who are you callin' a homozygote?
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mollymoon asked. I wrote this up a while ago, to get my own thoughts in order. Yeah, I know the wizarding world doesn't obey the laws of biology. But if it did...
The Genetics of Harry Potter
Introduction
Before we get started, here's a quick overview of basic genetics: Each gene determines one physical trait. A gene comes in two parts, called alleles, which are usually represented by letters of the alphabet. In some genes, one allele is dominant (represented by a capital letter) and the other is recessive (represented by a lower case letter). If the dominant allele is present, the trait it determines always shows up, whether the other allele is the dominant one or the recessive one. A recessive trait only appears if both alleles are recessive.
An individual who has two of the same allele is called homozygous. An individual who has two different alleles from the same gene is called heterozygous.
The physical traits of an individual are called the individual's phenotype. The actual alleles that underlie these physical traits are called the individual's genotype.
During reproduction, the genes of each parent split into their component alleles, and one allele from each parent is contributed to the offspring, making one whole gene. It's random which allele is contributed.
It's really more complicated than this, of course, but that's all you need to know to start with.
One Gene, Complete Dominance
In this theory, magical ability is determined by a single gene; its two alleles are the dominant M (Muggle) and the recessive m (wizard). There are two possible phenotypes (Muggle or wizard), but three possible genotypes:
Two wizard parents (homozygous by definition) will always produce wizard
offspring:
Two homozygous Muggle parents will always produce homozygous Muggle offspring:
A homozygous Muggle and a homozygous wizard will also produce all Muggle offspring, but they will all be heterozygous:
If one of these heterozygous Muggles marries a wizard, their offspring will have a 50% chance of being a heterozygous Muggle, and a 50% chance of being a wizard. Wizards with such parents are "half-bloods", like Seamus Finnegan. We can see that the elder Mr. Finnegan must have been a heterozygous individual — in other words, he must have had at least two wizard ancestors somewhere in his family tree (assuming no sibling incest). We can also see that Seamus has exactly the same genotype (mm) as any other wizard — genetically, his magic is just as "pure" as Draco Malfoy's:
Now, the children of two heterozygous Muggles have a 25% chance of being a homozygous Muggle, a 50% chance of being a heterozygous Muggle, and a 25% chance of being a wizard. That one-in-four shot is a "Muggle-born", like Hermione. Again, we see that Hermione's magical genotype is aboslutely identical to that of a "pure-blood" wizard:
But there's a problem with this theory. If magic is a simple recessive trait, two wizard parents should always produce wizard offspring. What about Squibs? Mutation could account for some, but there could be another explanation: incomplete dominance of the Muggle allele.
One Gene, Incomplete Dominance
If this is the case, we still have two alleles: MM (Muggle) and MW (wizard). But neither one is completely dominant over the other. There are still three genotypes, and now there are three phenotypes as well:
In incomplete dominance, we would expect the heterozygous genotype to be found in individuals with some Muggle and some wizard traits. There is now no such thing as a heterozygous Muggle.
Homozygous wizards still produce all wizard offspring:
Homozygous Muggles still produce all Muggle offspring:
A homozygous Muggle and a homozygous wizard still produce all heterozygous offspring, but unlike in the complete dominance theory, they will all be wizards, though we will expect them to have weaker magic than their wizard parent:
A homozygous Muggle and a heterozygous wizard may produce either Muggle or (half-)wizard offspring, but there is only a 25% chance that their child will be a wizard. Under this theory, wizards who marry Muggles are running a greater risk that their children will be Muggles too:
The child of two heterozygous wizards has a 25% chance of being a homozygous wizard, a 50% chance of being a heterozygous wizard, and a 25% chance of being a homozygous Muggle (in other words, a Squib):
Now we see the value of keeping the magical bloodline "pure". Wizards with Muggle ancestry run the risk of having Squib children, whereas pure-blood wizards do not. If we accept this theory, we're forced to admit that Voldemort and his followers are on the right track: intermarriage is harmful to the wizarding community, and pure-bloods are more talented than half-bloods.
