The Interpretation of Traces Found on Adhesive Tapes

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The Interpretation of Traces Found

on Adhesive Tapes

Remi Wieten, 10456600, 10/10/2014.

Research Project (36 EC: 03/02/2014 - 01/09/2014) as part of the MSc in Forensic Science at the University of Amsterdam (Amsterdam, the

Netherlands). Research Institute :

Netherlands Forensic Institute (NFI), The Hague, the Netherlands. Supervisors :

dr. Bas Kokshoorn*, drs. Bart Blankers*, ir. Jacob de Zoete†,** Examiner :

prof. dr. Marjan Sjerps**

†

University of Amsterdam

* NFI Department of Human Biological Traces

** NFI Department of Science, Interdisciplinary Research, Statistics and Knowledge Management

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Abstract

In violent crimes (e.g. homicides and terrorist attacks) adhesive tapes such as duct tape are often used by perpetrators, for example to tie up a victim or to bind together parts of an improvised explosive device. In the forensic examination of such tapes many different types of traces can be found, such as finger marks, human biological traces and fibres. These traces are first interpreted at source level. However, even when it is certain that a trace was donated by the suspect, this does not necessarily mean that he donated the trace while taping the victim, as he could have, for example, used the tape roll from which the pieces came previous to the crime. Therefore, the trace can also be interpreted at activity level. For this, factors such as transfer, persistence and recovery have to be taken into consideration, as well as the location of the trace as it would have been on the original roll. At the moment these factors are subjectively combined by a forensic expert, but a more transparent and uniform approach making use of Bayesian networks may be preferable. The factors which have the most influence on the likelihood ratio were determined by performing a sensitivity analysis. In future projects, data can be gathered on these factors to make the networks more robust.

Acknowledgments

I would like to thank Ate Kloosterman, as well as Marjan Sjerps, for their effort in helping me find this project. I would like to thank Richard Visser for helping me understand the process of physical end matching, Yvonne van der Wal for her insight in the interpretation of human biological traces found on adhesive tape, and Linda Koomen and Jeannette Leegwater for helping me understand the process by which finger marks are analysed and interpreted at the NFI. I would like to thank my supervisors Bart Blankers, Bas Kokshoorn and Jacob de Zoete for their many insightful conversations. Bart Blankers’ developed network for the interpretation at activity level of human biological traces and Jacob de Zoete’s network for crime linkage have been a great help to this project. Finally, I would like to thank Marjan Sjerps and Jan de Koeijer for their suggestions during the NFI BayesNet group sessions. They have helped make the networks more correct at a fundamental level.

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1 Introduction

In violent crimes (e.g. robberies, sexual assaults, homicides and terrorist attacks) adhesive tapes are often used by perpetrators. Duct tapes are for example used to tie up a victim or to bind together parts of an improvised explosive device. Due to its adhesive qualities, many different types of traces can be found on tape pieces during forensic examination. Here, one can think of human biological traces, finger marks and fibres from garments, but also all kinds of micro traces. These traces can be analysed by forensic experts and subsequently compared to suspected sources. For example, fibres found on tape can be compared to fibres from a suspected garment.

While the characteristics of a control sample and a trace can be similar, this does not automatically mean that the source from which the trace came is the same source from which the control sample came, as different sources can have similar characteristics. Therefore, forensic experts try to determine how probable it is to see matching characteristics when the control sample and the trace came from the same source (within source variation) com-pared to when they came from a different source (between source variation). From this the evidential value of a match can be determined. This is called interpretation at source level (see Cook et al. (1998)).

However, even when it is absolutely certain that the suspect was the donor of the trace, this does not automatically mean that he donated the trace while taping the victim. It could for example be that he had contact with the tape roll from which the pieces came previous to the crime. Source level interpretation cannot be used to resolve these issues. One level higher would be to interpret the evidence at activity level. Here, the forensic expert wants to determine how likely it is to see the evidence under these specific conditions if it came there when the suspect taped the victim com-pared to when an unknown person taped the victim (i.e. when the suspect only used the tape for normal purposes).

The forensic expert would then have to determine how likely it is that traces from the suspect were transferred prior to the crime and whether these traces would have persisted. In tape cases, the location of the trace as it would have been on the original roll can also be taken into consideration. When the suspect states that he previously only used the roll for innocent reasons, we expect that he would almost only leave behind traces on the outside of the roll (i.e. the backing of the outer layer of the roll). When the

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tape pieces found at the crime scene are then reassembled in the order in which they most likely came from the roll (by a process called physical end matching) and a trace is found at a location where it would have originally been deep into the roll of tape, then it would be unlikely that that trace would have ended up there due to innocent reasons. This would then be incriminating for the suspect.

At the moment all the above factors are subjectively combined by a forensic expert to come to a conclusion at activity level. However, a more transparent and uniform approach making use of Bayesian networks may be preferable (see Taroni et al. (2006)). A Bayesian network is a mathematical tool in which all the relevant variables used in interpretation and the dependencies between these variables can be charted. In order to perform calculations in a Bayesian network, many of the subjective probability assignments which forensic experts might use subconsciously in their interpretation have to be made explicit. The variables which most influence their conclusions can be determined by performing a sensitivity analysis. Further studies can then be set up to collect data to buttress the probabilities used in these nodes. In Chapter 2, we will first briefly describe the likelihood ratio approach, the hierarchy of propositions (which includes source and activity level) and the theory behind Bayesian networks. In Chapter 3, we will describe the network that was developed for the interpretation at activity level of a single human biological trace. Here, the different steps in the analysis and inter-pretation process are described, and for every step the corresponding parts in the network are explained. Afterwards, a sensitivity analysis is performed in a specific case example.

In Chapter 4, we will look at the network for the interpretation of two human biological traces. Here, it is important to model the dependencies that can exist between the two traces, as there might be a large prior prob-ability that these traces were left by the same donor. In Chapter 5, the network for a single finger mark is described, as well as networks for mul-tiple finger marks, and DNA found inside a finger mark. In Chapter 6, suggestions for other types of traces are given. In Chapter 7, we will discuss the limits and possibilities of these networks and look at future directions that can be taken to further optimize them. In Chapter 8, we will conclude the thesis and express and underline the use and limitations of the networks in casework.

