A Litigators Guide to DNA: From the Laboratory to the Courtroom
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Competing interests: Dr. Mark Perlin is a shareholder, officer and employee of Cybergenetics in Pittsburgh, PA, a company that develops genetic technology for computer interpretation of DNA evidence. Alex Sinelnikov is an employee of Genetica in Cincinnati, OH, a company that conducts genetic testing. Sinelnikov was an employee of Cybergenetics at time he worked on this study. DNA identification is a powerful forensic tool for solving and preventing crime .
However, DNA evidence is collected from the field under real world conditions, and may produce less pristine data than a reference specimen obtained from an individual in a controlled setting. DNA mixtures can be highly probative evidence in a sexual assault crime e. Mixtures of culprit and victim in other violent crimes e. Property crime DNA evidence  is often mixed, low template, or both. A low amount of DNA template in any type of crime produces less amplified signal, creating ambiguous data whose forensic interpretation may yield less identification information .
These DNA challenges have a major impact on crime laboratory practice.
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Difficult samples may consume inordinate examiner time and produce suboptimal information, generating DNA backlogs and inconclusive results . Yet such challenging evidence may be extremely important in protecting the public from dangerous criminals. One laboratory estimated that timely DNA examination of all property crimes and sexual assaults would prevent , stranger rapes in the United States .
This is partly because burglary and rape are both crimes of opportunity perpetrated by similarly specialized career criminals  , so incarcerating burglars can help prevent rapes.
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DNA data are generated through a linear amplification and readout process in which quantitative allele events are combined arithmetically. Such linearly generated DNA data can be mathematically described through a quantitative linear model  , . Some practitioners do analyze mixtures using quantitative peak information .
However, most forensic DNA interpretation currently uses instead a qualitative Boolean logic of all-or-none allele events . Qualitative methods begin by applying a peak height threshold to the quantitative DNA signal to retain or discard data peaks, removing peak height information.
The current controversy questions the choice of numerical threshold value ranging from 50 to units , and how many thresholds to apply one  , two  or many . Practitioners debate whether mixture interpretation should account for known contributors  ,  , or instead ignore victim genotypes  , . Some scientists propose how to interpret LT-DNA  , while others decry the practice altogether . This ongoing debate raises some important questions. What are the true limits of DNA interpretation for mixtures and low template samples? What available interpretation methods can extract the most DNA information for identifying criminals?
How do quantitative DNA mixture interpretation approaches compare with current qualitative practice?
A Litigator's Guide to DNA by Ron C. Michaelis, Robert G. Flanders, and Paula Wulff - Read Online
Understanding these issues can help society allocate effective crime fighting DNA resources for increasing public safety. In this paper, we examine the information extracted by quantitative and qualitative DNA interpretation methods.
We apply both methods to the same mixture data set of varying contributor weights and DNA quantities. We identify an information gap between the two approaches: qualitative methods are limited to culprit DNA quantities above pg, whereas quantitative methods can extend meaningful interpretation down to 10 pg.
We show how analyzing the information gap was helpful in presenting DNA evidence in court. The overall aim of the study was to compare the relative efficacy of newer quantitative computer-based methods of DNA mixture interpretation to current qualitative manual methods. We did this by measuring the sensitivity of each method, exploiting a new observation that a linear relationship exists between the logarithm of DNA quantity and DNA match information. We observed that quantitative mixture interpretation extends the current detection limits of qualitative methods by an order of magnitude, thereby achieving the aim of the study.
We examine alternative approaches to DNA mixture interpretation. We first present a quantitative linear model for understanding the generation of mixed and low template STR data. We explain how the probability model accounts for stochastic effects. We then show how computer implementation of this quantitative model can infer genotypes for the contributors to the data. We also describe the current qualitative mixture interpretation methods used in crime laboratories.
We use an information measure based on genotype match rarity that can be used to compare these quantitative and qualitative inference methods. We also show how standard DNA match statistics can be derived from this information measure. For objectivity  , we always first infer a genotype committing to an answer at all loci , and only afterwards in a second step match it against another genotype .
We also describe the data design, software and parameters used in this study. In short tandem repeat STR genotyping, alleles correspond to the length of an amplified polymerase chain reaction PCR product, which is assayed by size separation on a DNA sequencer  , . A nanogram of DNA from a single individual produces one or two tall allele peaks, along with smaller artifact peaks.
A DNA mixture, though, has multiple contributors and may produce a more complex data pattern  , . Lower DNA amounts reduce the observed peak heights and increase stochastic effects. In STR analysis, both PCR amplification and sequencer detection are fundamentally linear processes, so a mixture of genotypes produces a signal that is approximately the sum of the separate genotype signals . We can model the quantitative data at STR locus of loci using several variables. Data vector forms a pattern that maps DNA product lengths into their observed quantitative peak heights or areas.
With contributors to the data, we represent the contributor genotype parameter at locus as a vector , where the DNA length entries contain allele counts that sum to 1 .
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A heterozygote genotype vector contains two 0. The mixture weight parameter is represented as a vector whose components sum to 1 i. The total DNA quantity at locus is given by the mass parameter. With these three variables, a quantitative linear model of data pattern at locus has an expected vector value given by the weighted genotype sum in equation 1. A useful hierarchical refinement models mixture weight individually at every locus, with each weight drawn from a common DNA template mixture distribution . There is random variation in the observed peak heights resulting from PCR amplification and sequencer detection.
PCR is a branching process  where the random element comes from DNA replication efficiency, modeled by a copy or not Bernoulli event for each DNA molecule at every cycle . Computer simulations  in this Bernoulli model show that the amplification variance scales with the peak height y , an estimate of DNA quantity. Empirical studies demonstrate that PCR follows a stochastic Poisson count distribution, where the product variance is proportional to DNA quantity . As with other event count models, it is useful to add a dispersion factor to account for model deviation  , so we model the amplification variance of a peak as.
Sequencer detection variation is independent of the DNA quantity, and can be modeled separately by a constant variance parameter. We also note that the data peaks should be independent of one another. With these considerations in mind, we write the data covariance matrix as in equation 2 where is the amplification dispersion, is the detection variation, and is a diagonal matrix of peak heights. We can then linearly model the data vector using a truncated multivariate normal distribution of the mean vector and covariance matrix  as in equation 3.
We show an example data signal Figure 1a from the Penta D locus of sample C3, described below in the Data section.
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There are three alleles in the overlapping allele pairs of two contributor genotypes and. The weighted sum of the genotype vectors forms an ascending peak pattern Figure 1b. The total allelic peak mass is 1, relative fluorescent units rfu. Visually, we see a good fit between the quantitative peak height data pattern and the quantitative linear estimate of equation 1.
5.1. DNA as Applied to Criminal Law
Suppose that is a questioned evidence sample. To make comparisons with other genotypes, we want to infer a contributor genotype Q for sample. We are particularly interested in situations where there is uncertainty in Q.