Evaluating Mixture Solution™- rapid and non-MCMC probabilistic mixture analysis.

We compare DNA mixture analysis via DNAˑVIEW® Mixture Solution™ and the current combined probability of inclusion (CPI) method of the South African Police Service (SAPS). South Africa has a high incidence of property-related crimes and sexual offences and consequently a great deal of low-template (LT-DNA) forensic DNA mixture casework and a perpetual backlog. A range of casework and laboratory-prepared sexual assault mixtures with initial male DNA amounts varying from about 2 to 200 cells were analysed to evaluate the benefits of a continuous model program. Unfortunately CPI methods are nearly useless for LT-DNA cases because of dropout-common from a mixture contribution of fewer than 20 or 30 cells. We further argue that proposed CPI elaborations to circumvent dropout lack supporting research or even explanation. Mixture Solution models mixture data as continuous rather than binary, with a mathematically coherent ("probabilistic") model which incorporates dropout and other phenomena realistically. Much more information is thereby utilised resulting in applicability to more cases (7 or fewer contributor cells suffice), stronger evidence against a suspect who is a mixture contributor and stronger evidence to absolve a non-contributor. Mixture Solution incidentally provides information which, along with rfu data, allows estimating contributions in terms of number of cells, which is a useful perspective. The method of calculation is explained.

Extensive evaluation of DNA polymerase performance for highly degraded human DNA samples.

Highly degraded human DNA is commonly encountered in the forensic studies. Despite many efforts, the poor quality and quantity of the DNA often result in unsuccessful DNA analysis. There has been no extensive evaluation of DNA polymerase performance for the successful PCR of highly degraded DNA samples. We evaluated the most efficient DNA polymerases, based on real-time PCR and agarose gel electrophoresis analyses for a single copy gene amplification, with 200 ancient DNA (aDNA) samples of various origins. Nine commercially available DNA polymerases were tested, which included enzymes that are reportedly effective for PCR-inhibitory samples. The first screening test for the polymerases with 20 aDNA samples showed that Pico Maxx HF, FastStart Taq, and Ex Taq HS DNA polymerases were the most effective. Further tests with 180 aDNA samples showed that AmpliTaq Gold (control) amplified PCR products from 52 aDNA samples, PicoMaxx HF from 62, FastStart Taq from 64, and Ex Taq HS from 65. The use of two or more of Ex Taq HS, FastStart Taq, and PicoMaxx HF resulted in a significantly higher success rate than that of AmpliTaq Gold alone. With 37 positive samples tested in duplicate, Ex Taq HS showed the highest reproducibility (13 samples) and AmpliTaq Gold, the lowest (four samples); this difference was significant. The data also showed preferential amplification by the enzymes; Ex Taq HS exclusively produced amplification from two samples, FastStart Taq from one, and PicoMaxx HF from one. We suggest that the initial use of these three DNA polymerases will increase the probability of successfully amplifying DNA from highly degraded human DNA samples.

Understanding Y haplotype matching probability.

The Y haplotype population-genetic terrain is better explored from a fresh perspective rather than by analogy with the more familiar autosomal ideas. For haplotype matching probabilities, versus for autosomal matching probabilities, explicit attention to modelling - such as how evolution got us where we are - is much more important while consideration of population frequency is much less so. This paper explores, extends, and explains some of the concepts of "Fundamental problem of forensic mathematics - the evidential strength of a rare haplotype match". That earlier paper presented and validated a "kappa method" formula for the evidential strength when a suspect matches a previously unseen haplotype (such as a Y-haplotype) at the crime scene. Mathematical implications of the kappa method are intuitive and reasonable. Suspicions to the contrary raised in rest on elementary errors. Critical to deriving the kappa method or any sensible evidential calculation is understanding that thinking about haplotype population frequency is a red herring; the pivotal question is one of matching probability. But confusion between the two is unfortunately institutionalized in much of the forensic world. Examples make clear why (matching) probability is not (population) frequency and why uncertainty intervals on matching probabilities are merely confused thinking. Forensic matching calculations should be based on a model, on stipulated premises. The model inevitably only approximates reality, and any error in the results comes only from error in the model, the inexactness of the approximation. Sampling variation does not measure that inexactness and hence is not helpful in explaining evidence and is in fact an impediment. Alternative haplotype matching probability approaches that various authors have considered are reviewed. Some are based on no model and cannot be taken seriously. For the others, some evaluation of the models is discussed. Recent evidence supports the adequacy of the simple exchangability model on which the kappa method rests. However, to make progress toward forensic calculation of Y haplotype mixture evidence a different tack is needed. The "Laplace distribution" model of Andersen et al. [3] which estimates haplotype frequencies by identifying haplotype clusters in population data looks useful.

