28

In Harry Potter and the Methods of Rationality, Harry explains muggles, squibs and wizards with a genetic marker (a single gene on two chromosomes). So, muggles have none, squibs have one and wizards have both.

But that would mean that for a wizard to have a squib child, s/he needs to mate with a muggle. Else both parents have two copies of the gene and so would all of their children, they would only ever have wizard children (until they mate with muggles).

Chapter 23:

if two Squibs marry. One quarter of the children would come up magic and magic, and be wizards. One quarter would come up not-magic and not-magic, and be Muggles. The other half would be Squibs. It's a very old and very classic pattern.

But there seem to be Squibs born to Wizards (Chapter 7):

We are fading [...] as we [...] allow our Squibs to live.

The other sciences in the story where either other my head or correct as far as I understood them, so I assume to understand something wrong.

  • 1
    Certainly. You'd need to have some Muggle ancestry in you. Let's take 2 Wizards who are heterozygous (Gg x Gg) for the Wizard gene (G) and the Muggle gene (g). We draw up a genetic diagram and we get the genotypes for their children: GG, Gg, Gg, gg. Let's assume the alleles are codominant, thus we'll have a 25% chance for the child to be a Wizard (GG), 50% for a Squib (Gg) and 25% for Muggle (gg). This is the biological logic for your first quote, basically. Won't bother writing an answer 'cause this might seem complicated (not to mention utterly ridiculous if you never studied Biology) – Mat Cauthon Aug 11 '17 at 11:52
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    @Olórin Please do write an answer! Its complicated, is the reason I asked. If it were easy I would have understood it yet. – Angelo Fuchs Aug 11 '17 at 11:56
  • It's still in the HP franchise, though. You can add the [genetics] tag back, if you wish. – Gallifreyan Aug 11 '17 at 12:01
  • Hang on, Aren't Squibs essentially wizardborn muggles? As in children from wizards with no magical powers of themselves, but privy to the wizarding world? Then how can Wizards get Muggle offspring? – Nzall Aug 11 '17 at 13:34
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    @Olórin your "Wizards" and "Squibs" are both Gg; assuming that only that gene affects it, this is impossible. – Tin Man Aug 11 '17 at 19:20
25

If you assume that Harry is correct, then a Wizard/Squib cross could have either Wizard or Squib offspring, at 50% each; you don't need a Wizard/Muggle cross to get Squibs. However, two Wizards could not produce anything other than Wizards, as you point out. There's a reason that I emphasized the initial phrase in this answer, however - and if you consider the hypothesis in light of the true definition of the scientific method and the methods of rationality, you inevitably have to come to the conclusion that the hypothesis of a single allele controlling Wizard/Squib/Muggle status is wrong, because it doesn't match reality's facts.

(It should be noted that even if Harry's hypothesis were correct, and two Wizards could not produce a Squib, for Squibs to exist at all would necessarily require some Muggle ancestry.)

Let's look at the single-allele model. We'll call it M (for can-do-MAGIC). If a person has the M allele, we mark it in upper-case (M); if they lack it, we mark in lower case (m). A person carries two copies of the allele, one from Mom, one from Dad. Thus, by Harry's hypothesis, a Wizard has MM, a Muggle has mm, and a Squib has Mm. So, the crosses appear as follows:

Wizard with Wizard: Both wizards only pass on the M allele, so all children are MM, or Wizards.

Muggle with Muggle: Both muggles only pass on the m, so all children are mm, or Muggles.

Wizard with Muggles: The Wizard parent always passes M, the Muggle parent always passes m, so all children are Mm, or Squibs.

Those are the simple ones. Now for the complex ones:

Squib with Squib: There are four cases:

  1. Mom passes M, Dad passes M. Child is MM, or Wizard.
  2. Mom passes M, Dad passes m. Child is Mm, or Squib.
  3. Mom passes m, Dad passes M. Child is Mm, or Squib.
  4. Mom passes m, Dad passes m. Child is mm, or Muggle.

