You have seen in the video on the analysis of DNA that generally, if the DNA comes from one person, if it is in good quantity and good quality, then one will have one or two peaks for each locus depending if the person has received the same allele from the parents or different one. If the person has two alleles, then the peaks will be approximately of the same size. Thus, if we have a profile with sometimes one peak for one localization and sometimes two peaks with the same height, but for another localization and if from the case information, we can assume that the trace came from one person then the evaluation is fairly simple. Let us say that there's been lots of blood recovered on the crime scene and that I am a suspect. The DNA scientist, after having performed tests to indicate if the substance is blood. So, this scientist will first look at the DNA profile of the blood trace without knowing my DNA profile and will designate the alleles from looking at the peaks. The electropherogram, the EPG, as we call it. So, the profile that you can see here. Having designated the alleles, she then will compare the profile of the trace with my DNA profile and assign the probability of observing the trace DNA profile and my DNA profile if the DNA came indeed from me. If the designated alleles are the same and if we omit the possibility of an error, then the probability of the results, given I am the source, will be one. We will have certainty. Then, the scientist will assign the probability of observing the DNA profile of the trace if it came from some unknown person. This is not done by observing and counting full profiles in a database. This is done by using a genetic model taking into account sub-population effects. What we call sub-population effects and therefore, the fact that we are all related somehow. It uses the occurrence of the alleles in a surveyed, considered as relevant, population. Generally, a sample of that population is available. It is composed of a few hundred unrelated persons. As we generally analyze loci on different chromosomes, we assign the probability of the trace DNA profile for each locus, considering also the profile of the known person. Then, we simply multiply all the probabilities together. With 15 loci, this can give astronomical numbers, but as Alex said, because the assumptions of the model cannot be tested for extremely small numbers, it is recommended not to give numbers smaller than one in a billion. Now, this is with single simple stains, but with traces recovered on the crime scene, reality can be more complex. One can have, for example, a mixture of DNA coming from different persons and thus, we can see a large number of peaks. Our first difficulty is that we do not know how many persons contributed to the trace. A second difficulty is that with small quantities or bad quality, we will observe artifacts, but let us see what are those artifacts. DNA analysis is usually done using samples containing the equivalent of 20 to 100 cells. When the samples contains only one to five cells, they are called low template. DNA analysis has to be adjusted to push the sensitivity to the maximum. DNA profile artifacts may then appear. To understand them, let me use an allegory from Raphael Coquoz, an excellent forensic scientist and a friend. Suppose a man begins to have gray hair, so that half his hairs have their original black color and half are white. If he loses 100 hairs at a crime scene, about 50 will be white and 50 will be black. We may also have 48 white hairs and 52 black, but it is unlikely to find 70 white hairs and 30 black. If now, the man loses only four hairs at the scene. There are maybe two white and two black, three white and one black, or simply by chance we may even have zero white and four black. This is not really unlikely. The hair analysis, made thus in that case, provide an inaccurate picture of the hair color of the men, were of the proportion of the colors. It is the same with DNA analysis with low amount of DNA in the trace. The two alleles at a specific locus may not be equally visible at the end of the analysis. Random events during the process. For example, survival of the molecules, recovery of the trace, DNA extraction, analysis may lead to an unequal visibility of the two alleles in the DNA profile or even lead to the absence of one of the two alleles. In ideal conditions, we will have the same quantity of DNA targets for both alleles and therefore should have the same height for both alleles. Here, we can see that alleles 12 and 15 have about the same peak height, but with little DNA template. One can have one allele that is in less quantity. In that case, the peaks are in-balanced. One peak is higher than the other. One allele can also be in such a small quantity that it appears to be completely absent. In that case, one will speak of allele dropout. Of course for a trace, we do not know if the allele is absent because it does not exist or if it has dropped out. It is only if we consider that it came from a given person that we can suppose it has dropped out. Sometimes there are no results for a given locus. In that case, we know that there is a locus dropout and sometimes instead of having an allele that drop outs, we have some alleles that drop in. They are not peaks from a person, but what we call alleles that drop from the ceiling. In the real world, there may be some dust with DNA present in the sample. Providing single bits of DNA pieces. When the sensitivity of DNA analysis is pushed to its maximum, this DNA dust may provide spurious allele peaks in the DNA profile. They are called drop-ins. These additional alleles are not reproducible. If there are more than two possible drop-ins, then the trace ought to be considered to be a mixture. On the figure, you can see a small peak on the left just before allele 12. This is what we call a stutter, an artifact stutter. During the PCR, it is unavoidable that the copying is partially imperfect. One repetition is sometimes not well copied, leading to a copy with one repeat less than it should. Thus, in front of allele 12, we will see a little peak that looks like an allele 11, but it is a stutter artifact. The peak size remains low in comparison with the true allele 12, but when the DNA analysis is pushed to its maximum, the peak size of the stutter artifacts maybe higher. Sometimes even as high as the true allele. Then, one does not know if it is an allele, a stutter, or as Tim Clayton, also a famous forensic scientist calls them a mixture of both [inaudible]. So, with small quantities, we have peaks that dropout. Some that jump in and some stutters that are as big as alleles. As you may imagine, this does make the interpretation process much more complex. Also as mentioned earlier, traces are not often single stains, but can come from multiple donors. This makes the situation even more complex. Hopefully, to deal with this complexity, they are also analytical solutions. If a mixture is from a male and a female. One can analyze the Y chromosome. Thus, focusing only on the male. These analysis are less discriminating than non-sexual DNA, but it can be very useful and indeed, in the murder of Meredith Kershaw, this technique, the use of Y chromosome was applied as you will see later. In the murder of Meredith Kershaw, the traces were difficult to assess. In such cases as indicated by DMC or the ISFG guidelines, by the way, ISFG stands for International Society for Forensic Genetics, which is an international association promoting scientific knowledge in the field of genetic markers analyzed for forensic purposes. For those societies, it is essential to use appropriate models to assess the probability of the results given propositions. In order to assess the results properly. We can refer to probabilistic software that takes into account all the possibilities mentioned before. These softwares allow to assess the value of mixtures and low quantity DNA from different contributors. Of course, they need to be validated and fit for purpose, but this represents another topic that is out of scope of this presentation.