Wizarding Genetics: More Complicated
“A Squib is almost the opposite of a Muggle-born wizard: he or she is a non-magical
person born to at least one magical parent. Squibs are rare; magic is a dominant
and resilient gene.” – jkrowling.com
“Why are some people in the wizarding world (e.g., Harry) called 'half-blood'
even though both their parents were magical?”
“The expressions 'pure-blood', 'half-blood' and 'Muggle-born' have been coined
by people to whom these distinctions matter, and express their originators'
prejudices. As far as somebody like Lucius Malfoy is concerned, for instance,
a Muggle-born is as 'bad' as a Muggle. Therefore Harry would be considered
only 'half' wizard, because of his mother's grandparents…. The Nazis used
precisely the same warped logic as the Death Eaters. A single Jewish grandparent
'polluted' the blood, according to their propaganda.” (Therefore, Half-blood
would be defined as having one Muggle grandparent.) – jkrowling.com
“How does a Muggle-born like Hermione develop magical abilities?”
“Nobody knows where magic comes from. It is like any other talent. Sometimes
it seems to be inherited, but others are the only ones in their family who
have the ability.” – Barnes and Noble interview, March 19, 1999
“How can two Muggles have a kid with magical powers?”
“It's the same as two black-haired people producing a redheaded child.
Sometimes these things just happen, and no one really knows why!” – Online
chat transcript, Scholastic.com, 3 February 2000
The Wizarding World
J.K. Rowling is telling us several things about magical inheritance.
Magic is a “dominant and resilient gene”. Yet, Muggle-borns are “the same
as two black-haired people producing a redheaded child”, which implies that
the gene for Muggle-borns is recessive. (Hair color is more complicated than
that, but that is the implication.)
Harry’s class list suggests that the wizarding population is subdivided as
|| Type 1: Muggle-born Parent
||Type 2: Muggle Parent
||Type 3: Muggle Grandparent
Since Muggle-borns are 20%, it follows that another 20% would be the
children of Muggle-borns (people like Harry). That means the other Half-bloods
are equally divided between literal “half-and-halves” (those like Dean and
Seamus, who have one Muggle parent) and the children of those half-and-halves
from the previous generation. There is only one type of Pure-blood – any wizard
with two magical parents and four magical grandparents – but those in Slytherin
are likely to share Voldemort’s racist agenda. This affects their choice of
marriage partner and makes them more vulnerable to the genetic problems of
The Rules of Wizarding Genetics
From canon and JKR herself, we can deduce quite a few rules of wizarding
- Magic is a "dominant and resilient" gene.
- Magic shows before age 11 in all magical people, with very rare
- 40% of magical people are Pure-blood; they have no Muggle grandparents.
- None of the Pure-blood families are really "pure"; they disown
- Pure-blood families are decreasing.
- 40% of magical people are Half-blood; with one Muggle parent or grandparent.
(We assume only 10% are actually half-and-half.)
- Half-bloods are magical, with rare exceptions (Seamus and Dean).
- 20% of witches and wizards are Muggle-born.
- Muggle-born inheritance of magic seems to be recessive.
- Muggle-borns may have non-magical siblings (Petunia).
- Squibs are the non-magical offspring of one or more magical parents.
- Squibs are rare (1 in 100 at the most, 1 in 1,000 at the least).
- Squibs have a higher chance of having magical children than Muggles do,
even if they marry a Muggle (e.g., Mafalda Prewett, the missing Weasley
- Pure-bloods, Half-bloods, and Muggle-borns have magical children, regardless
of the blood status of the other parent, with only rare exceptions.
How can we explain this phenomenon from a genetic point of view? Is magic
inherited like hair color or eye color? Is it a simple cross of two genes?
Or is it more complicated?