But there's a problem with the incomplete dominance theory too. If all Muggles are homozygous, how do we account for the existence of Muggle-born wizards? We might theorize that apparent "Muggle-borns" are actually children of heterozygous individuals whose genotype includes the magical allele, but whose actual magical ability is negligible. (In order to calculate the degree of dominance of one allele over the other, we'd have to know the genotypes of the individual's ancestors, and how long ago the last intermarriage took place.) If this is so, then we would expect the parents of Muggle-borns to have some magical talent — perhaps the occasional prophetic dream, or the ability to see ghosts — but I see no support for this in canon.
And there's another problem, too: we know several wizards who must be heterozygous under this theory, and though we would expect them to be weak, some are exceptionally talented: Hermione is one, as is Voldemort himself. Perhaps this can be attributed to high intelligence, ambition, and proper training (this is probably how Voldemort justifies his own power to himself), but is it really reasonable to accept that individuals with such a weak phenotype that they may as well be Muggles can produce a prodigy like Hermione?
It seems that neither complete nor incomplete dominance fully accounts for
what we see in canon. But there's another possibility.
Multiple Genes
Many different types of magic are taught at Hogwarts, and the students show differing degrees of ...predisposition (as Snape might say) to one subject or another. Most tellingly, some magical skills are spoken of as entirely or partly inborn (Divination and Metamorphmagic, for example). This suggests that magical ability is not determined by one single gene, but many.
This really opens up the possibilities. There may be a gene (or multiple genes) for each ability, plus a single wizard gene that triggers the expression of the magical alleles. There will be countless genotypes and phenotypes that are all lumped together under the general category "wizard". This also allows for both Muggle-born wizards and Squibs.
In this case, the trait of being a Squib would have a separate gene. Let's say the alleles are a recessive s (Squib) and a dominant S (non-Squib). A homozygous wizard may be a carrier of the recessive Squib trait without even realizing it. If two carriers marry, 25% of their offspring will not carry the recessive Squib allele, 50% will carry the allele but not express it in their phenotype, and 25% will in fact be Squibs:
This gets even more interesting when you look at intermarriages between wizards and Muggles (assuming that magical and Squib genes are not linked in such a way that Muggles can't carry the Squib alleles). For example: With a homozygous wizard parent and a heterozygous Muggle parent who are both heterozygous for the Squib trait, 12.5% of the offspring will be non-carrier Muggles, 25% will be carrier Muggles heterozygous for the Squib trait, 12.5% will be carrier Muggles homozygous for the Squib trait, 12.5% will be non-carrier wizards, 25% will be carrier wizards, and 12.5% will be true Squibs (genotype mmss). Phenotypically, it will be impossible to distinguish between the Muggle children (MmSS, MmSs, and Mmss) and the true Squib children (mmss); two recessive Squib alleles will have no effect on individuals who already had the dominant Muggle allele in the first place:
A number of fans have theorized that Squibs may have latent magical abilities, or a different kind of magic all their own. The multiple gene theory allows for this: perhaps the Squib gene overrides some magical genes, but not others.
Dudley's Decision
We don't have enough information about the different types of magical ability and how they correlate to work out what the full "magical genome" would look like. But here's an example of how it might work: let's assume the existence of a Divination gene (dominant D [Seer] and recessive d [non-Seer]) and a Metamorphmagic gene (dominant P [non-Metamorphmagus] and recessive p [Metamorphmagus]).
Their son Harry has the phenotype "wizard, non-Squib, non-Seer, non-Metamorphmagus", so his genotype must be either mmSSddPp or mmSSddPP. Given his parentage, the former had a 25% chance of occurring, and the latter a 12.5% chance. (It will be impossible to tell which genotype Harry has until he has children with a woman whose genotype is known. Stay tuned, folks...)
Now, Lily is Muggle-born. One or both of her parents must have carried the dominant Divination allele (D), but not expressed it in their phenotype due to the overriding presence of the dominant Muggle allele (M). (It's also possible that the D allele was partially expressed through occasional prophetic dreams or somesuch, if the M allele is incompletely dominant.)
Let's say Mr. and Mrs. Evans both had the genotype MmSSDdPp. Focusing on the Muggle and Divination genes (so that the chart doesn't get too out of hand), we see that each of their children stood a 25% chance of being a wizard, and an 18.75% chance of being a wizard with Divination talent; also, a 75% chance of being a Muggle, and a 56.25% chance of being a Muggle
who carries the dominant Divination allele.