Wizard with Squib: There are two cases, because the Wizard always passes M:

  1. Squib passes M. Child is MM, or Wizard.
  2. Squib passes m. Child is Mm, or Squib.

Squib with Muggles: There are two cases, because the Muggle always passes m:

  1. Squib passes M. Child is Mm, or Squib.
  2. Squib passes m. Child is mm, or Muggle.

Note that in no case can two Wizards produce anything other than Wizards. If they produce Squibs, then either the hypothesis is wrong, or there has been a mutation during embryo development that changed a M to a m. Similarly, for two Muggles to produce a Wizard, either they're both actually Squibs, or there was a mutation during embryo development that changed both m to M.

Or, by Occam's Razor, Harry's hypothesis is wrong.

  • 2
    Or, the gene must inherently be very long and is thus subject to a stupidly high mutation rate. Or, the magic selection imposes an allowed mutation of zero so any mutation to the gene at all disables it completely. – Joshua Aug 11 '17 at 16:31
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    It's possible for squibs to be created by mutation, and genes with high mutation rate do exist. However, this leads to two different meanings for "squib" - a non-magical person born to wizards (due to a mutation), or a person with a latent magical gene (e.g. Mr&Mrs Granger). – ugoren Aug 13 '17 at 21:47
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    @ugoren, that's not a problem. There's no evidence of any practical difference between a non-functional magical gene and a Muggle gene, they can be thought of as the same thing, the m in Jeff's answer. So both cases are Mm the only difference being how the m arose. – Harry Johnston Aug 13 '17 at 22:45
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    @Jeff, in the absence of a competing hypothesis that more simply explains the existing evidence, I think you're misusing Occam's Razor. The mutation hypothesis seems the most reasonable explanation, given that wizard-born Squibs are very rare. – Harry Johnston Aug 13 '17 at 22:48
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    @E.Huckabee - which would, in fact, make both parents squibs, rather than muggles, even if neither of them actually knows it. – Jeff Zeitlin Nov 29 '17 at 13:01
31

Chapter 23 discusses the genetic situation as a method of discovering why magic appears to be getting less powerful. In later chapters he concludes that the simplistic genetic marker is used as a method for whatever causes magic to work to recognize a person as capable of being answered.

It is as if there is a computer that actually performs the magic when someone with the correct genetic marker issues the appropriate voice command.

chapter 25

So. There was only one thing that made you a wizard.

That wasn't surprising, when you thought about it. What DNA mostly did was tell ribosomes how to chain amino acids together into proteins. Conventional physics seemed quite capable of describing amino acids, and no matter how many amino acids you chained together, conventional physics said you would never, ever get magic out of it.

And yet magic seemed to be hereditary, following DNA.

Then that probably wasn't because the DNA was chaining together nonmagical amino acids into magical proteins.

Rather the key DNA sequence did not, of itself, give you your magic at all.

Magic came from somewhere else.

And for some reason the Source of Magic was paying attention to a particular DNA marker among individuals who were ordinary ape-descended humans in every other way.

The actual use of magic is not as simplistic as just having the correct genetic marker.

Some intelligent engineer, then, had created the Source of Magic, and told it to pay attention to a particular DNA marker.

Thus, the birth of a squib to two wizards (as in your question) is possible for different reasons than the genetic marker involved. That is MM could still produce a squib for different reasons. The logic cited below and in other chapters explains this.

He shows that it is not the reason that magic is not a powerful as it used to be. I think that he actually thinks to himself that the methodology is more complicated than that and that he is using the explanation that he gives in order to get Draco to follow the rationality logic. However, he is careful in what he says and what he does in order to get the results that he needs. He is also trying to get Draco to analyze the situation and learn to use logic.

Please remember that he is single handedly trying to raise the level of civilization of a medieval culture to modern times as well as prevent the destruction of the "muggle" world.

Observation:

Wizardry isn't as powerful now as it was when Hogwarts was founded.

Hypotheses:

  1. Magic itself is fading.
  2. Wizards are interbreeding with Muggles and Squibs.
  3. Knowledge to cast powerful spells is being lost.
  4. Wizards are eating the wrong foods as children, or something else besides blood is making them grow up weaker.
  5. Muggle technology is interfering with magic. (Since 800 years ago?)
  6. Stronger wizards are having fewer children. (Draco = only child? Check if 3 powerful wizards, Quirrell / Dumbledore / Dark Lord, had any children.)

