muggleborns in canon, there's pretty much no way all of them can just be because of random mutations. (Unless, of course, something was in the water supply or likewise, but, even so, I have to imagine that the Creeveys, Grangers, Clearwaters, Finch-Fletchleys, et al. all live in vastly different parts of Britain, so the odds of them all drinking the same water before the conceptions of their Muggleborn kids are astronomically high.) Anyway... ACT THREE ...which is an appropriate heading, because I wound up figuring things out (in a way that makes sense to me) with a trihybrid cross! Click Here for Figure 3. WARNING: BIG IMAGE. Fig. 3: A hypothetical trihybrid test-cross between two magical individuals, with the genotypes XXmqAa and XYmqAa. Now, to explain what that big mess means, beyond the little notations in the squares. XX vs. XY: Sex. We've been over it. mm vs. mq vs. qq: The continuum of magical possibility. We've been over this too, but, writ short: m is the vaguely dominant allele in this situation, but it and q are more cooperative than a standard dominant/recessive pattern. mm means definite magical ability; mq, in most cases, will mean magical ability, but does not always; and qq means a definite absence of magical ability. AA vs. Aa vs. aa: The genes that regulate the expression of magical ability. I honestly do not remember how I came upon this idea, but while I was sitting on my bed, staring at my punnet squares in photoshop, it came and whalloped me upside the head. THIS pattern of inheritance IS dominant/recessive. In this case, the dominant genes express magical powers, which is to say that someone with the genotypes AA or Aa, and at least one m in their magical potential genotype, would be a Witch or Wizard; the magical genotypes are, given this: mmAA, mmAa, mqAA, and mqAa. aa, on the other hand, turns magical potential off. So, any magical potential genotype that ends up with aa tacked on the end ends up being a Squib. A person with the genotype mqaa is, then, someone with the potential to cast spells... but without the natural ability to do so. They're the Squibs who are most likely to be helped by the Quik-Spell course, because, I imagine, it taps into the fact that they do have this potential and helps them find ways to tap into it, even if only to a very limited degree. Fun fact: There are a lot of reasons for why I went with a dominant/recessive pattern, but my favorite is the one where, if you look at patterns and trends in inbreeding (specifically, how recessive traits often end up becoming more dominant in inbred lines), it's entirely possible that Purebloods (meaning Blood Purists) are breeding their own demise by keeping everything in the family. The more you inbreed and keep a recessive trait around, the more likely you are to have it crop up and get fully expressed, so, in this case, the more likely you are to get Squibs. Mwahaha. EXCEPTIONS TO THIS (or just colorful, interesting anomalies) mmaa: Now, according to my above rules, the mmaa genotype should be turned off. However, as JKR said wherever she did so, the genes in charge of magic are very powerful and ornery, and so I've reasoned that having two m alleles would outweigh having two recessive a alleles. As such, people with the mmaa genotype are still perfectly capable of using magic like normal witches and wizards. qqAA and qqAa: Good for these people. They have a theoretical possibility of expressing magic. Too bad, they have no actual ability to do so. But, wait, Kassie, doesn't this mean there are too many Witches and Wizards in Britain?: In theory, yes. BUT, that said, this test-cross is of two magical people, so more magical offspring are to be expected. The "typical" Muggle genotype (i.e., the one I imagine Uncle Vernon would have) would be qqaa, so no potential for magic and no ability to express it, besides. The question of why a recessive gene is the most prominent one in a population is a tough one to answer, especially since, theoretically, having magic is a great survival advantage. This debate could wander off down too many different paths and, really, would deserve its own post, but here are a few possibilities: 1. squibs procreating with Muggles who had the qqaa genotype, thus creating lines of Muggles with a theoretical possibility of expressing magic, but no ability to do so; 2. persecution of magic users throughout the ages was, occasionally, more successful than the Spanish Inquisition and ideologically-related witch-burnings that got sporked at the beginning of PoA; 3. early witches and wizards tended to remove themselves from the gene pool more often than not; and 4. "I don't know, but things like this do happen in the real world, so let's accept it and move on." AND WHAT ABOUT THAT ASTERISK ON THE CHART, EH? IN THEORY, it is possible for Muggles to display the genotypes: mqaa, qqAA, and qqAa. Possessing the m allele and a dominant A allele would seem to be indicative of magical ancestry (and, if we acknowledge that squibs could have abandoned magical life, like Ron's random relative who works in a Muggle office, and had children with Muggles, this is very possible), but this is not necessarily true. As I've said before, the possibility of random mutation is one that JKR vaguely mentioned, but she did so without really considering what she was talking about. Which, again, is understandable. Now, random mutations would be rare occurrences, even considering how volatile and easily mutable the genes in charge of magical