15/19 or 15/37 & 100% or NOT 100%

There are people in the world who are convinced that Madeleine McCann was not abducted. They believe that Kate & Gerry McCann hid Madeleine's body following her death. One central plank of evidence in this hypothesis is the DNA that was found in the boot of the car hired by the McCann's about three weeks after Madeleine was reported missing. They argue that the only way her DNA could have been in the car is if they moved her body at some time after they hired the car.

There has been considerable debate about whether the DNA profile obtained contained Madeleine's DNA or not. The report by the now disbanded FSS (Forensic Science Service) says clearly that it is impossible to say for certain. Unfortunately it does not go on to say anything else about this sample. There is no attempt to say how likely it is that the DNA came from Madeleine or not. So we are left not knowing whether the chance it is Madeliene's DNA is 1%, 50%, or 99%. All we know is that according to John Lowe of the now defunked FSS that it is not 100%.

Perhaps that would be the end of the matter, but people have taken sides on this issue. Some say it was her DNA some say it wasn't. Both points of view are wrong because no one can say for certain either way. However it is possible to gain some understanding how likely it is that this sample does contain DNA from Madeleine McCann. This blog will attempt to do that over the next few weeks.

First of all some background about DNA identification.

The FSS test involves looking at 10 different loci (locations) in human DNA. Each location (locus) has two copies sometimes called markers or alleles. The two markers at a locus are often different to each other but can be identical. So by looking at 10 loci the FSS identify a maximum of 20 markers.
In Madeleine's case there are actually only 19 markers because at one locus the two markers are identical.

Each individual person has a unique combination of markers and this is called their DNA profile or fingerprint. Some elements of a DNA profile will be shared but the total combination of 20 markers is unique to an individual except in the case of identical twins who will share identical profiles.

You may find it helpful to think of the following analogy. Imagine that each marker is a coloured disc. Now imagine that each locus is a number from 1 to 10 and that one of these numbers is written on each disc. The discs can be any one of many different colours and they can have any number from 1 to 10. Each person gets two discs with the number 1, two discs with the number 2 and so on till they have 20 discs. Can you see how unlikely it is that any two people will get exactly the same set of discs?

In reality everyone gets 10 markers or coloured+numbered discs from their father and 10 from their mother. This means that everyone shares exactly half their DNA profile with their mother and the other half with their father. See the diagram below

The selection of discs from mother and father is completely random. This means that although two children (even twins though not identical twins) have the same parents they have very different DNA profiles. See diagram below:

The one exception is identical twins because they form from a single embryo identical twins will have identical DNA profiles to each other. As far as we know Maddy did not have an identical twin sister so there is no need to worry about this possibility.

15/19 OR 15/37 

Now we know the genetics behind DNA profiles we can push on to the next subject namely was it 15/19 or 15/37?

The answer is BOTH! Here is why.

Maddy has only 19 markers because at one locus she inherited exactly the same marker (numbered+coloured disc) from Kate as she did from Gerry. In the example above this happens at location 6 (child 1).

We have to assume that when the FSS tested the sample only 8 loci gave a positive response. That is to say they were not able to determine the colour of the discs at two loci. This can happen and I may deal with why in a later blog. For now all we need to know is that 8 loci gave a result (colours in our analogy) and 2 loci didn't. One of the eight that did give a result gave only one colour while the other seven gave two colours making a total of 15. This is exactly what you might expect if loci 1 to 8 gave a result and 9 & 10 didn't in the example above.

Great you say, that means 15 markers (out of a total of 19) all matching Maddy's DNA. So it's 15/19! Yes that is true. However the FSS say that they didn't just get one or two colours for each locus, they got more. This can happen if DNA from two or more people gets mixed in the sample. So if we take loci 1 to 8 from the sample above and count the number of markers we get from a mixture of Mum,Dad and Child 1 in the example above we get 31 markers. The exact number of markers obtained will depend on how many people's DNA is mixed and how many markers they share. In the McCann case FSS say they found a total of 37 markers at the 8 loci. It is not possible in a mixed DNA sample to say which marker came from which person unless you already know who the contributors were. So while we can say that 15/19 of Maddy's markers are present in the sample we must also say that 15/37 of the total number of markers in the sample match Maddy's DNA.

100% MATCH OR NOT

Once again the answer is BOTH! (Well sort of) 

We know that only 8 loci gave a result and we know that all 15 of Maddy's markers for those 8 loci were present so it is a 15/15 i.e. 100% match. If only 14 of Maddy's markers for those 8 loci had been present the match would be 14/15 i.e. 93.333% and we would be able to say with a high degree of certainty that Maddy's DNA is NOT present in the sample. 

However because it is a mixed sample it is not possible to say for sure (i.e. 100%) that all the markers that match Maddy's DNA came from the same person. So although the match IS 100% we cannot be certain that the DNA came from Maddy. This seems to be the bit that confuses many people. If you are confused perhaps thinking about the coloured+numbered counters can help. Here is another diagram to help.

This diagram clearly shows that it is theoretically possible for the same 37 marker profile to be produced from Maddie's DNA mixed with two strangers DNA or from Kate's DNA mixed with DNA from two strangers. (These are only representations of what Kate & Maddy's DNA profiles look like as numbered discs, but they provide an accurate illustration of principle).

In my next installment I will consider how likely it is that the 37 markers contain DNA from Maddy.