Tests:

A. Are there spells we know but can't cast (1 or 2) or are the lost spells no longer known (3)? Result: Inconclusive due to Interdict of Merlin. No known uncastable spell, but could simply have not been passed on.

B. Did ancient first-year students cast the same sort of spells, with the same power, as now? (Weak evidence for 1 over 2, but blood could also be losing powerful wizardry only.) Result: Same level of first-year spells then as now.

C. Additional test that distinguishes 1 and 2 using scientific knowledge of blood, will explain later. Result: There's only one place in the recipe that makes you a wizard, and either you have two papers saying 'magic' or you don't.

D. Are magical creatures losing their powers? Distinguishes 1 from (2 or 3). Result: Magical creatures seem to be as strong as they ever were.

"A failed," said Harry Potter. "B is weak evidence for 1 over 2. C falsifies 2. D falsifies 1. 4 was unlikely and B argues against 4 as well. 5 was unlikely and D argues against it. 6 is falsified along with 2. That leaves 3. Interdict of Merlin or not, I didn't actually find any known spell that couldn't be cast. So when you add it all up, it looks like knowledge is being lost."

And the trap snapped shut.

Note this

"I didn't know anything you didn't know," Harry said, still quietly. "I admit that I suspected. Hermione Granger was too powerful, she should have been barely magical and she wasn't, how can a Muggleborn be the best spellcaster in Hogwarts? And she's getting the best grades on her essays too, it's too much coincidence for one girl to be the strongest magically and academically unless there's a single cause. Hermione Granger's existence pointed to there being only one thing that makes you a wizard, something you either have or you don't, and the power differences coming from how much we know and how much we practice. And there weren't different classes for purebloods and Muggleborns, and so on. There were too many ways the world didn't look the way it would look if you were right. But Draco, I didn't see anything you couldn't see too. I didn't perform any tests I didn't tell you about. I didn't cheat, Draco. I wanted us to work out the answer together. And I never thought that magic might be fading out of the world until you said it. It was a scary idea for me, too."

  • 8
    This is probably the best answer, as the point of the whole passage - and the whole story - is to illustrate the reasoning process, not analyze Mendelian inheritance. – Jeff Zeitlin Aug 11 '17 at 13:05
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    It's also possible that Harry is right and magic is that simplistic, and all Squibs are bastards (and not just in their fathers' eyes). – Tin Man Aug 11 '17 at 19:21
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    This is just wrong. The passage you link to concludes that wizarding genetics are the simplistic sort. "Result: There's only one place in the recipe that makes you a wizard, and either you have two papers saying 'magic' or you don't." This is also taken for granted later in the story, IIRC. – Harry Johnston Aug 12 '17 at 7:43
  • @Walt You can also get a squib by a witch marrying a squib, though - so only the first squibs necessarily had a muggle parent. As is alluded to later in the story, it isn't entirely uncommon for a witch to enchant a muggle and have a bit of fun (Voldemort's parents are implied to be the same case, IIRC). And of course, there may be some extra complications - mutations, weird chromosomal crossover, variations in the code of the original cells in the embryo (e.g. calico cats)... and that's still considering the marker to be natural, rather than artificial in nature. – Luaan Aug 12 '17 at 8:03
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    Yes. And the reason Harry concluded that genetics isn't sufficient to explain the loss of power is that the evidence showed it to be the simplistic sort, with only a single gene. The eventual conclusion was that it had nothing to do with genetics at all, it was because wizards had lost the knowledge necessary to perform the most powerful magics, presumably due to the Interdict of Merlin though that part was never quite spelled out. – Harry Johnston Aug 13 '17 at 3:40
10

If we are talking about gene crossing, as in Mendelian model, then there is something wrong about that chapter 7. I did not read the mentioned fanfiction, so... Let's science.

This is scientifically accepted approach to how parental genes work. Based on this model, you would have to define a dominant allele. In your question, this would be being Squib or being Wizard.

