MORE COMPLEX PROBABILITIES

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MORE COMPLEX PROBABILITIES

Mixtures ......................................................................................................... [80A.2100]

Identifying the presence of a mixture ........................................................... [80A.2120]

Characteristics of single-source DNA profiles .............................................. [80A.2140]

Procedure for the interpretation of mixtures ................................................. [80A.2160]

Simple mixed stain example ......................................................................... [80A.2180]

Random man not excluded........................................................................... [80A.2200]

Application of subpopulation theory to mixtures ........................................... [80A.2220]

Complex mixtures ......................................................................................... [80A.2240]

Implementing guidelines for mixture interpretation ....................................... [80A.2260]

Resolving mixtures........................................................................................ [80A.2280]

Unresolvable mixtures................................................................................... [80A.2300]

Low-level profiles with the possibility of drop-out ......................................... [80A.2320]

[80A.2100] Mixtures

Stains containing DNA from more than one person are termed mixtures, and their profiles can be analysed in a variety of ways, depending on the assumptions that one is prepared to make.

[80A.2120] Identifying the presence of a mixture

In essence, a mixed DNA profile is one which does not fit the known characteristics of a DNA profile from one person (a single-source profile). Therefore it is helpful to summarise the features of single-source DNA profiles before embarking on a consideration of mixtures.

[80A.2140] Characteristics of single-source DNA profiles

A single-source profile has either one (homozygous) or two (heterozygous) alleles at each locus: see Chapter 80. DNA Profiling in Criminal Investigations. In modern STR multiplex DNA typing systems, alleles are identified by the presence of peaks in the output of automated DNA analysis instruments (commonly Applied Biosystems Genetic Analyzers) which are used to analyse the products of amplification of DNA by the Polymerase Chain Reaction (PCR). In a heterozygote, the two peaks at a locus are of approximately equal height.

There are well-recognised exceptions to these general principles. In rare cases of trisomy, one allele or chromosome is duplicated, leading to the appearance of three alleles. In other rare cases, mutation may result in the total absence of one allele (a so-called null allele) causing a heterozygous individual to appear as a homozygote. Mutations in the primer binding site may lead to unequal amplification and thus unequal peak heights in a heterozygote. The presence of such genetic abnormalities may be detected in a reference sample from a person suspected to be the source of the DNA. However, this is not always the case. Somatic mutations are mutations in (some of) the tissues of the body rather than in the germ line. These mutations are not inherited and produce differences between cells from different parts of the body (mosaicism). While the possibility of such genetic abnormalities must be borne in mind when interpreting a DNA profile, it should be noted that they are relatively rare.

Much more common are artefacts of the DNA typing process. Some artefacts can be discounted in the typing process based on location and morphology such as pull-up (bleed-through) of the signal in one dye channel or colour appearing as a peak in another channel; baseline noise and other artefacts which often produce misshapen peaks. Additional peaks in a DNA profile can also occur due to the formation of stutter products during the PCR process or through drop-in. Absence or extreme imbalance of peaks due to stochastic (random) effects are prevalent in samples containing low amounts of DNA or degraded DNA, and procedures for the statistical analysis of such profiles are discussed more fully at [80A.2320].

The existence of these artefacts adds complexity to the interpretation of DNA profiles. There are at least three approaches to this problem:

1. The binary model, where thresholds or cut-offs are used to decide whether a particular genotype is accepted or rejected (examples are limits of detection; stutter cut-offs; and stochastic, or drop-out, thresholds);
2. The semi-continuous model, where thresholds are replaced with expressions incorporating the probability of the evidence given a particular genotype (examples are drop-out and drop-in probabilities); and
3. The continuous model, where the probability of the profile as a whole is calculated, given a hypothesis (an example is the use of a computer algorithm called Monte Carlo-Markov Chain to find the best fit to the data: Perlin, Kadane and Cotton, 2009 and Taylor et al, 2013).

Kelly, Bright, Buckleton and Curran (2014) compared these approaches and highlighted their weaknesses and strengths. Binary methods have served well for a number of years; however, they are not recommended for the interpretation of samples containing non-concordances as they do not incorporate the probability of drop-out. Consequently, they can produce a non-conservative assessment of the results. In addition, binary methods cannot take into account multiple amplifications of a sample.

The use of a semi-continuous model provides an improvement in the assessment of complex and low level DNA profiles as such methods incorporate the probability of drop-out and drop-in into the likelihood ratio calculation and can handle multiple amplifications of a sample. This model however still suffers from the use of cut-offs to assign and to remove stutter peaks from the profile before interpretation. Both binary and semi-continuous methods do not make full use of the peak height information when designating genotype combinations that could give rise to the observed profile (ie, each genotype combination is given the same weight in the interpretation despite some genotypes providing a better explanation of the observed peaks than others).

The continuous model is considered to be the most complex of the three models; nevertheless, in the opinion of Kelly et al (2014), it is the premier choice as it makes best use of all the available profile information. In this model, the probability of drop-out and drop-in is incorporated into the interpretation, all peaks, including stutters, are considered in the analysis and the peak height information is used to assign a weight to each genotype combination that could give rise to the observed profile. As a result, each genotype combination is assigned a probability between 0 and 1 based on how well that combination explains the peaks in the profile (rather than a value of 0 or 1 as per the binary and semi-continuous models). A continuous method requires models to describe the stochastic behaviour of peak heights and stutter as well as computer software to perform the analysis. Possible objections include the fact that the method requires proprietary software that may not be freely available to the forensic community, and that its workings are difficult to convey to an audience without extensive training.

[80A.2160] Procedure for the interpretation of mixtures

Guidelines for the interpretation of mixtures were proposed by Clayton et al (1998), and were endorsed by the DNA Commission of the International Society for Forensic Genetics (Gill et al, 2006). The specific procedure employed depends largely on laboratory processes and interpretation methodology. Generally, the following process is applied:

1. Identification of a mixture by the presence of either more than two allelic peaks at a locus or extreme peak height imbalance, such that it cannot reasonably be explained by the phenomena described above;
2. Designation of allelic peaks;
3. Identification of the potential number of contributors;
4. Determination of the approximate proportion of the components in the mixture to help inform the best-supported combination or combinations of genotypes; and
5. Comparison with reference samples of suspected or known contributors.

Some of these steps may be performed manually or automatically by computer software depending on the method that is used to interpret the DNA profile. When computer software is used, as is the case for a continuous model, it is recommended that the analyst verify the output to ensure that it conforms to expectations based on knowledge and experience of profile behaviour. These steps are discussed in more detail at [80A.2260].

One of the most common, and simplest, scenarios is that in which the mixture can be assumed to contain DNA from only two people, one of whom can be assumed to be a person whose DNA profile is known (a "known" or "assumed" contributor). The question then simplifies to a consideration of the genotype of the second contributor, and the likelihood of those genotypes occurring in a randomly selected member of the population (an "unknown" contributor).

The following section discusses an example of a simple, two-person mixture in which some of the complex issues mentioned above can often be safely ignored.

[80A.2180] Simple mixed stain example

Consider a semen stain on a garment worn by the victim of an alleged rape. Stains containing small numbers of spermatozoa mixed with large amounts of blood or vaginal secretions often present problems in attempts to separate spermatozoa from white blood cells, vaginal epithelial cells and other somatic (non-sperm) cells. Sometimes, complete separation of the so-called "male" (sperm) and "female" (non-sperm) fractions is not achieved. The result is that the fraction that is enriched in sperm DNA also contains DNA of non-sperm (or somatic) origin. There is usually no doubt as to the...