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2 Methods and techniques

2.1 The hierarchy of propositions

The last decade it has become common practice for the trier of fact (i.e. the judges and/or jury) to address two competing propositions in the courtroom: one from the prosecution and one from the defence. When trying to assess the probabilities of these propositions given the available evidence, Bayes’ theorem has proven to be valuable. If we denote the evidence by E, and the propositions as put forward by the prosecution and defence by Hp and Hd

respectively, then we have (using Bayes’ theorem): P (Hp | E) P (Hd| E) = P (E | Hp) P (E | Hd) ·P (Hp) P (Hd) (1)

Here, we call P (E|Hp)

P (E|Hd) the likelihood ratio (LR),

P (Hp)

P (Hd) the prior odds

and P (Hp|E)

P (Hd|E) the posterior odds. It has generally been agreed upon that

the likelihood ratio is for the forensic expert to decide, while the prior odds are left to the trier of fact (see for example AFSP (2009)). The likelihood ratio is determined by estimating the probabilities of seeing the findings un-der Hp and Hd. It is a number between 0 and ∞ that will be 1 when it is

equally probable to see the findings under Hp as Hd, higher than 1 if it is

more probable to see the findings under Hp than under Hd, and lower than

1 if it is more probable to see the findings under Hd than under Hp.

In 1998, Cook et al. introduced the concept of a “Hierarchy of Propo-sitions”. This hierarchy consists of three levels, namely propositions at source level, activity level and crime level (of which we mentioned the first two in the introduction). These three levels follow a hierarchy, in which source level is the lowest and crime level the highest level. The higher the addressed level the more valuable the answer will be for the trier of fact. However, the probabilities of observing the evidence given the set of propo-sitions (the likelihood ratio) become more difficult to assess as we go higher into the hierarchy (more information is needed).

An example of a set of source level propositions is:

Hp: The suspect is the donor of the trace found on the tape.

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An example of a set of activity level propositions is: Hp: The suspect taped the victim.

Hd: An unknown person taped the victim.

At crime level, the issue under consideration is whether a crime was com-mitted, and we want to address propositions that state who would have been the offender of this crime. Here, to determine the likelihood ratio, all the information in the case file is needed, as well as judicial information. Therefore, forensic experts will not address propositions at crime level to not overstep their bounds.

An example of a set of crime level propositions is: Hp: The suspect assaulted the victim.

Hd: An unknown person assaulted the victim.

As the trier of fact generally has trouble understanding the evidential value when presented with a single number, it has become general practice in the forensic community to convert the numerical LR to a verbal equivalent. At the NFI, the following verbal scale is used to make the strength of the evi-dence more transparent for the trier of fact.

Verbal term Likelihood ratio

Equally probable 1 - 2 Slightly more probable 2 - 10

More probable 10 - 100

Much more probable 100 - 10 000 Very much more probable 10 000 - 1 000 000 Extremely more probable > 1 000 000

Table 1: Verbal terms and corresponding LRs for LRs larger than 1 (in favour of the prosecution). For LRs smaller than 1 (in favour of the defence) we would have to take the multiplicative inverse of these numbers.

For example, an LR of 1000 for the above activity level propositions can be converted to: “It is much more probable to see the findings when the suspect taped the victim than if an unknown person taped the victim.”

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2.2 Bayesian networks in forensic science

Bayesian networks are mathematical tools which can be used to graph-ically display the way different variables of interest are causally related to each other (see Taroni et al. (2006)). The variables in the network are called nodes, and the different instantiations of a node are called states. The de-pendencies between the nodes are displayed with arrows. When an arrow points from node A to node B, then A is called a parent of B. For every node in the network, the conditional probability table of the node given its parents has to be determined. This means that for every collection of states of the parents we need to know the probabilities for the different states of the child. When it now becomes clearer in which states certain nodes can be, then the probability distributions for other nodes in the network can be readjusted by invoking standard probability theory. If a node has no parents we call the node a root node. For root nodes, we only need to know the prior probability distribution of the different states. In this thesis we will indicate nodes with capitals and states with italics.

Figure 1: Bayesian network for the wet grass example, with corresponding probability tables.

We now look at a brief example of a Bayesian network. Say we find a certain patch of wet grass somewhere and we want to estimate the probability that it has rained. Before viewing the grass, we estimate the probability that it has rained to be 2 out of 3. Furthermore, we believe that in 99% of the cases when it has rained the grass will be wet, and in 1% of the cases when it has not rained the grass will be wet. We can then model this situation as in

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Figure 1. If we now denote the evidence (the fact that we have seen wet grass) by E and if we write H1: It has rained, and H2: It has not rained,

then we have (using Equation 1): P (H1 | E) P (H2 | E) = P (E | H1) P (E | H2) ·P (H1) P (H2) = 0.99 0.01 · 2 3 1 3 = 99 · 2 = 198 (2)

As P (H2 | E) = 1 - P (H1 | E), we obtain P (H1 | E) = 198₁₉₉. Thus, knowing

that the grass is wet, the probability that it has rained is now ≈ 0.995. Calculations quickly become too time-consuming and complex to be able to perform them manually. With the use of software packages such as AgenaRisk and HUGIN these calculations can be performed automatically. These software packages can also be used to perform a sensitivity analysis. After choosing a target node and a set of sensitivity nodes, it can be de-termined which of the sensitivity nodes has the biggest effect on the target node by varying over the different states of the sensitivity nodes. In forensic science, the factors which have the biggest effect on the likelihood ratio can be determined. If the sensitivity nodes that have the biggest impact on the target node have conditional probabilities tables in which the probabilities are mostly estimated or subjectively determined by experts, one could de-cide to set up experiments to better buttress these probabilities.

Bayesian networks have already proven to be valuable tools in the modelling of complex forensic cases. They can be used to facilitate expert reasoning, to clarify the assumptions on which this reasoning is based and to discuss cases more easily and clearly with fellow experts, as well as prosecutors and lawyers. As put by Berger and Sjerps (2012, p. 322): “The construction of the network ... provides insight in the problem and serves as a visual aid to structure thought, making sure he [the expert] does not overlook considering some variable, dependency, probability or assumption.”

When the input data of the model is sufficiently reliable (in the sense that the probability tables consist of probability estimates from ’hard’ data) the calculated likelihood ratio can even be reported directly to the trier of fact. More often, however, a Bayesian network should not be used as a black box. The forensic expert should assess changes in the likelihood ratio by varying probability values, especially when mostly subjective probability assessments are used.

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3 Network for a single human biological trace

In this chapter, we will discuss the factors that are taken into consideration by forensic experts when they interpret a single human biological trace that was found on adhesive tape at activity level. Per factor we will outline the manners in which this factor can be modelled in a Bayesian network and discuss which way of modelling has our preference.

Many of the terms that we will be using can be found in Rudin and Inman (2001). However, up front we will explicitly state some important terms: 1) A human biological trace (or trace for short) is human cellular ma-terial that is present on a specific location on a secured piece of evidence (such as a piece of tape). Here, with secured we mean that the evidence lies safely stored at the forensic laboratory and is ready for examination. 2) A sample consists of cellular material that was recovered from a trace by forensic examiners using a collection technique such as swabbing or stub-bing. A sample will generally contain only part of the actual trace that is present on the item; this depends on the effectiveness of the used recovery technique. The obtained sample can subsequently be subjected to DNA analysis.