Based on this quote:

One quarter of the children would come up magic and magic, and be wizards.

I would say S allele for being Squib is the dominant factor because 2 Squibs can produce a magical child if they have the recessive allele of not being a squib.

enter image description here

This model also explains;

  • If you have S alleles (SS) from your parents, you become a muggle,
  • If you have S allele and s allele (Ss) from your parents, you become a squib,
  • If you have s alleles (ss) from your parents, you become a magical being.

So, it is obvious the author of this fanfiction used a simple version of Mendel's gene crossing law and it works fine.

However, I could not verify how the quote from chapter 7 works as well. In this model, two magical beings cannot produce a squib unless there is an exception.

There are more complex models that includes multiple alleles but the author gives the quote from chapter 23 and admits the usage of simple version of the Mendelian crossing.

P.S. R.I.P MS Paint.

  • Good on you for using pictures; I couldn't do that (imgur is blocked from my office), and I also couldn't figure out how to do tables in SE-flavored Markdown, so I had to list out the crosses textually. – Jeff Zeitlin Aug 11 '17 at 13:00
  • Glad to help guys. – apollo Aug 11 '17 at 13:17
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    This is a good explanation of Mendelian genetics but since his time we've learned a lot. In the real world, even if this is a single allele trait, it would be entirely possible for 2 wizards to have a muggle child in a variety of ways. Simply having a gene does not guarantee that the gene will be expressed. There could be problem with the enzymes required for replication, there could be a problem with utilization (cells that proteins made by this allele should use don't accept them), there could also be a blocking gene elsewhere (producing a prot that fills locations these need to go to).... – krowe2 Aug 11 '17 at 21:48
  • @krowe2, you should post that as an answer. Also see my comment on the question. – Wildcard Aug 11 '17 at 22:13
  • @krowe2 as mentioned in my answer, you are correct. This version of the gene crossing might not work under some circumstances. The author uses the simpler model to describe how things work and assumes there are no complications. That is why the quote from chapter 7 does not work for us, unless there are exceptions and mutations. – apollo Aug 12 '17 at 7:18
6

I am going to bring up what the writer himself has brought up when asked about this:

There is indeed one critical location, as the Mendelian pattern shows pretty strongly - from a Bayesian perspective, it's significantly more likely to show up if there's a single critical location, and that's by far the simplest explanation for what shows up. Harry thought the Squibs were being caused by witches Imperiusing Muggles and sleeping with them. The possibility Harry didn't think of is this: there isn't a "wizard gene", there's a Muggle gene. Damaged Muggle genes create wizards; sometimes two wizards mate and one of the damaged Muggle genes ends up repaired via chromosomal crossover. Since recent Muggleborns tend to have less damaged Muggle genes compared to old wizard families, the chromosomal repair is much more likely to happen among wizarding lines which recently accepted Muggleborns into their ancestry.

I didn't find any good way to work this into the story before the end, unfortunately.

The ensuing discussion is also fairly interesting.

Source:

https://www.reddit.com/r/HPMOR/comments/3btuto/question_about_genetics_of_magic/csri94d/

5

The only way for this to work would be for magic to be recessive on one gene and then another, unrelated, gene that can prevent someone who should be otherwise able to cast from doing so.

So two genes. One recessive for a positive trait (Wizardry : W) and the other recessive for a negative trait (Squibness : S). I will follow the usual genetic notation of a uppercase character meaning the dominant trait, so a WW would be a Muggle with no chance of having a wizard child and SS would be someone not a squib and no potential to pass such a trait on.

For the vast majority of the population (Muggles) the S trait will have absolutely no effect and be impossible to detect without doing DNA analysis.

A population of pure-blooded wizards (ww) who expel or execute the squibs among them will be made up of a population of wwSS and wwSs. The occasional squib can still pop up, though with the squibs removed and their family likely deemed at least a little undesirable, it would remain a rare event.

A wwss (Squib) would very likely have a magic using child if mated with a wizard. Worst case (mating with a wwSs) would result in a 50% chance of each child still being able to use magic.

Though this would propagate Squibness through the wizard community, which would confirm the statement that magic may be fading because they "allow their squibs to live".