First, we will quickly review a bit of biology
(skip to the next paragraph if you know it, please). Remember, first of all, that everyone has 23
pairs of chromosomes (which have all of your genes on them) – 22 regular pairs
which are called autosomes and two sex chromosomes. Everyone inherits 23 chromosomes from their
mother and 23 from their father, which (except for the sex chromosomes) are
basically identical. These 46 chromosomes
are divided in half when forming sperm and eggs (gametes), only one chromosome
from each pair going to a sperm or egg, so that each sperm or egg carries
only 23 chromosomes. There is a 50%
chance that the 1st chromosome in an egg will be from the maternal
side and 50% chance that it will be from the paternal side.
That’s all I want to say about biology, now
to genetics. Everyone has two copies
of each gene, but they may not be exactly identical, and these different forms of a single gene are called
alleles. (I will use the word allele
a lot, if it is confusing, simply substitute the word gene and it should make
sense.) The brown/blue eye color gene has two alleles,
brown (B) and blue (b). Brown is the
dominant gene, blue is the recessive gene.
So if a brown-eyed person had a child with a blue-eyed person, the
Mendelian cross would look like this, where the mother is blue-eyed person,
bb, on the side, and the father is the brown-eyed person, BB, at the top.
Each letter represents one allele, and each parent
has two alleles.
Or, BB x bb = children will
all be Bb, having one B allele and one b allele
The brown allele (B) is dominant, so because
brown is dominant, all of those children will have brown eyes, even though
they carry a blue allele. What happens
if we cross someone with two blue alleles with someone with one brown, one
Or, Bb x bb = ½ Bb and ½ bb
One half of these children would have brown
eyes, and the other half would have blue eyes.
What if we took two people with one brown allele and one blue allele
Or, Bb x Bb = ¼ BB, ½ Bb,
you can see, three-fourths of the children will inherit a brown allele, which
means their eyes, like their parents’ eyes, will be brown. One-fourth of the children, however, inherit
two blue alleles, which means they will have blue eyes. This is statistically accurate – 25% will get
two brown alleles, 50% will get one of each, and 25% will get two blue alleles. In crosses of more than one gene, there are
still firm statistical ratios of which alleles go where, that most genes follow.
The reason this is called Mendelian genetics is because Mendel was
the man who first realized there were dominant and recessive genes by experimenting
with pea plants.
Magical Mendelian Genetics
Surprisingly, genetics for magical people
are not actually very magical, but they are very unique. They do not follow traditional Mendelian genetics,
which is why I’m writing this in the first place. If they followed Mendel exactly, it would be
fairly easy to figure out. How do we
know magical genetics don’t follow Mendel?
Mendelian genetics cannot fit the rules in the HP world stated above.
This is what Mendel’s rules would look like
in the wizarding world. There is a
gene called the magic gene, with two forms, M and N. There are magical people, with an M (magical)
allele. There are Muggles who have
an N (normal) allele. The M allele
here is dominant over the N allele. Pure-bloods
would have two copies of M, Half-bloods (the ones with one Muggle parent,
also known as Half-and-half) would have one copy of each, MN, and Muggles
would have two copies of N. That doesn’t
leave much room for Muggle-borns or Squibs, but let’s pretend that Squibs
also have two copies of N, like Muggles, and Muggle-borns have a copy of M,
like magical people. The biggest problem
right away is where the Muggle-borns got the M allele.
If it is dominant, then they couldn’t have gotten it from their parents!
There’s a slim chance that it was a new mutation, but the odds are
not in favor of a new mutation happening so frequently that 20% of the magical
population would have it. Besides, mutations almost always hurt people,
not enhance them.
For the sake of argument, let’s pretend that
Muggle-borns have one M allele and one N allele, like Half-bloods. Purebloods have MM, Squibs are NN. These would be the results of several different
crosses (Squibs are emphasized by an asterisk *):
x Muggle, Muggle-born x Muggle
x Squib, Muggle-born x Squib
Some of the time these crosses work and produce
all-magical offspring, especially when it comes to Pure-blood crosses.
Whenever it comes to Half-bloods or Muggle-borns, however, the crosses
produce as many Squibs as magical children, and we know that Squibs are very
rare (rule #12). We also know that magical people (no matter
what their blood) have magical offspring almost exclusively (rule #14). We also know that Squibs have a better chance
than a Muggle of having a magical child, and these Squibs do not, they are
effectively Muggles (rule #13). This
theory breaks several of our rules, as stated above. It also shows that the “Pure-blood” ideology
may be right, that one Muggle grandparent taints the entire line, and we can
be fairly certain that is not correct. We must find another theory.