3) The sampling location is the surface area of an item of evidence where sampling takes place. Sampling locations are chosen such that they will contain DNA from the perpetrator a high percentage of the time.

Furthermore, we will address the following set of activity level propositions: Hp: The suspect taped the victim.

Hd: An unknown person taped the victim.

However, the victim can be replaced by any other taped person or object (such as an improvised explosive device). We will often use the word “per-petrator” to refer to the person who performed the activity (i.e. taped the victim). However, when someone has taped a person this does not necessar-ily mean that a crime was committed. It should thus be noted that we are not interpreting at crime level, but strictly using the word “perpetrator” for shortness of notation. Similarly, the word “crime” refers to the activity or incident that took place.

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In Appendix A, the developed network for the interpretation at activity level of a single human biological trace that was found on adhesive tape is presented. Here, we assume that DNA analysis has been performed on a sample obtained from a certain sampling location, and that the forensic expert wishes to interpret the results of this analysis at activity level. In Appendix B the conditional probability tables of the different nodes of this network are presented. Some of the probabilities presented in these tables should be regarded as suggestions. When the network is used in a specific case these probabilities can be adjusted if necessary.

We will now present and discuss the developed network step-by-step. 3.1 The process by which the trace is formed

We start by modelling the process by which a trace is formed on tape. For this, the factors transfer and persistence have to be taken into consideration. In Figure 2 this part of the network is displayed.

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3.1.1 Transfer

With the term transfer we mean the transfer of cellular material from a certain person to a certain area on the tape pieces (which will later turn out to be the sampling location). Transfer depends on a number of factors, including the duration, intensity and frequency of contact. Tape generally consists of an adhesive side and a non-adhesive side (also called the backing of the tape). One could argue that cellular material is more easily trans-ferred to the adhesive side than to the backing. However, this also depends on the properties of the tape in question (i.e. how sticky the adhesive side is and how coarse the backing is).

In this chapter, we will mainly consider contact traces, which are traces that were transferred when the skin of a person came into direct contact with the tape. In this case, skin cells (i.e. epithelial cells), sweat and saliva can (among others) be transferred, and (partial) finger marks (which are impressions of ridge patterns present on the human skin) can be left behind. We will deal with finger marks and DNA inside finger marks in Chapter 5. As a person might use his teeth to tear of a piece of tape, saliva can also be transferred. As tape is used in violent crimes such as homicides and rob-beries, blood can also be left behind by the perpetrator (and the victim). In sexual offences semen can be left behind. Furthermore, hairs can be trans-ferred to tape, but we will discuss this later (in Section 6.2), because the interpretation of hairs at activity level will differ from the interpretation as presented in the current chapter.

At the NFI, the areas on tape that are generally sampled for DNA are (partial) finger marks, bite marks, and tape ends, as these locations will likely contain DNA from the perpetrator. Blood is sometimes also sampled, but in most cases this blood would have originated from the victim.

We will distinguish between three different kinds of transfer scenarios: (1) transfer from the perpetrator to the sampling location while he was taping the victim, (2) background transfer from the suspect to the sampling loca-tion, and (3) background transfer from unknown(s) to the sampling location. Here, we assume that there is only a single perpetrator (although a solution for multiple perpetrators is suggested in Section 3.1.3). As these three types of transfer are not mutually exclusive it is possible that a mixture can be formed over time. Cellular material has transferred to the sampling location as background if it came there due to some innocent reason (i.e. if the

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cellular material was not transferred from the perpetrator to the sampling location while he was taping the victim). For instance, one can think of background material of a person being present because that person touched the tape at some moment before or after the crime, or because material was retransferred from an object previously touched by that person to the tape before, during or after the crime. For example, the perpetrator could have used the suspect’s gloves while taping the victim. When the suspect’s cellular material was then present on the outside of the gloves, it could have retransferred to the tape.

In the network, the probabilities of transfer under the three above-mentioned scenarios have to be estimated by the forensic expert. Here, we make the important restriction that transfer is only considered successful in the net-work if DNA was transferred. Cellular material could be transferred, but this does not mean that DNA is present in this material. We make this dis-tinction as this will be of importance later (when defining persistence and recovery). The amount of transferred DNA should not be taken into con-sideration when determining these probabilities, as this will cause problems elsewhere in the network (see Section 7.3). We will thus treat transfer as binary: either DNA has transferred, or it has not.

As there are a large number of variables to be taken into consideration when determining the probabilities for the three scenarios, it was opted not to model all these variables in the network, especially since the probabil-ities are mostly determined subjectively. It would become challenging to objectively determine the necessary probability tables. Therefore, we opted to create a transfer node for each of the three scenarios, which can be in state Yes or No (see Appendix B, Table 9). The probabilities that have been subjectively estimated by the forensic expert can then be entered in the probability tables of these nodes. According to Champod (2013), the forensic expert should be able to assess these probabilities (i.e. he is more in a position to do so than the trier of fact), but he should mostly base his opinion on data gathered from case specific experiments rather than his own personal experience. The number and type of experiments that should be set up will depend on the specific case circumstances.

For the first scenario, the forensic expert will need to determine the proba-bility that DNA of the perpetrator was transferred to the sampling location when he was taping the victim. This probability will generally be high, as forensic examiners will sample at locations where they expect to find DNA

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from the perpetrator. For bite marks, this probability will be close to one, as the probability that the bite mark is activity related is generally very high, and the intensity of the contact will also be high. As the perpetrator would have to touch the roll end every time he tears of a piece of tape, the probability of transfer to tape ends of pieces is also high (though this also depends on the properties of the tape and whether the tape end is sampled on the adhesive side or the backing). To estimate the probability of transfer of DNA, the forensic expert also has to take into consideration specific case circumstances. For example, the victim can state that the perpetrator tore the tape with his bare hands and touched it excessively (high probability of transfer) or that the perpetrator wore gloves while taping (low probability of transfer). Other tactical information (such as video footage from cameras) can also be used.

