If there’s one thing that definitely hasn’t been developed yet in Westeros, it’s modern DNA profiling techniques. DNA profiling uses DNA like a fingerprint: we can tell which suspect was at a crime scene, find long lost relatives, and pretty conclusively determine parentage by comparing DNA. All of those things would be incredibly useful in Westeros, where several criminal investigations appear to consist solely of blaming Tyrion Lannister, and so much power rides on questions like “How closely related are you to a Targaryen?” and “Are you Robert Baratheon’s child?” In the case of Joffrey Baratheon, in particular, accusations about his parentage caused the war that motivates much of Game of Thrones. So without being able to sequence Joffrey and Robert, did Ned have enough information to tell that Joffrey was definitely not Robert’s son? What would be enough? And how do we actually make those calls today?
Ned Stark knew that Joffrey, Tommen, and Myrcella weren’t Robert Baratheon’s kids basically because they didn’t have black hair. Here’s why this works, at least according to Ned: since Robert Baratheon has untold numbers of bastard children, presumably many with fair-haired mothers, and presumably all with dark hair, it follows that Robert is most likely homozygous for a dominant, dark-hair-causing, Baratheon (B) allele of a hair pigment producing gene. If Joffrey, Tommen, or Myrcella were his children, then they would have at least one copy of said B allele and would have dark hair. But they all have Lannister blonde hair, and therefore are very unlikely to be Robert’s children.
If we consider just the bastard children that are mentioned in the books, he didn’t have enough evidence to really make this determination. We know of four bastard children, all with dark hair. If Robert is homozygous BB, then this is by far the most likely outcome. However, if Robert is heterozygous Bb, he would still have dark hair, and it would still be fairly likely for four bastard children to have dark hair (think about flipping a coin and getting four heads in a row). When you add in the fact that some of his mistresses and whores likely had dark coloration as well, it becomes even more likely that all four illegitimate children have dark hair. So as far as Ned knows, Robert could well be Bb. And if he is, then the fact that he had three blonde children with the almost certainly bb Cersei Lannister is again reasonably likely. This is why Tyrion remarks that Joffrey’s – and hence Cersei’s – claim would be foolproof if she had had even one child with Robert: someone with dark hair married to someone with light hair having some children with light hair and some children with dark hair is utterly normal.
Ned does have an additional piece of evidence: the fact that all of Robert’s ancestors had dark hair. Now, the relevance of this observation depends on whether Ned is counting only those Baratheons who were Robert’s direct male ancestors in a paternal line or if he’s counting aunts and uncles and cousins and brothers and sisters and so on. In the former case, it’s not a compelling piece of evidence either way: Robert certainly has at least one B allele (as evidenced by his dark hair), and it had to come from somewhere. And since Ned gets his information from looking at Robert’s brothers (not particularly useful) and a book of histories detailing the adventures of the Lords of Storm’s End, the latter seems unlikely. (The possibility of this is also the topic of a separate post.)
So what would Ned have needed to make a reasonably confident call that Robert Baratheon was, in fact, homozygous for the dominant dark-haired allele? In effect, more bastard children from blond-haired mothers. We’d need at least seven dark haired bastards with blond mothers before we could say that there was less than one chance in a hundred that Robert was heterozygous. If Robert isn’t so discriminating in the hair color of his paramours, then we have to take into account that not all women are blond. Assuming a very high proportion blond (50%, roughly equivalent to that in Scandinavia), the allele frequency – the chance that a random woman would pass on a blond allele to her child – is about 0.7. In which case, with a heterozygous Robert you’d expect brown-haired children at a rate of 0.65, and you would need 11 dark haired bastards before you could say there was less than one chance in a hundred that Robert was a heterozygote. As a comparison, most modern paternity tests give a result closer to one in 100,000. That would be the equivalent of seventeen dark haired bastards with blond haired mothers, or twenty-seven with mothers of unknown hair color. That’s a lot even for Robert Baratheon.
Clearly, checking the hair color of nearly thirty bastard children is a hugely inefficient way to perform a paternity test. How do we do it nowadays? The short answer is by looking at the DNA instead of the phenotype, and by checking a lot more things than just hair color. Checking DNA is great for three reasons. First, we can know absolutely for sure if a kid could have gotten an allele from his father, because we can check which two alleles the father has and which two alleles the kid has. There’s no ambiguity there; we don’t have to verify that Robert is homozygous by checking what his other kids look like. We can just check. Second, it’s easy to look in ten or twenty places; we don’t have to search for the handful of human traits that are easy to see and roughly follow Mendel’s laws. And third, we can choose places that have three or four or ten different options: so we’re not considering just brown and blond, but black and brown and blond and red and purple and green, all occurring at about the same rate in the population.
The longer answer goes like this: your genome is full of repetition. Almost two percent of your genome, on average, is made up of what’s called “short tandem repeats” or “microsattelite repeats” — sequences of one to six nucleotides that are repeated up to a hundred times. In other words, once every couple thousand base pairs, your genome will skip like a record, and start playing the same couple bases over and over again. These sequences are especially variable, too, because it’s easier for the two strands of DNA to slide against each other there, and so it’s easier for mistakes to be made when a cell divides: you start with “…CACACACACACACACACACA…” and it’s easy to get from there to “…CACACA…” or “…CACACACACACACACACACACACACACACACA…”. Because of this slipping, every short tandem repeat changes in length about once every thousand generations. And since most of them don’t do anything, there’s a good deal of variation between people. We can measure the length of a repeat at a specific spot in the genome, and that gives us a great phenotype. Instead of blond versus brown hair, what we’re looking at in most forensic DNA tests is the length of short tandem repeats at specific places in the genome.
In the US, we generally test thirteen places, all over the genome. If you tested two places, you would get a result that looks something like this:
Here, the first line doesn’t differentiate between the two fathers: both Jaime and Robert have 24-copy alleles, so either could be Joffrey’s father. But the second line has useful information. The only allele Joffrey and Cersei share is 28 copies long, so he must have gotten the 32-copy allele from his father. Jaime has this allele and Robert doesn’t, so Jaime is much more likely to be the father. In fact, while there’s a 1 in 2 chance that Jaime could pass that allele on to his kids, Robert’s chance is much, much smaller: somewhere around 1 in 1000, which is the likelihood that whichever allele he passes on will change in this generation. Add a few of these differences over 13 sites – which is highly likely because these sites are so variable – and you can pretty conclusively say that Robert isn’t Joffrey’s father, whether or not you have Jaime’s DNA to compare it to.
In fact, in this case, we don’t need Cersei’s help at all: we can look at the Y chromosome (since it’s passed directly from father to son it should be essentially identical between father and son). That’s how we generally do paternity tests for boys anymore, and it’s also of particular use for finding genealogical information with groups like 23 and me or ancestry.com. And apart from proving that Joffrey isn’t the heir to the Iron Throne, DNA evidence could have a huge number of other uses in Westeros, doing everything it does in the real world: proving that the girl married to Ramsey Bolton isn’t a Stark, letting Cersei determine who visited Tyrion’s cell in the hours before his escape, and helping Daenerys find the long-lost or distant Targaryen relatives who have enough dragon blood to control and fly her dragons.