The Magic Gene
A better theory starts by comparing magical
genetics to blood type. There are three
alleles of the gene for blood type - A, B, and O. (I apologize if you already
know this, skip ahead to the next paragraph.) Everyone has two alleles, giving
possible combinations of AA, BB, OO, AO, BO, and AB. A and B are both enzymatically 'active' and are dominant, whereas O is not
active and is recessive. So the four
blood types then become A (AA and AO), B (BB and BO), AB (AB), and O (OO).
The O gene is most common, followed by the A
gene, then the B gene (although it is relatively rare). This gives percentages of blood type like so
(in the US, and it is similar in most of Europe): O is 45%, A is 42%, B is 10% and AB is 3%.
Now imagine that there are four
alleles of the magic gene in the HP universe (instead of the two alleles mentioned
above). There is M for magical, dominant;
N for normal, or Muggle; r for magical, recessive; and o is a recessive mutation
of M that can cause Squibs, seen primarily in Pure-blood families. Now assume that the dominance of these genes
is as follows, from the most dominant to the least dominant:
M > N > r > o
So then we have MM (Pure-blood), Mo (still
Pure-blood with mutation), and oo (Squib). We also have NN (Muggle), Nr (Muggle), and rr (Muggle-borns, magical). To complicate things more, we have MN (half and
half, usually magical), No (offspring of Muggle/Squib union), Mr (Half and
half or Pure-blood, magical), and ro (offspring of Squib/Muggle union, magical).
The reason ro children are magical is because r is dominant to the
o allele, even if it is not dominant over the M or N alleles.
Approximately 2% of the Muggle population carries one r allele, so
2% of these (0.04%) will marry another r-carrier.
The chances that any one of their children will inherit the r allele
from both parents are 1 in 4, so the odds of having a Muggle-born (rr)
child are about 1 birth in 10,000. Not
common, but common enough that there are a good number of Muggle-borns.
Since the o allele is a mutation of M and
it originated in the wizarding community, it is found almost exclusively in
wizarding families. If two wizards
carrying the mutant o allele marry, 1 in 4 of their children will be Squibs,
2 in 4 will be magical but will pass the mutant o to the next generation,
and 1 in 4 will inherit two healthy M alleles.
In case all of this sounds confusing, here are some examples:
Vernon is more than likely NN. Petunia and Lily's parents were probably Nr,
making Petunia NN or Nr (Muggle) and Lily rr (magical).
Dudley is NN or possibly Nr (Muggle). Filch
and Arabella Figg are
both oo (Squibs), meaning their parents were likely both Mo. The Malfoys, Blacks, Potters, and Weasleys
are all MM (Pure-blood magical), with perhaps an o here or there. Harry would be Mr (magical). Hermione is rr (magical),
her parents are both Nr (Muggles). Seamus
and Dean both are half-and-half, MN most likely.
x Pure-blood mutation
Wait, you say, how is that any better than
the last theory? Half-bloods and Muggle-borns
still are not able to have all magical children, Muggle-borns now have a recessive
r gene, and the Half-bloods still carry that N gene! There are more Squibs than before, and we know
that Squibs are rare.
The Half-Blood Quandary
What do we do about the N allele in the Half-blood
population? The solution to the Half-blood
quandary is a second gene, a very special gene called Q. The Q gene is responsible for suppressing Muggle
genes in each egg or sperm formed. Each egg or sperm (called a gamete) has ½ of
each parent’s genes, so we have the possibilities of M, N, r, and o alleles
being passed on, if a parent has that allele. Now then, if Q (an enzyme of some sort, made
from the gene Q) were to stop the N gametes from ever becoming mature, allowing
only M, r, and o to exist, then you would have an extremely high probability
of having only magical offspring. (There
is a recessive q that does not suppress genes, we will get to that!) Why doesn’t Q stop the o gametes as well? The Q gene cannot tell the difference between
M and o, because o is simply an inactive mutation of M and looks similar enough
to M that Q does not recognize it.