The possibility of retransfer of DNA from another location on the tape to the sampling location should not be taken into consideration by the foren-sic expert, as little is known about retransfer behaviour. This probability could cancel out the probability of retransfer from the sampling location to another location on the tape, but since we do not know where DNA can re-transfer to, we will ignore this here. In Section 7.1, a general outline is given how experiments should be set up to gather data on retransfer behaviour. For the second scenario, the forensic expert will need to estimate the proba-bility that background DNA of the suspect was transferred to the sampling location. Background transfer of DNA of the suspect to the tape pieces in general will depend on his relation to the roll of tape. For example, if the roll of tape from which the tape pieces (probably) originated was found at his house and he used that roll regularly, then background transfer is likely. Also, retransfer of DNA from another object to the sampling location has to be taken into account. For this, contamination at the crime scene by forensic examiners also has to be taken into consideration (but we will deal with contamination during examination and analysis at the forensic labo-ratory separately in Section 3.2.1 and Section 3.3.1). DNA could also have transferred from the side of the roll or the inner cardboard roll to the sur-face area of the tape. As in the first scenario, retransfer of DNA from one location on the tape pieces to another should not be taken into consideration. When the suspect has given a statement regarding how his DNA could have been transferred to the tape, then the forensic expert will also need to take into account how probable it is that this statement is true when assessing

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the probability of background transfer. For this, the prosecutor could be consulted, as it is outside the area of expertise of the forensic expert. This would preferably be done in consultation with the trier of fact, but as the trier of fact can only provide feedback during the actual hearing of a case it would be impossible for the forensic expert to take his assessment into consideration when performing calculations in the network. One could also estimate the probability of transfer for when the suspect’s story is assumed to be true and for when his story is assumed to be false. The effect of this on the likelihood ratio at activity level can then be determined and reported. As we want to estimate the probability of background transfer to a spe-cific sampling area we will have to scale the total probability of background transfer to the tape accordingly. Here, the size of the sampling area com-pared to the whole tape has to be taken into consideration, as well as the proportion of the tape to which the suspect likely transferred DNA. Also, the properties of the tape should be taken into account, and whether the sampling location is positioned on the adhesive side or the backing of the tape. The location of the sampling area on the pieces itself should not be taken into account, but only the size of the sampling area. The forensic expert should thus not take into account that the sampling area was near a tape end, or in the middle of a tape piece. After physical end matching (see Section 3.4), the forensic expert can deduce where the sampling area would have been on the original roll (see Section 3.4.2). We can then for example determine whether background DNA would have had to transfer to a deeper layer or a more superficial layer of the roll. With this, we can thus also update the probability of transfer (see Section 3.4.3).

For the third scenario, the forensic expert will need to estimate the proba-bility that background DNA of unknown(s) was transferred to the sampling location. Here, an unknown person can be any person other than the suspect who could have had direct or indirect contact with the tape, where we will not take into account people whose reference DNA profiles are known (such as the victim and forensic examiners) and who can thus later be excluded from a DNA profile. Transfer mostly depends on the number of people who could have had contact with the tape, which can be estimated from case circumstances. For example, the police or emergency personnel could have contaminated the scene. The number of perpetrators present at the scene can also be taken into consideration, as well as other people present at the crime scene during the crime. People who lived in the perpetrator’s house and used the roll of tape for innocent reasons, as well as people who could

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have previously touched the tape in the hardware store where the roll was sold could be considered. Retransfer scenarios should be taken into account, as DNA could have been present on the taped object or person before the crime, or DNA could have been retransferred from the hands/gloves of the perpetrator to the tape. Like in the second scenario, the size of the sam-pling area has to be taken into consideration, as we want to determine the probability of transfer to the specific sampling area. The actual location of this area should again not be used.

3.1.2 Persistence

After DNA has been transferred, it will need to persist will forensic exam-iners be able to find and recover DNA from the sampling location. Here, two factors have to be taken into consideration: (1) the degradation of DNA due to environmental conditions, and (2) the retransfer of DNA from the sampling location to another object.

The degradation of DNA due to environmental conditions

When cellular material is exposed to the environment, DNA present in this material will degrade over time. The rate of decay depends on the specific environmental conditions in which the material resided. DNA will degrade faster in a warm, humid environment and in the presence of UV light than in a cold, dry environment in the absence of UV light (see Rudin and Inman (2001)). Whether DNA will be present in a trace on a secured tape piece will thus mostly depend on the surroundings of the tape. At the police sta-tion and at the NFI, evidence is stored under DNA neutral condista-tions (room temperature, dry and dark). Therefore, only environmental conditions prior to storage will have an influence on persistence.

Consideration has to be given to the fact that DNA will not degrade as fast if it is covered by another item. For example, if DNA was transferred to the adhesive side of a piece of tape and that piece was subsequently stuck on an item, then the DNA will be protected from environmental conditions and will thus not degrade as fast compared to when it was originally trans-ferred to the backing of that piece. However, the forensic expert should not yet take into consideration the fact that background DNA could originally have been present at a deeper layer of the roll, and thus covered by other layers of tape on the roll. We will take this possibility into consideration when we know the position of the sampling location on the original roll. The

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probability of persistence will thus be updated after physical end matching (see Section 3.4.3).

The retransfer of DNA from tape to another object

Retransfer of DNA to another object (i.e. the loss of DNA) can occur at any time from when the DNA was deposited up to the moment that the evidence is secured. If an object comes into contact with the tape, DNA can move from the tape to that object and thus not be present on the tape dur-ing forensic examination. For example, DNA might be lost when the victim is freed, or when evidence is handled at the crime scene and subsequently packaged and transported to the forensic laboratory. Here, retransfer may occur more easily for certain types of cellular material. It is important to note that DNA will more easily retransfer from the backing to another ob-ject than from the adhesive side to another obob-ject, as cellular material will tend to stick to the adhesive side. As stated in Section 3.1.1, retransfer from one location on the tape pieces to another should not be taken into consideration, as there is no data available on retransfer behaviour (see also Section 7.1).

In the network (see Appendix A), the forensic expert will again have to esti-mate probabilities for three different scenarios: (1) the persistence of DNA of the perpetrator (that was transferred when he was taping the victim), (2) the persistence of background DNA of the suspect, and (3) the persistence of background DNA of unknown(s). Here, the expert only has to estimate the probability of persistence given that DNA has transferred; the probability of persistence when transfer is in No will be 0 (see Appendix B, Table 10). The main difference between the three scenarios will be the time span since transfer. If the suspect has had background contact with the roll six months ago and the perpetrator taped the victim three days ago, we would expect that if DNA transferred in both scenarios it would persist more likely in the latter, as there would be less chance of degradation and retransfer. Also, studies like van Oorschot et al. (2014) could be set up to determine the probability of persistence of DNA of previous user(s) of a tape roll. Persistence, like transfer, is treated binary: DNA will either persist or not. The probability of persistence should not be based on the amount of DNA that was transferred, as we have treated transfer as binary (see also Section 7.3).