inheritance likely are, but it's entirely plausible that: a. they could happen, and b. they would happen. Muggleborns do not come out of nowhere, and even if Squibs were tossing magical life aside to procreate with Muggles, the incidence of that happening is likely just as rare as, if not rarer than, random mutations. Both are possibilities, and neither is inherently more valid than the other (though, I personally, do believe more in random mutation), and both would, technically, be natural occurrences. It's also very possible for various mutations within families to pile up and still not result in a magical person. At a certain point, it would start getting to a credulity-straining low probability, but it's still possible. The interesting conundrum that this led to, for me, involved the protective spells that get used to keep Muggles from seeing Hogwarts, the Quidditch World Cup, et al. Now, I'm pretty sure we're all clear on the basics: some folks used said spells, and they make the magical places in question look like something other than what they are. On a biological level, though, if Muggles and Squibs can potentially have the same genotypes, then they should all, theoretically, be able to see through the spells like Squibs can (or, conversely, the Squibs shouldn't be able to see Hogwarts, et al.). So far, the only potential explanation I have goes back to the volatility and otherwise special-ness of the genes in charge of magic: in the case of a squib, he/she would be from a family with already extant magical blood, and so the genes would recognize themselves as magical and be immune to the anti-Muggle effects. In the case of Muggles, their genes would have mutated, but they wouldn't recognize themselves as magical because they couldn't actually make magic happen, ergo they would be affected by said spells. This does complicate things, if we think about the possibility of squibs and Muggles intermarrying, but it's possible that, after so long without the ability to express magic, the genes would stop identifying themselves as magical. ACT FOUR Examining some canon cases of Muggleborns. Fig. 4: a possible explanation for Hermione Granger, Petunia Dursley (nee Evans), and Lily Potter (nee Evans). This one started out as just trying to figure out how likely it would be for Hermione to have a magical sibling, but once I got into it and filled in the boxes, I found that it could be a potential explanation for the Evans sisters as well. I've given the hypothetical parents the genotypes XXmqaa (so a mutation or history of familial mutations left the mother with the potential for magic, but no ability to do anything about it) and XYqqAa (a mutation or history of them left the father with the ability to express magic, but no magic to express). Given these mutations, it's unlikely that Hermione would have a very low chance of having a magical sibling, and she herself only had a 12.5% of existing in the first place. Same went for Lily. Now, Petunia has the mqaa genotype in my theoretical punnet square, which I think makes sense because of the memory in DH where Lily calls her out on having harassed Dumbledore into giving her an invitation to Hogwarts. It wouldn't have meant much, because she has the genotype that I gave to Squibs who'd be most helped by Quik-Spell, but, theoretically, given her possible genotype and the fact that Lily was magical (c.f., the JKR quote I referenced before, which made a point of how magical genes are resilient and worm their way into families), there could be a slim, highly theoretical chance that she could learn to do magic, given the right mindset. She'd probably never have the right mindset, but it's possible. I will also note, because Penny and Kira's Dursley twins at nextgen remain two of my favorite characters from that adventure (which doesn't say much, because I had a lot of favorites, but either way), that while Dudley is most certainly a Muggle, it's very possible for him to have magical kids. Even if Vernon had the qqaa genotype for certain, Dudley has a fifty-fifty chance of getting Petunia's m allele and, so, would end up with mqaa as well. Since he's a Muggle, he couldn't have a mutation to get a dominant A, but we don't know who he marries and has children with, so she could be mqaa, qqAa, or qqAA (or possibly one of the magical genotypes, but I'm assuming that he wouldn't marry a Witch), and then, from those combinations, it's possible for him to have magical kids. Fig. 5: a possible explanation for the Creeveys. And here, we finally get back to the question I originally set out to answer: how likely is it for Colin and Dennis Creevey to both be magical? In the case of the Creeveys, the genotypes I saddled their parents with were: XXmqaa and XYmqaa, which wound up having the same outcome for magical children as the Granger/Evans punnet square. Now, to more accurately answer this question: barring a random mutation that made one of them (most likely in Dennis, since Colin is the first, he's already magical, and JKR's stance is that magic is rather difficult to get rid of, once it's in a family), the Creevey family has a 25% chance of having a magical child in general, a 12.5% chance of having a magical son, and about a 1.6% chance of having two magical sons. So, it's very unlikely, but still possible, and there's probably some adjustments to things to be considered, given that Colin was already magical... but I've spent a lot of time on this already, it's almost 6 AM, and I want to sleep.