If this Q gene keeps N from being passed on, why are there any Muggles
left? Wouldn’t they all have died out by now? No, because the Q gene is only
active in magical people. That part of the chromosome in Muggles is “covered
up” by special proteins and cannot be uncovered, so the Q gene cannot do anything
in a non-magical person. In a magical person, whether they are magical by
inheriting the M allele or two r alleles, a chain-reaction begins in every
cell of that person's body, which makes a lot of modifications (one of which
is longer life). One of those modifications is "uncovering" the
Q gene. So then the genes would be passed on like so:
Half-blood x Pure-blood mutation
Now the Half-blood N gene cannot be passed
to the next generation, guaranteeing magical ability to all the children of
Half-bloods. That fixes the Half-blood
blood line. But the Muggle-borns are
still turning out a very large number of Squibs.
The Muggle-Born Dilemma
The solution to this Muggle-born
dilemma is another job for the Q gene. Along
with filtering out non-magical genes, the Q gene is responsible for changing
the Muggle-born "r" allele (whether by itself or by turning on another
gene). Why must the r allele be changed?
So that Muggle-borns can pass on the magical trait as a dominant trait.
So in a Muggle-born magical child, before they are even born, in every
cell of their bodies, the Q gene produces enzymes that “cut” the r gene in
different places and "stick" them back together again to look and
act like the M allele. (This is cutting
and gluing is called splicing, it is something that happens very often in
our bodies, it is one of the reasons why we have so much “junk” DNA, and it
is how we have so many different types of antibodies.)
We could call this new, modified r allele the R allele, but
since it looks and acts like M in every way, we will call it M as well and
simplify things. So, keep in mind that
even though Muggle-borns begin by being rr, they
become MM, and pass on only M alleles. The
modified r allele is in all respects identical to the M allele, and is, like
the M allele, dominant to N. The Q
gene then would cause Muggle-born pairs to make offspring like this:
x Pure-blood mutation
Muggle-borns now have the same benefits
as Half-bloods, as far as their genes go. Now both of them can only pass on the dominant
M allele, even if they themselves had an r allele to begin with. Now that changes things a little. Vernon is still NN. Petunia
and Lily's parents were probably Nr, making Petunia NN or Nr (Muggle) and
Lily rr (magical). Lily’s
rr genes would have been changed to MM. Dudley is NN or possibly
Nr (Muggle). Filch and Arabella Figg are both oo (Squibs),
meaning their parents were likely both Mo. The Malfoys, Blacks, Potters, and Weasleys
are all MM (Pure-blood magical), with perhaps an o allele here or there. Harry would be MM (magical), as his mother would
have passed him an M gene instead of her r gene. Hermione is rr (magical),
her parents are most likely both Nr (Muggles), but she will pass only M alleles
to her children. Seamus and Dean both
are half-and-half; MN most likely, but they will pass only M alleles to their
The Squib Enigma
So where do Squibs come from? Isn't the Q gene supposed to prevent N from
being passed on? Don’t forget about that nasty o mutation running through
Pure-blood bloodlines. All oo wizards and witches are Squibs. That’s all well
and good, but how could two half-and-halves have a Squib, or anyone else that
wasn’t Pure-blooded? Well, there is a recessive q allele as well, that does
not stop N from being passed on. (It does, however, still transform
the Muggle-born r to M.)