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3.1.3 Composition of the trace and manner of deposition (sum-mary node)

The three persistence nodes are connected to the summary node, which states whose DNA is present in the trace present at the sampling location, and how that DNA was transferred to the sampling location (see Appendix A). propositions (which contains the propositions under consideration at activity level) is also connected to summary. This node determines who the perpetrator is in persistence perpetrator. The prior odds for propo-sitions are set to 1 (see Appendix B, Table 11), and therefore the posterior odds which we will eventually obtain from this node will be equal to the likelihood ratio. In practice, these prior odds are based on all the case infor-mation that was not used in the network, and they are for the trier of fact to decide (see Section 2.1).

summary can be in 12 mutually exclusive states (see Appendix B, Table 12). Background DNA from unknown(s) can persist or not, background DNA from the suspect can persist or not, and DNA from the perpetrator (that was transferred when he taped the victim) can persist or not. When DNA from the perpetrator has persisted, the particular state in which summary will be will depend on the state of propositions. However, if persistence perpetrator is in No, then the state of propositions will not matter. The last state corresponds to the situation in which no DNA persisted. In this case, no DNA will be present at the sampling location.

In Section 3.1.1 the possibility of transfer by multiple perpetrators was men-tioned. One can deal with this situation by adding an extra transfer and persistence node for each other possible perpetrator. We would then have to estimate probabilities of transfer and persistence for perpetrator 1, for perpetrator 2, etc. The set of propositions would then change to Hp: The

suspect is one of the perpetrators, and Hd: The suspect is not one of the

per-petrators, and the states and the conditional probability table of summary would have to be adjusted accordingly.

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Figure 3: Subnetwork: Recovery.

3.2 Recovery

To be able to perform DNA analysis, forensic examiners will first need to recover the cellular material that is present at the sampling location. For the collection of cellular material several methods exist, such as swabbing and stubbing. As these methods are not 100% successful there exists un-certainty whether sampling will succeed. In the network (see Figure 3), we will say that recovery was successful if DNA has been collected (i.e. if the sample contains DNA). While it is possible to collect cellular material, but not DNA, we will not be interested in this situation in the network.

An arrow points from recovery and summary to composition of the sample. This last node can be in one of the following four states:

DNA of suspect in sample DNA of unknown(s) in sample

DNA of suspect and unknown(s) in sample No DNA present in sample

When recovery is in No, there will be no DNA present in the sample (i.e. composition of the sample is always in No DNA present in sam-ple, independent of summary). Only if DNA was recovered (i.e. recovery is in Yes) will the state of summary matter (see Appendix B, Table 13). Here, we will purely look at the “who” component of summary and not at how the DNA was originally deposited (i.e. as background, by the perpetra-tor when he was taping the victim, or both). When recovery was successful

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(i.e. recovery is in Yes), but no actual DNA was present in the trace (i.e. summary is in No DNA) then composition of the sample will be in No DNA present in sample. The meaning of this is that the recovery method would have been effective if DNA would have been present, but since no DNA is present there will be no DNA in the sample.

recovery is not meant to be instantiated; if in the end no DNA profile was obtained from the sample this will allow us to reason that either no DNA was present at the sampling location or that the recovery method must have been unsuccessful. The prior probability of recovery can, for example, be set to 0.8 when the forensic expert expects that in 80% of the cases forensic examiners will be able to collect DNA if it is present at the sampling loca-tion (for the probability table, see Appendix B, Table 14). This probability can be changed on a case by case basis, where the forensic expert could take into account the efficiency of the specific collection technique that was used and the error rate of examiners. Like transfer and persistence, we will treat recovery as binary: either DNA was recovered or not. While we would expect a higher probability of recovery if there is a larger amount of DNA present at the sampling location, we cannot deal with this in the network at the moment (see Section 7.3).

3.2.1 Contamination during recovery

At this point, we can also account for the possibility of contamination during examination at the forensic laboratory. With this, we mean that somehow DNA that was originally not present at the sampling location but does be-long to the suspect or unknown(s) ends up at the sampling location due to errors in the examination process. Contamination can, for example, oc-cur because the examiner previously touched another piece of evidence that did contain DNA of the suspect/unknown(s). However, pieces of convic-tion from the suspect and from the victim are usually examined in separate rooms. Therefore, there is only a small probability that DNA from an item belonging to the suspect is transferred to tape (an item ‘belonging’ to the victim). As in the sections on transfer and persistence (Section 3.1.1 and Section 3.1.2), we should not take into account retransfer from one location on the tape pieces to another, as no data is available on this type of transfer. Contamination can be seen as a kind of background transfer, and therefore one could slightly raise the probabilities of background transfer of the sus-pect and unknown(s). However, for the sake of transparency we have added

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two contamination nodes to the network instead (see Figure 3). When a contamination node is in Yes this will lead to the presence of DNA of that person at the sampling location. Recovery still has to be successful in order for the contaminated DNA to end up in the sample (see Appendix B, Table 13). The contamination nodes (like recovery) are meant to be kept open. This will allow us to reason that a DNA match with the suspect must have been due to contamination in situations where the probabilities of transfer and persistence were believed to be very low.

The prior probabilities for these nodes are now set to 0.0001, which means that in one in 10 000 cases we expect there to be contamination during ex-amination (see also Appendix B, Table 15). This number is set quite low as we expect that the recovery process will generally be performed without errors. It can be changed per forensic laboratory, but also per case, as some-times the forensic expert can deduce from the case file that procedures were not adhered to. As it could also be that samples were accidentally swapped and that therefore DNA of the suspect will “end up in our sample”, we will also account for this possibility at this point. As contamination can also occur after recovery (i.e. during DNA analysis, see Section 3.3.1) it is still possible to obtain a profile when recovery is in No.

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3.3 DNA analysis

After recovery, DNA analysis will be performed to obtain a DNA profile from the sample. During DNA analysis the available DNA will be ampli-fied, after which it will be typed. For certain specified locations on a DNA strand (called loci), the number of repetitions of a certain base sequence (called alleles) will be determined. The number of repetitions differs from person to person. The end product of DNA analysis will be a DNA profile, in which for each pre-determined loci the alleles are mapped out against intensity. Here, intensity depends on the concentration with which an allele was present in the sample. For a complete overview of the DNA analysis process in forensic science, see Rudin and Inman (2001).

After a profile has been obtained, the interpretation process will start. First, the forensic expert will determine whether the profile is suitable for interpre-tation. When not enough DNA characteristics are present, or when there is too much noise present in the profile, the evidential value of the profile will be minimal and the profile will be discarded. An unsuitable profile could be obtained due to faulty equipment, due to mistakes made by the ana-lyst, or because an insufficient amount of DNA was present in the sample. Some DNA techniques are more efficient than others, thus whether a certain amount of DNA will lead to a profile will also depend on, for example, the extraction technique that was used, the types of PCR and CE that were used, and how many different loci were considered in the profile (see Rudin and Inman (2001)).

If the DNA profile is suitable for interpretation, the forensic expert will compare the suspect’s reference profile to the profile obtained from the sam-ple. The forensic expert will generally exclude the suspect when too few of his alleles are visible in the profile to (realistically) consider him as a con-tributor (although interpretation according to the likelihood ratio approach is still possible, see the bottom of p.21). The forensic expert will not be able to exclude the suspect if (almost) all of his alleles are visible in the profile. It is possible that some of the suspect’s alleles are not present due to stochastic effects such as dropout (see Rudin and Inman (2001)). Because of dropout, the suspect should not automatically be excluded when not all of his alleles are present.