Let's say Lily's sister Petunia has the genotype MmDd. And let's say Petunia's husband Vernon has the genotype MMDD. As Vernon is a "pure-blooded" Muggle (could he be any other kind?), their son Dudley cannot be a wizard. However, he will certainly carry the dominant Divination gene. Without the recessive wizard gene, can Divination manifest itself in his phenotype (shades of Clyde Bruckman)? Does it make a difference if he has one recessive wizard allele? Only time will tell...
In any case, Dudley may want to be picky in his choice of partners. If he is heterozygous for the wizard gene, and happens to marry another heterozygous Muggle, he stands a 25% chance of giving Vernon and Petunia a grandchild who prophesizes the gory demise of everyone he meets.
Toujours Pur
So, now what can we say about Voldemort's theory of wizard genetics? Are pure-bloods any better than half-bloods or Muggle-borns? The multiple gene theory suggests not. If Muggles can carry magical genes (as the very existence of Muggle-borns implies), then a wizard of mixed blood should be just as likely to have a powerful genotype as any pure-blood. Any wizard may unknowingly carry the recessive Squib allele — and obsessive inbreeding will only exacerbate the problem.
The conclusion is inescapable: Voldemort's beliefs have their basis not in fact, but in delusion. But it's not too much of a stretch to imagine an aspiring young Death Eater poring over genetics textbooks in an effort to justify his resentment through science.
On a somewhat similar note,mollymoon also brought up the question of whether lycanthropy can be passed from parent to child (presumably only mother to child, since it's an acquired illness and not genetic). To know that, we'd have to figure out how it's passed... Saliva apparently carries the virus(?) -- perhaps blood does too. Any thoughts?
mollymoon asked. I wrote this up a while ago, to get my own thoughts in order. Yeah, I know the wizarding world doesn't obey the laws of biology. But if it did...The Genetics of Harry Potter
Introduction
Before we get started, here's a quick overview of basic genetics: Each gene determines one physical trait. A gene comes in two parts, called alleles, which are usually represented by letters of the alphabet. In some genes, one allele is dominant (represented by a capital letter) and the other is recessive (represented by a lower case letter). If the dominant allele is present, the trait it determines always shows up, whether the other allele is the dominant one or the recessive one. A recessive trait only appears if both alleles are recessive.
An individual who has two of the same allele is called homozygous. An individual who has two different alleles from the same gene is called heterozygous.
The physical traits of an individual are called the individual's phenotype. The actual alleles that underlie these physical traits are called the individual's genotype.
During reproduction, the genes of each parent split into their component alleles, and one allele from each parent is contributed to the offspring, making one whole gene. It's random which allele is contributed.
It's really more complicated than this, of course, but that's all you need to know to start with.
One Gene, Complete Dominance
In this theory, magical ability is determined by a single gene; its two alleles are the dominant M (Muggle) and the recessive m (wizard). There are two possible phenotypes (Muggle or wizard), but three possible genotypes:
|
|
|
| MM | homozygous | Muggle |
| Mm | heterozygous | Muggle |
| mm | homozygous | wizard |
Two wizard parents (homozygous by definition) will always produce wizard
offspring:
| m | m | |
| m | mm | mm |
| m | mm | mm |
Two homozygous Muggle parents will always produce homozygous Muggle offspring:
| M | M | |
| M | MM | MM |
| M | MM | MM |
A homozygous Muggle and a homozygous wizard will also produce all Muggle offspring, but they will all be heterozygous:
| M | M | |
| m | Mm | Mm |
| m | Mm | Mm |
If one of these heterozygous Muggles marries a wizard, their offspring will have a 50% chance of being a heterozygous Muggle, and a 50% chance of being a wizard. Wizards with such parents are "half-bloods", like Seamus Finnegan. We can see that the elder Mr. Finnegan must have been a heterozygous individual — in other words, he must have had at least two wizard ancestors somewhere in his family tree (assuming no sibling incest). We can also see that Seamus has exactly the same genotype (mm) as any other wizard — genetically, his magic is just as "pure" as Draco Malfoy's:
| M | m | |
| m | Mm | mm |
| m | Mm | mm |
Now, the children of two heterozygous Muggles have a 25% chance of being a homozygous Muggle, a 50% chance of being a heterozygous Muggle, and a 25% chance of being a wizard. That one-in-four shot is a "Muggle-born", like Hermione. Again, we see that Hermione's magical genotype is aboslutely identical to that of a "pure-blood" wizard:
| M | m | |
| M | MM | Mm |
| m | Mm | mm |
But there's a problem with this theory. If magic is a simple recessive trait, two wizard parents should always produce wizard offspring. What about Squibs? Mutation could account for some, but there could be another explanation: incomplete dominance of the Muggle allele.