The Q and q alleles are fairly equally distributed
– 25% of the population has two Q alleles, another 25% has two q alleles,
and the remaining 50% have one Q and one q allele. A magical person only needs one Q allele to
pass on only magical genes, and 75% of the magical community has at least
one Q gene. However, 25% of the population
is qq, and these individuals do not suppress non-magical genes, so they could
very well pass an N allele! (Assuming
they have one.) This N allele may be
directly from the parent with qq, but it may also have been passed along a
few generations before it showed up. If
someone with an N allele (or an o) married another magical person, this wouldn't
be too big a problem, unless they also were qq and also had an N (or an o)
gene. If someone who was Moqq married someone who was MNqq,
their child could very well be Noqq, a Squib. Some of the combinations that could produce
Squibs (Squibs indicated with an asterisk *):
(qq) x Half-blood (qq)
mutation x Pure-blood mutation
(qq) x Pure-blood mutation
(qq) x Muggle
Notice that with Muggles, it does
not matter what their Q status is, because the Q gene is completely inactive
in them. The Muggles could be qq, Qq,
or QQ, it does not matter. Overall,
marrying Muggles does increase your chances of having a Squib slightly, simply
by introducing the N allele. However,
the N allele is only passed on to the third generation if the parents both
are qq. If the Muggle that marries
in has a Q allele (or two), it actually slightly decreases the likelihood
of having Squibs later, because more of the offspring would have a functional
Q allele, and that will eventually “weed out” the N alleles (in their magical
How Many Squibs Are There, Anyway?
What is the likelihood of having a Squib?
Squibs can be NN, No, or oo.
The oo Squib. Approximately 6% of the total wizarding population
has one o allele. It is never found
among first generation Muggle-borns or Half-and-halves, but it occurs in 10%
of Pure-bloods (4% of total wizarding population), just under 8% of Muggle-born
offspring (1.5% of total wizarding population) and 5% of Half-and-half offspring
(0.5% of total wizarding population). Assuming half of all Pure-bloods (20% of the
total wizarding population) are prejudiced against others, 10% of these (2%
of total wizarding population) carry the mutant o gene, and their insistence
on marrying only another Pure-blood means that 10% of them (0.2% of total)
will marry another o-carrier. In a
marriage between two Mo wizards, a quarter of the children will be oo Squibs,
so 1 in 2,000 wizard births will be Squibs born to prejudiced Pure-blood parents.
The other 4% of the wizarding population (the
other half of the Pure-bloods, 2% of the population, and then the second generation
Muggle-borns and Half-and-halves, another 2% of the population) who carry
the o allele are presumably willing to marry anyone, but in practice seven
out of eight will marry another wizard. In
most cases, the person they marry is not another Pure-blood, since many of
the Pure-bloods have married each other. Of this 3.5% of the total population, the chances
of marrying someone else who also carries the o allele is 4% (0.14% of the
total). Again, a quarter of the children
will be oo Squibs (0.035% of the total population, or 1 wizard birth in every
The No Squib. About
10% of wizards marry a Muggle, but none of these would be the prejudiced Pure-bloods,
so 0.4% of wizarding marriages are between an o-carrier and a Muggle (NN).
Half of their children will be No Squibs, or 1 wizarding birth in every
500. This theory would explain very well the character
of Thaddeus Thurkell who shows up in the "Famous
Witches and Wizards" card set of the CoS video game. Thaddeus
Thurkell "produced seven Squib sons and turned
them all into hedgehogs in disgust”.
The NN Squib. What about
the offspring of half-and-halves that are qq, and therefore pass the N allele
on to their offspring? First we will
consider a marriage of two half-and-halves. We will assume half-and-halves are not too particular
about whom they marry within the wizarding community. Approximately 10% of the wizarding community
is actually half-and-half (remember, the other 30% of Half-bloods are children
of Muggle-borns or other half-and-halves) and only a quarter of those carry
qq. The odds of a qq (25%) half-and-half
(10%) marrying another half-and-half (8.75%) that was also qq (25%) are 1
in 1,824, and only 1 in 4 of their children will end up NN, for an additional
1 Squibs per 7,000 births – next to none.
Now we will consider a half-and-half with a Muggle. If a half-and-half (10%) that was qq (25%) happened
to marry a Muggle (which we can assume does not happen much more often than
10% of the time), the odds of a Squib being born to that couple are 50%.
So that could account for another 12 per 10,000.
Notice that a Muggle-born (rr -> MM) who marries a Muggle (NN) never has a Squib child;
however, Squib grandchildren are possible.