When alleles are visible which are not present in the reference profile of the suspect, the forensic expert might conclude that unknown(s) are present in

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the profile. However, it could also be that only the suspect was present in the sample and that some extra peaks are visible due to stochastic effects such as drop-in (see Rudin and Inman (2001)). However, at a certain point the probability of seeing a number of non-matching alleles if the suspect was the only source of the material becomes small enough to make a deduction that unknown(s) were also present.

It is possible to see the suspect’s alleles in a DNA profile obtained from the sample although he did not contribute to the sample, as an unknown person with the same alleles could have donated instead. Similarly, it could also be that multiple unknowns in a mixture can together form the DNA profile of the suspect. When a forensic expert is presented with a mixed DNA profile from which he cannot exclude the suspect, he will address the following propositions:

Hp : Unknowns U1, ..., Un and suspect X are the source of the DNA.

Hd : Unknowns U1, ..., Un+1 are the source of the DNA.

For a single source profile (i.e. a profile only containing alleles of one source), the following propositions are addressed:

Hp : The suspect is the source of the DNA.

Hd : An unknown person is the source of the DNA.

Both pairs of propositions are sub-source level propositions, which are lower in the hierarchy than source level propositions (see Evett. et al (2002)). In sub-source level propositions, we do not speak of a trace, but of DNA. As a trace is defined as cellular material that is present at the sampling location, and because DNA can also end up in the sample due to contamination, it could be that we obtain a DNA match with the suspect while he was not the donor of the trace. Therefore, we simply want to know whether he is the source of the DNA in the sample.

If we denote the obtained profile by E, then the forensic expert would have to determine P (E | Hp) and P (E | Hd), i.e. the probabilities of seeing the

profile if the suspect was a contributor and if he was not a contributor. For single source profiles, P (E | Hp) is equal to one if we assume no errors in

analysis and interpretation occurred. Furthermore, P (E | Hd) is equal to

the probability that someone else has exactly the same profile as the sus-pect’s (also called the random match probability). This probability can be

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calculated based on the frequencies with which alleles appear in the popu-lation.

For profiles in which unknowns could be present, these probabilities are usually calculated by using one of the many software tools available for mix-ture calculations (e.g. DNAmixmix-tures or TrueAllele). These tools can be used to perform calculations automatically instead of manually, and they can take more information from profiles into account (such as peak height information). The different software tools are all based upon different mod-els. Therefore, when a different program is used a different number for the likelihood ratio may be obtained.

At the NFI the software package LRmixstudio was recently developed, which can also be used to calculate likelihood ratios for mixtures. There has as of yet not been published on this software. In LRmixstudio, the forensic expert can enter the crime profile and the reference profile of the suspect, enter the number of unknowns under consideration in the propositions, en-ter probability estimates for drop-in and drop-out for the suspect and for unknown(s) separately, and obtain a likelihood ratio. Probabilities of drop-out and drop-in are estimated manually by the forensic expert based on the amount of DNA that was present in the sample. He can determine this from DNA quantification and peak height information.

When multiple pairs of source level propositions are possible (i.e. the exam-iner is uncertain about the number of unknowns) the LR can be calculated for every pair of propositions separately. Also, even when only some of the alleles of the suspect are present in the profile an LR can be calculated, although the expert would normally exclude the suspect. In this case, many alleles would have to miss from the profile because of dropout. However, as the probability of dropout is generally very small, the LR will be extremely small (and the evidence will thus be extremely in favour of Hd). It would

thus be extremely more likely to see this profile if only unknowns were con-tributors than if the suspect also was a contributor.

In the network (see Figure 4), we will move down from composition of the sample to dna profile. This node can be in the following states: Suspect

Unknown(s)

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Figure 4: Subnetwork: DNA analysis.

No useable profile

dna profile is also dependent on dna analysis successful?, which can be in states Yes and No and is not meant to be instantiated. When dna analysis successful? is in state No then dna profile will be in No use-able profile. Otherwise, dna profile will be in the same state as composi-tion of the sample (see also Appendix B, Table 16). A prior probability for dna analysis successful? has to be chosen by the forensic expert in each case, based on the specific analysis equipment that was used and the error rates of DNA analysts. The forensic expert can, for example, set this probability to 0.99 if he believes that the efficiency of the DNA analysts and the equipment is high (see Appendix B, Table 17). When determining this probability in a specific case, the amount of DNA should not be taken into consideration, as otherwise this will cause problems elsewhere in the network (see Section 7.3).

In software programs such as AgenaRisk and HUGIN, the LR at source level can be entered in dna profile by using specific software features (“Soft evidence” and “Enter likelihood” for AgenaRisk and HUGIN respectively). Due to the probabilities that were entered in the transfer, persistence, re-covery and contamination nodes, dna profile will already have a prior probability distribution. In the case of a single source profile, the numera-tor of the LR at source level can be used to turn the prior of Suspect into a posterior, and the denominator can be used to turn the prior of Unknown(s) into a posterior. The other states will then have posterior probability zero. In the case of mixtures, this can be done for Suspect and unknown(s) and Unknown(s) respectively.

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When the profile was not suitable for interpretation, the LR at source level will be equal to one, regardless the set of source level propositions that was chosen. The LR at activity level will then also be equal to one: the defence might argue that they would have expected the suspect’s DNA to be present if he taped the victim, but the same can be said when an unknown person taped the victim. Extensions of the network can be made in which the DNA sheddability of the perpetrator (see Rudin and Inman (2001)) can be taken into consideration. It might be that the suspect is a better shedder than an average person. Absence of his material may then favor him.

3.3.1 Contamination during DNA analysis

We can account for contamination during DNA analysis in a similar way as we did with contamination during recovery (see Section 3.2.1 and Figure 4). Here, we define contamination during DNA analysis as the transfer of cellular material of a person to the sample in a sufficient enough amount to see his complete DNA profile back in the crime profile. It is thus different from drop-in, as then we would only expect to see a single allele of that person back in the profile.

The probability of contamination is very small in most cases. Careful proce-dures and protocols are set out to reduce this probability to a minimum. For example, analysis materials (such as cups and syringes) are used only once, and the rooms and equipment are cleaned after every analysis. Reference samples of the suspect are analysed in a different room than the room where crime samples are analysed. Furthermore, a reference profile is taken from everyone who has access to the DNA analysis room. When contamination then does occur these people can be excluded from the profile later.