One Gene, Incomplete Dominance
If this is the case, we still have two alleles: MM (Muggle) and MW (wizard). But neither one is completely dominant over the other. There are still three genotypes, and now there are three phenotypes as well:
|
|
|
| MMMM | homozygous | Muggle |
| MMMW | heterozygous | (half-)wizard |
| MWMW | homozygous | wizard |
In incomplete dominance, we would expect the heterozygous genotype to be found in individuals with some Muggle and some wizard traits. There is now no such thing as a heterozygous Muggle.
Homozygous wizards still produce all wizard offspring:
| MW | MW | |
| MW | MWMW | MWMW |
| MW | MWMW | MWMW |
Homozygous Muggles still produce all Muggle offspring:
| MM | MM | |
| MM | MMMM | MMMM |
| MM | MMMM | MMMM |
A homozygous Muggle and a homozygous wizard still produce all heterozygous offspring, but unlike in the complete dominance theory, they will all be wizards, though we will expect them to have weaker magic than their wizard parent:
| MM | MM | |
| MW | MMMW | MMMW |
| MW | MMMW | MMMW |
A homozygous Muggle and a heterozygous wizard may produce either Muggle or (half-)wizard offspring, but there is only a 25% chance that their child will be a wizard. Under this theory, wizards who marry Muggles are running a greater risk that their children will be Muggles too:
| MM | MM | |
| MM | MMMM | MMMM |
| MW | MMMM | MMMW |
The child of two heterozygous wizards has a 25% chance of being a homozygous wizard, a 50% chance of being a heterozygous wizard, and a 25% chance of being a homozygous Muggle (in other words, a Squib):
| MM | MW | |
| MM | MMMM | MMMW |
| MW | MMMW | MWMW |
Now we see the value of keeping the magical bloodline "pure". Wizards with Muggle ancestry run the risk of having Squib children, whereas pure-blood wizards do not. If we accept this theory, we're forced to admit that Voldemort and his followers are on the right track: intermarriage is harmful to the wizarding community, and pure-bloods are more talented than half-bloods.
But there's a problem with the incomplete dominance theory too. If all Muggles are homozygous, how do we account for the existence of Muggle-born wizards? We might theorize that apparent "Muggle-borns" are actually children of heterozygous individuals whose genotype includes the magical allele, but whose actual magical ability is negligible. (In order to calculate the degree of dominance of one allele over the other, we'd have to know the genotypes of the individual's ancestors, and how long ago the last intermarriage took place.) If this is so, then we would expect the parents of Muggle-borns to have some magical talent — perhaps the occasional prophetic dream, or the ability to see ghosts — but I see no support for this in canon.
And there's another problem, too: we know several wizards who must be heterozygous under this theory, and though we would expect them to be weak, some are exceptionally talented: Hermione is one, as is Voldemort himself. Perhaps this can be attributed to high intelligence, ambition, and proper training (this is probably how Voldemort justifies his own power to himself), but is it really reasonable to accept that individuals with such a weak phenotype that they may as well be Muggles can produce a prodigy like Hermione?
It seems that neither complete nor incomplete dominance fully accounts for
what we see in canon. But there's another possibility.
Multiple Genes
Many different types of magic are taught at Hogwarts, and the students show differing degrees of ...predisposition (as Snape might say) to one subject or another. Most tellingly, some magical skills are spoken of as entirely or partly inborn (Divination and Metamorphmagic, for example). This suggests that magical ability is not determined by one single gene, but many.