This would likely work out even better if Squibness was the result of 2 or more recessive traits of its own that each had a dampening effect on magic, culminating in a complete lack of magical ability when one person has all the recessive traits.

3

Assuming Harry's genetic model to be correct, there are at least two ways in which a Squib could be born into a wizard family. One is that the Squib's biological father might have in fact been a Muggle; so far as I'm aware, wizards do not have paternity tests. The other is a deleterious mutation in one of the two magical genes, causing it to become non-functional.

  • 1
    I suspect that somewhere there's an Identificatem Patris spell, the casting of which is often rapidly followed by AVADA KEDAVRA, "unforgivable curse" or not... :-) – Bob Jarvis - Reinstate Monica Aug 12 '17 at 4:54
  • This is a very good point! – Angelo Fuchs Aug 14 '17 at 8:50
1

I'll argue that the wizarding gene, W, must be dominant. Let's consider:

  1. What is the difference between a muggle and squib? Both of them are not capable of using magic; thus, they either don't have W or they have a defective copy of W (dw). The only difference between a squib and a muggle is parentage; the squib has at least one W parent (who must, barring random mutations, be (W-dw) or (dw-W)), while the muggle has none.
  2. How can a pair of pure-blood parents have a squib child? If both parents carry a single defective copy of W (dw) then genetically their makeup is (W-dw). Their offspring can then be (W-W)=wizard, (W-dw)=wizard, (dw-W)=wizard, or (dw-dw)=squib. And it could happen that pure-blood parents, both of whom are (W-W), could still produce a squib if both copies of W received by the child were defective - thus the child is (dw-dw) and therefore a squib.
  3. What is a muggle, genetically speaking? A muggle has two copies of (dw), as does a squib. Thus muggle = squib = non-magic-user. The only difference between them is a matter of knowledge (the squib knows that magic exists and he/she can't do it, while the muggle is spared this embarrassment).
  4. How can two muggles have a wizard child (e.g. Hermione Granger)? The (dw) gene, carried by both muggle parents, can on rare occasions mutate to (W), so that the child has either (W-dw) or (dw-W), and is thus a wizard.
  5. Why isn't (W) more common? Who says it's not? :-) Good old-fashioned human fear of the "different" accounts for some of it, ignorance for the rest. In antiquity if someone could use magic he/she often found themselves being burned at the stake, strapped to the ducking stool, or killed in some other manner - but dead is dead. In self-defense magic users learned to hide their abilities, and would only interbreed with others like them, thus forming a closed community. Also, there may be a lot of people wandering around as muggles who have the ability to use magic, but due to lack of knowledge and training never learn to do so.

Basically, when it comes to wizarding ability, you've either got it or you don't. In the Potterverse I suspect that the reality (so to speak) is more complex, and there may be several genes which grant the ability to manipulate magic. Some of these genes could reinforce each other, and thus it might be that not all magic users are created equal; the use of a single W gene here is just for a simplified demonstration.

  • I don't think that's consistent with the data Draco obtained, though. – Harry Johnston Aug 12 '17 at 7:45
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    This, while interesting for main canon, contradicts the hpmor canon. Muggles have trouble looking straight at magic, most potions don't work for them and they can't use magic tools. Squibs can use magic tools, potions etc. but can't do magic. – Angelo Fuchs Aug 14 '17 at 8:49
0

I feel obligated to point out that the dominance/recessiveness of magic does not relate to being a Squib at all. A Squib is an entirely different pathology - either psychological or genetically influenced is arguable but any wizard/witch (double recessive by the simplified Mendelian chart above) can separately be affected by "Squib Syndrome". Recall that in the canon many Squibs can perform magic, but are just really terrible at it. And some can lose their powers from tragedy or abuse (Tom Riddle's mother for example). As such, there's nothing wrong with modeling magical inheritance through a classic Punnett square - in this model, many people are simply Mm carriers.

  • Never mind, that's in an answer above... my apologies – Edlothiad Aug 13 '17 at 22:29
  • In canon that may be right. In HpMor its definitely not. – Angelo Fuchs Aug 14 '17 at 8:45

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