Contamination can still occur when protocols are not adhered to. How-ever, in most cases the probability of contamination will be so low that it will not have an effect on the likelihood ratio at activity level. For this rea-son, we set this probability to one in 100 000, though this can be changed for different forensic laboratories. This probability can also be increased when contamination seems more likely in a specific case. This can be deduced from log files, as every anomaly in the procedure is registered by forensic analysts. Though it is not strictly contamination, we will again see the swapping of samples as contamination. For the corresponding conditional probability table, see Appendix B Table 18.

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3.4 The position of the sampling location on the original roll When a suitable sampling location has been chosen, forensic experts will not only perform DNA analysis on the sample obtained from this location, but they will also try to determine the position of the sampling location on the original roll. After determining the circumference of the roll and the order in which the tape pieces came from the roll, it can be determined whether the sampling location originally would have been on the outside layer of the roll or at a deeper layer.

When someone previously only used the roll for innocent reasons, one would expect that DNA is mostly left behind on the outside of the roll (i.e. the backing of the outer layer of the roll). For example, the suspect can state that his DNA could indeed be present on the tape, but that it was originally left behind when he used the tape in household chores (and that someone else used his roll to tape the victim). If a DNA profile matching the suspect is then obtained from a sampling location which would have originally been a couple of layers deep into the roll, then it would be unlikely that this DNA would have ended up there as stated by him. It would be more likely that it ended up there when he taped the victim.

3.4.1 Using physical end matching to determine the order in which the tape pieces came from the roll

To be able to determine the position of the sampling location on the origi-nal roll, forensic experts will first have to determine the order in which the pieces of tape came from the roll. This is done by a process called physical end matching (see Smith (2007), McCabe et al. (2013)). First, the examiner will determine whether it is likely that the different pieces of tape came from the same roll or not. To this end, the colour and thickness of both adhesive layer and backing layer are compared for the different pieces of tape. As the backing layer is often laminated, the several layers of which this back-ing consists can also be compared for the different pieces. In some types of adhesive tapes (for example duct tape) there is a reinforcement fabric layer made of yarn in between the adhesive layer and backing. The construction of the fabric (knitted or woven), the number of yarns in the direction of the length of the tape (called warp yarns), as well as the thickness, colour and structure of the yarns themselves can be compared for the different tape pieces.

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Figure 5a: Macroscopic comparison of tape ends.

Figure 5b: Comparison of fabric mats.

When enough similarities exist the examiner will conclude that the different pieces could have come from the same roll. To further confirm this, and to determine in which order the pieces would have come from the roll, the tape ends of the different pieces are compared morphologically to each other. First, the tape pieces are compared macroscopically to determine whether the tape ends could fit complementary (see Figure 5a). Characteristics that can be looked at are the way the tape is separated and whether production lines or creases continue from one piece to another. The general structure of the backing and shifts in colour can also be used. Furthermore, during the production process specific types of striations and markings can be left on the backing. It can be determined whether these production characteristics continue from one piece to another.

When a potential order has been determined, the tape ends of a poten-tial match are further examined under an electron microscope. Here, it can be determined whether micro-striations continue from one piece to another, and whether the positions of the warp yarns are the same for both pieces (by separating the fabric from the tape, see Figure 5b). During the process by which duct tape is torn, the loops of the yarns at the different tape ends will break. Loops on one piece of tape will often be broken, but be intact on the other piece (although the possibility exists that loops break on both

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Figure 6: Order determination as performed by physical end matchers. The highlighted area is the position of the sampling location.

sides). For different pieces these loops can thus also be compared (see also Section 7.2).

After comparison, the examiner will give a conclusion on his findings. Exam-iners were until recently able to give categorical statements of the form “In my firm opinion the tape pieces originally formed a whole in this specific or-der”. The NFI has recently made it common practice to report results from every discipline probabilistically to the trier of fact. Therefore, instead of a categorical conclusion now the probability term “extremely more probable” is reported instead: ”It is extremely more probable to see these character-istics when the tape pieces originally formed a whole in this specific order than when they formed a whole in a different order or did not connect.” This corresponds to a likelihood ratio of over 1 000 000 (see Table 1 in Section 2.1). In the network, we will neglect the very small probability of a false negative/false positive. In Section 7.2, we will discuss issues with this gen-eralisation further.

We will assume that all the found tape pieces can be reassembled in one group and not multiple groups. In Section 3.4.4, we will propose a solution to deal with multiple groups of tape pieces.

3.4.2 Determining the position of the sampling location on the original roll

After an order has been determined, physical end matchers will try to deter-mine the position of the roll of tape from which the pieces came respective to this order. When a roll of tape is available (if it was for example found at the suspect’s house or at the crime scene), physical end matchers can try to match the tape end of that roll to one of the ends of the determined order. If this succeeds they can proceed with a known roll position. It might, how-ever, be that the roll cannot be physically matched to the pieces because

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the tape ends are too distorted or because there were originally pieces in between the found pieces and the roll end which are now missing. The roll position can, however, be determined even when the roll does not connect to the order or when no roll is available. For example, the tape piece which was last applied to the victim also likely came from the roll last. This is especially true when tape has been coiled around, for example, the victim’s wrists. Here, one also has to take into account the possibility that the per-petrator could have coiled the tape around another item before coming to the crime scene, which would reverse the roll direction. Perpetrators would perform such actions to not bring the entire roll to the crime scene, but only a part of it.

When the tape has warp yarns with knitted loops it is possible to deter-mine the position of the roll based on the direction and the position of the loops respective to the fill yarns (yarns in the direction of the width of the tape). The position/direction of the loops is almost always the same within a roll (assuming normal production conditions). However, to our knowledge no publications have been made on the accuracy of this method.

When the most probable roll position has been determined, physical end matchers will want to determine the distance from the sampling location to the roll end. For this, they will assume that the found pieces originally did connect to the roll, even when there could have originally been missing pieces in between the order and the roll. These possible missing pieces do not influence the distance from the sampling location to the roll end, thus this assumption will not influence the final conclusion of the forensic ex-perts regarding whether a trace would have ended up there as background or during the crime. There could also be missing pieces on the side on which the roll would not have been, and this would increase the distance from the sampling location to the roll end. However, if there is no indication that pieces are missing we will ignore this fact, which will generally be in favour of the suspect.

As can be seen in Figure 7, the distance from the sampling location to the roll end is determined by reassembling the tape pieces in the determined order and by measuring the distance from one end of the order to the sam-pling area. When the roll was positioned on the left, we will measure the distance from the utmost right part of the sampling area to the right of the determined order; when the roll was positioned on the right, we will measure the distance from the utmost left end of the sampling area to the left of the

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Figure 7: The distance we are interested in is the distance from the sampling location (the highlighted area) to the roll end. These distances are represented by the black arrows.

determined order. We will pick the outer parts of the sampling area to be in favour of the suspect, as this way the distance from the sampling location to the roll end will be lower. During the measuring process, careful considera-tion has to be given as to how much the pieces may have been stretched and whether there is overlap between the pieces. Depending on whether the roll was positioned on the left end or on the right end of the determined order we will obtain different distances from the sampling location to the roll end. Different conclusions may therefore also be drawn.