This really opens up the possibilities. There may be a gene (or multiple genes) for each ability, plus a single wizard gene that triggers the expression of the magical alleles. There will be countless genotypes and phenotypes that are all lumped together under the general category "wizard". This also allows for both Muggle-born wizards and Squibs.
In this case, the trait of being a Squib would have a separate gene. Let's say the alleles are a recessive s (Squib) and a dominant S (non-Squib). A homozygous wizard may be a carrier of the recessive Squib trait without even realizing it. If two carriers marry, 25% of their offspring will not carry the recessive Squib allele, 50% will carry the allele but not express it in their phenotype, and 25% will in fact be Squibs:
| mS | mS | ms | ms | |
| mS | mmSS | mmSS | mmSs | mmSs |
| mS | mmSS | mmSS | mmSs | mmSs |
| ms | mmSs | mmSs | mmss | mmss |
| ms | mmSs | mmSs | mmss | mmss |
This gets even more interesting when you look at intermarriages between wizards and Muggles (assuming that magical and Squib genes are not linked in such a way that Muggles can't carry the Squib alleles). For example: With a homozygous wizard parent and a heterozygous Muggle parent who are both heterozygous for the Squib trait, 12.5% of the offspring will be non-carrier Muggles, 25% will be carrier Muggles heterozygous for the Squib trait, 12.5% will be carrier Muggles homozygous for the Squib trait, 12.5% will be non-carrier wizards, 25% will be carrier wizards, and 12.5% will be true Squibs (genotype mmss). Phenotypically, it will be impossible to distinguish between the Muggle children (MmSS, MmSs, and Mmss) and the true Squib children (mmss); two recessive Squib alleles will have no effect on individuals who already had the dominant Muggle allele in the first place:
| MS | mS | Ms | ms | |
| mS | MmSS | mmSS | MmSs | mmSs |
| mS | MmSS | mmSS | MmSs | mmSs |
| ms | MmSs | mmSs | Mmss | mmss |
| ms | MmSs | mmSs | Mmss | mmss |
A number of fans have theorized that Squibs may have latent magical abilities, or a different kind of magic all their own. The multiple gene theory allows for this: perhaps the Squib gene overrides some magical genes, but not others.
Dudley's Decision
We don't have enough information about the different types of magical ability and how they correlate to work out what the full "magical genome" would look like. But here's an example of how it might work: let's assume the existence of a Divination gene (dominant D [Seer] and recessive d [non-Seer]) and a Metamorphmagic gene (dominant P [non-Metamorphmagus] and recessive p [Metamorphmagus]).
Let's use as our example parents James (genotype mmSSddPp, phenotype "wizard, non-Squib, non-Seer, non-Metamorphmagus") and Lily (genotype mmSSDdPp, phenotype "wizard, non-Squib, Seer, non-Metamorphmagus"). Their offspring will all be wizards and none Squibs, and will have the Divination and Seer genes in the following assortment:
|
||||
| dP | dP | dp | dp | |
| DP | DdPP | DdPP | DdPp | DdPp |
| dP | ddPP | ddPP | ddPp | ddPp |
| Dp | DdPp | DdPp | Ddpp | Ddpp |
| dp | ddPp | ddPp | ddpp | ddpp |
Their son Harry has the phenotype "wizard, non-Squib, non-Seer, non-Metamorphmagus", so his genotype must be either mmSSddPp or mmSSddPP. Given his parentage, the former had a 25% chance of occurring, and the latter a 12.5% chance. (It will be impossible to tell which genotype Harry has until he has children with a woman whose genotype is known. Stay tuned, folks...)
Now, Lily is Muggle-born. One or both of her parents must have carried the dominant Divination allele (D), but not expressed it in their phenotype due to the overriding presence of the dominant Muggle allele (M). (It's also possible that the D allele was partially expressed through occasional prophetic dreams or somesuch, if the M allele is incompletely dominant.)