Overall, we have a Squib birth rate of just fewer than
3 in 1,000. These are 0.85 in 1,000 oo Squibs, 2 in 1,000 No Squibs, and 0.14
in 1,000 NN Squibs, for a total of 2.99 Squibs in 1,000 wizarding births.
If the wizarding community is about 30,000 people, there will be approximately
90 Squibs in all of the British Isles. As Ron said,
“They’re really rare”, but they are not so rare that we couldn’t have met
The likelihood of a Squib having a magical
child is better than that of any two given Muggles producing a Muggle-born
child, according to Rule #13 above, “Squibs have a higher chance of having
magical children than Muggles do, even if they marry a Muggle (e.g., Mafalda Prewett).” How
is that possible? Does the o allele
become an M allele again? No – it’s
For any two Muggles to have a magical child,
the odds are 2% x 2% x ¼ = 0.01%, or 1 in 10,000. As I said previously, the order of dominance
for the magic gene is M > N > r > o.
Of all Squibs, 28% are oo, 67% are No, and 5% are NN. This is important, because NN Squibs are the
exception to Rule #13. Now, if a Squib
that is oo marries any Muggle, the odds of having a magical child are much
higher than with a Muggle couple. How?
If a Squib that is oo marries a Muggle that
happens to be Nr (a 2% chance), and there is a 50% chance (the child will
be either No or ro) of having a magical child, 1%, or, 1 in 100, children
of Squib/Muggle marriages would be in fact magical. Squibs that are oo are 100 times more likely
to have a magical child than any two Muggles are. No Squibs also have a higher chance of having
a magical child than any two Muggles, 1 in 200. The NN Squib actually cannot have a magical child
with a Muggle, because they can pass on only the N allele. Fortunately, fewer than 1 in 20 Squibs are NN.
All of the ro magical children of oo
or No Squibs and Nr Muggles would then become Mo, due to the Q gene modifications,
and would re-enter the wizarding bloodline, carrying the o allele with them.
We can show this here, where an asterisk * this time indicates a magical child:
x Muggle (Nr)
x Muggle (Nr)
x Muggle (Nr)
Remember that we stated earlier that Muggle-borns
who are rr and marry Muggles (NN) do not have Squib
children? It is very possible that
a few Muggle-borns are actually ro children, descendants of Squibs a few generations
earlier. These ro Muggle-borns then
become Mo witches and wizards, and can very well pass the o gene on to further
generations. So it is actually possible
that a “Muggle-born” could have a Squib child, but they would have had to
have a Squib ancestor at some point.
Wizarding Genetics, A
The reason why the M gene has not taken over
the entire population of Britain yet is because for over 1,000 years, the Muggle and
magical communities have been separated, passing genes back and forth occasionally,
but mostly isolated. Approximately
90% of the wizarding population marries other wizards, effectively keeping
the M allele within the magical community and the N allele out of the magical
community. There is a very small proportion
of the o allele in the Muggle population, because of Squibs leaving the magical
community; however, the o allele is far more concentrated within the magical
population. There are also far more
r alleles than o alleles in the Muggle population, and the o allele in the
Muggle population isn’t noticed at all; however, an No Muggle with an Nr Muggle
could have an ro “Muggle-born” child.
It has been argued that eventually the r allele would be weeded out of
the Muggle population, if each rr child became MM and joined the wizarding
community. However, that would take many, many, many generations, because
for each rr child born, statistically, there are two Nr children born and
one NN child; thus, the r allele continues in the Muggle population undetected
until another rr child is born. Perhaps the r allele was more prevalent than
2% at one time. Perhaps that is how the magical community first started anyway
– with Muggle-born witches and wizards, whose Q genes became activated and
changed their r alleles to M alleles. These Muggle-borns began intermarrying
when Muggles first began to fear magic and created the first Pure-blood families.
The o mutation occurred sometime later, with the high population of Pure-blood
families. Perhaps all of the Pure-blood families have their roots in Muggle-born
ancestors. Magic had to start somewhere, after all.
A special thanks to Grace Has Victory, who did much of the dreadful number-crunching for
me, and to Corned Bee, who kept
finding the holes in my theory!