In the network (see Figure 8) the total length of the pieces and the dis-tance from the sampling location to the left end of the determined order can be inserted in the continuous nodes total length of the pieces and distance from sampling location to left end. Here, what is left and what is right is arbitrary: what only matters is that one is consistent with using the terms left and right for both the distance from the sampling location to the left end and the position of the roll. When a physical match was found between one of the tape ends of the determined order and the roll end, roll position can be set to Left or Right, depending on where the roll connects to the pieces. When the roll does not match to one of the ends or when no roll is available, the probability table of roll position can be changed depending on how certain the expert is that the roll was on one side or the other (see Appendix B, Table 19). This is done subjectively,

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Figure 8: Subnetwork: Distance from sampling location to roll end.

based on the factors as described above (such as the position/direction of the loops).

With the distances and the roll position entered, we can use programs like AgenaRisk or HUGIN to automatically determine the distance from the sampling location to the roll end. When the roll position is not certain two distances will be calculated, each with their own probability. When roll position is in Left, then distance from sampling location to left end will be equal to total length of the pieces minus distance from sampling location to roll end. When roll position is in Right, then distance from sampling location to left end will be equal to dis-tance from sampling location to roll end. Thus, disdis-tance from sampling location to roll end can easily be determined from the states of the other nodes.

For now, a single LR will be obtained from the network, depending on the priors we enter in the roll position node. However, another possibility would be to calculate the LR for when the roll would be located on the left end and for when it would be located on the right end. If we are then, for example, 99% certain that the roll was located on the left end, we can state that in 99% of the cases we will obtain an LR of, for example, 1000, but in 1% of the cases we will obtain an LR equal to 50. In this way, the variability of the LR can be made more transparent to the trier of fact.

To determine from the distance from the sampling location to the roll end whether the sampling location would have been present on the outside of the original roll (i.e. the backing of the outside layer of the roll) or at a deeper layer of the roll, we will need to know the circumference of the original roll.

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This is calculated by multiplying the diameter of the roll as it was before the activity by π. The diameter of the original tape roll can be deduced from the diameter of the found roll by adding to this diameter the number of layers used to tie up the victim times the thickness of each layer. Here, we assume that the found tape pieces can be physically matched to the roll. When no roll is available, the largest possible diameter for tape rolls (which is 16 cm) can be used. This is to give the suspect the benefit of the doubt, as in this case the distance from the sampling location to the roll end will need to be larger for this sampling location to end up at a deeper layer of the roll. However, this might be too conservative in most cases. When a tape roll was not found at the crime scene it is still possible to deduce the most likely diameter of the roll by visually and chemically comparing the found pieces to rolls of known types and brands (see also Section 3.4.4). Certain types and brands of tape are known to have larger diameters than others. When multiple diameters are possible an average can be taken, or the LR at activity level can be calculated and reported for each diameter separately.

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3.4.3 Deducing from the position of the sampling location on the original roll whether DNA present at this location ended up there as background and/or by the perpetrator when he was taping the victim

In Sections 3.1.1 and 3.1.2, we have stated that the forensic expert should estimate the probabilities of transfer and persistence of DNA without tak-ing into consideration the position of the sampltak-ing location on the original roll. With the position of the sampling location now known, we can thus “update” the probabilities of transfer and persistence.

In the network (see Figure 9) we move down from summary to manner of deposition, which will state how DNA that is present at the sampling location was originally deposited. It can be in the following states:

Background

By the perpetrator when he was taping the victim

Background and by the perpetrator when he was taping the victim No DNA present

The state of this node is determined by the state of summary (see Ap-pendix B, Table 20).

manner of deposition is in turn connected to distance from sam-pling location to roll end. For the conditional probability table of distance from sampling location to roll end, we need to know the most likely distances from the sampling location to the roll end given the different states of manner of deposition. For this, we need to know where on the original roll we would be able to find DNA if we know that it was deposited as background, by the perpetrator when he was taping the victim, or both. When no DNA is present we would have no preference for a specific position of the sampling location (we will discuss this further on pp. 38-39).

When determining where we would be able to find DNA on the original roll, we would also have to take into consideration retransfer of DNA from one location on the tape pieces to another. As mentioned throughout this chapter, not much is known about retransfer behaviour of DNA, and exper-iments will need to be set up to gather data on this (see Section 7.1). It seems logical to assume that retransfer from superficial locations to deeper

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Figure 9: Subnetwork: Manner of deposition.

layers will happen just as easily as vice versa. If this is the case, we could assume that the DNA present at a certain sampling location was also origi-nally deposited there. However, as we do not know whether this assumption holds, we will ignore the possibility of retransfer in this section.

We will now present a number of different conditional probability distri-butions for distance from sampling location to roll end. It has to be stressed that no actual data is available on transfer behaviour; we do not know where DNA can precisely end up on the roll (see also Sec-tion 7.1). The proposed probability distribuSec-tions are thus for illustraSec-tion purposes only. However, it does seem logical to assume that the distribu-tions which will be based on data will be of a similar shape as presented here. Probability distribution regarding the position of the DNA con-taining sampling location if DNA came upon the roll when the perpetrator was taping the victim

Firstly, we will present a probability distribution regarding the position of DNA on the original roll when the DNA was transferred by the perpetrator when he was taping the victim. Here, it seems logical to assume that DNA will be distributed uniformly to the roll by the perpetrator (see the straight

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Figure 10: Possible probability distributions regarding the position of DNA on the backing of the tape for varying diameters. The black lines represent distributions for background DNA and the straight (red) line represents the distribution of DNA transferred by the perpetrator when he was taping the victim. The solid black line represents the distribution of background DNA for a diameter of 16 cm and the dashed black line represents the distribution of background DNA for a diameter of 10 cm. For both background distributions, 95% of the density lies underneath the uniform part and 5% under the log-normal part.

(red) line in Figure 10). Though we expect that DNA will be transferred more often to tape ends and bite marks, we have already taken this into consideration in Section 3.1.1 and we should not do this again here to avoid using this observation twice. As stated above, this proposed distribution is for illustration purposes only. In certain cases the forensic expert may be able to take more specific case information into account when deriving this distribution. For example, the victim might state that certain areas of the tape were excessively touched by the perpetrator. In general, however, this will be difficult to do.

Examples of probability distributions regarding the position of the DNA containing sampling location when the DNA came upon the roll as background

The probability distributions for the location of background DNA on the original roll which we will present here will mainly depend on how this roll

The Interpretation of Traces Found on Adhesive Tapes