Let's say Mr. and Mrs. Evans both had the genotype MmSSDdPp. Focusing on the Muggle and Divination genes (so that the chart doesn't get too out of hand), we see that each of their children stood a 25% chance of being a wizard, and an 18.75% chance of being a wizard with Divination talent; also, a 75% chance of being a Muggle, and a 56.25% chance of being a Muggle
who carries the dominant Divination allele.
|
||||
| MD | Md | mD | md | |
| MD | MMDD | MMDd | MmDD | MmDd |
| Md | MMDd | MMdd | MmDd | Mmdd |
| mD | MmDD | MmDd | mmDD | mmDd |
| md | MmDd | Mmdd | mmDd | mmdd |
Let's say Lily's sister Petunia has the genotype MmDd. And let's say Petunia's husband Vernon has the genotype MMDD. As Vernon is a "pure-blooded" Muggle (could he be any other kind?), their son Dudley cannot be a wizard. However, he will certainly carry the dominant Divination gene. Without the recessive wizard gene, can Divination manifest itself in his phenotype (shades of Clyde Bruckman)? Does it make a difference if he has one recessive wizard allele? Only time will tell...
In any case, Dudley may want to be picky in his choice of partners. If he is heterozygous for the wizard gene, and happens to marry another heterozygous Muggle, he stands a 25% chance of giving Vernon and Petunia a grandchild who prophesizes the gory demise of everyone he meets.
|
||||
| MD | Md | mD | md | |
| MD | MMDD | MMDd | MmDD | MmDd |
| MD | MMDD | MMDd | MmDD | MmDd |
| MD | MMDD | MMDd | MmDD | MmDd |
| MD | MNDD | MMDd | MmDD | MmDd |
Toujours Pur
So, now what can we say about Voldemort's theory of wizard genetics? Are pure-bloods any better than half-bloods or Muggle-borns? The multiple gene theory suggests not. If Muggles can carry magical genes (as the very existence of Muggle-borns implies), then a wizard of mixed blood should be just as likely to have a powerful genotype as any pure-blood. Any wizard may unknowingly carry the recessive Squib allele — and obsessive inbreeding will only exacerbate the problem.
The conclusion is inescapable: Voldemort's beliefs have their basis not in fact, but in delusion. But it's not too much of a stretch to imagine an aspiring young Death Eater poring over genetics textbooks in an effort to justify his resentment through science.
On a somewhat similar note,
mollymoon also brought up the question of whether lycanthropy can be passed from parent to child (presumably only mother to child, since it's an acquired illness and not genetic). To know that, we'd have to figure out how it's passed... Saliva apparently carries the virus(?) -- perhaps blood does too. Any thoughts?
no subject
Date: 2003-09-08 11:31 am (UTC)no subject
Date: 2003-09-08 11:44 am (UTC)The idea was born out of a desire to give my young Remus a penpal and star-crossed lover. It was originally suppose to happen in the story I'm writing now, Return to Sender, but new canon from OotP changed the focus of that story slightly. Other factors needed in that plot bunny have pushed it into the next novella, Deliver Us from Evil.
That will give me time to brush up on my photoshop and HTML skills as well, as that aspect of the story, the penpal romance, is an homage to one of my favorite series, "Griffin and Sabine". If you've never read those little books, they are basically the correspondence between two people. The catch is that you get to open the letters within the book. Each character is somewhat of an artist and designs their own envelope, paper etc. Its all very beautiful and gives the reader a connection to the characters that really lasts the test of time.
no subject
Date: 2003-09-08 12:23 pm (UTC)no subject
Date: 2003-09-08 12:34 pm (UTC)JKR had said in an interview prior to OotP release, that when she created this world, she decided that Muggles diseases, such as cancer, didn't effect wizards, or were totally curable in their world. Meaning of course that there must be other afflictions that prey on this population. Otherwise, one would assume that Wizards would out populate Muggles.
Lycanthropy and vampirism could both be such diseases for the Wizarding community. Its an interesting jump in thought to look at how our modern mythology has evolved a war between werewolves and vampires... What if such a thing existed in the WW as well? Perhaps lycanthropy was first a "made" disease... we know that werewolves are unusual because they speficially target humans... Maybe lycanthropy was a potion gone wrong and instead of transforming the drinker into a vampire killing machine... well, that's enough supposition for the day. And probably enough abuse of elipses as well.
*waits for the release of Underworld (http://www.sonypictures.com/movies/underworld/) as only a reformed Goth can*