Fundamental problem of forensic mathematics--the evidential value of a rare haplotype.

Y-chromosomal and mitochondrial haplotyping offer special advantages for criminal (and other) identification. For different reasons, each of them is sometimes detectable in a crime stain for which autosomal typing fails. But they also present special problems, including a fundamental mathematical one: When a rare haplotype is shared between suspect and crime scene, how strong is the evidence linking the two? Assume a reference population sample is available which contains n-1 haplotypes. The most interesting situation as well as the most common one is that the crime scene haplotype was never observed in the population sample. The traditional tools of product rule and sample frequency are not useful when there are no components to multiply and the sample frequency is zero. A useful statistic is the fraction κ of the population sample that consists of "singletons" - of once-observed types. A simple argument shows that the probability for a random innocent suspect to match a previously unobserved crime scene type is (1-κ)/n - distinctly less than 1/n, likely ten times less. The robust validity of this model is confirmed by testing it against a range of population models. This paper hinges above all on one key insight: probability is not frequency. The common but erroneous "frequency" approach adopts population frequency as a surrogate for matching probability and attempts the intractable problem of guessing how many instances exist of the specific haplotype at a certain crime. Probability, by contrast, depends by definition only on the available data. Hence if different haplotypes but with the same data occur in two different crimes, although the frequencies are different (and are hopelessly elusive), the matching probabilities are the same, and are not hard to find.

A western Eurasian male is found in 2000-year-old elite Xiongnu cemetery in Northeast Mongolia.

We analyzed mitochondrial DNA (mtDNA), Y-chromosome single nucleotide polymorphisms (Y-SNP), and autosomal short tandem repeats (STR) of three skeletons found in a 2,000-year-old Xiongnu elite cemetery in Duurlig Nars of Northeast Mongolia. This study is one of the first reports of the detailed genetic analysis of ancient human remains using the three types of genetic markers. The DNA analyses revealed that one subject was an ancient male skeleton with maternal U2e1 and paternal R1a1 haplogroups. This is the first genetic evidence that a male of distinctive Indo-European lineages (R1a1) was present in the Xiongnu of Mongolia. This might indicate an Indo-European migration into Northeast Asia 2,000 years ago. Other specimens are a female with mtDNA haplogroup D4 and a male with Y-SNP haplogroup C3 and mtDNA haplogroup D4. Those haplogroups are common in Northeast Asia. There was no close kinship among them. The genetic evidence of U2e1 and R1a1 may help to clarify the migration patterns of Indo-Europeans and ancient East-West contacts of the Xiongnu Empire. Artifacts in the tombs suggested that the Xiongnu had a system of the social stratification. The West Eurasian male might show the racial tolerance of the Xiongnu Empire and some insight into the Xiongnu society.

Counterexample to a kinship conjecture of Krawczak.

A counterexample shows that a criterion proposed by Krawczak for a marker to be informative for a kinship case is not a necessary condition.

ISFG: Recommendations on biostatistics in paternity testing.

The Paternity Testing Commission (PTC) of the International Society for Forensic Genetics has taken up the task of establishing the biostatistical recommendations in accordance with the ISO 17025 standards and a previous set of ISFG recommendations specific to the genetic investigations in paternity cases. In the initial set, the PTC recommended that biostatistical evaluations of paternity are based on a likelihood ratio principle - yielding the paternity index, PI. Here, we have made five supplementary biostatistical recommendations. The first recommendation clarifies and defines basic concepts of genetic hypotheses and calculation concerns needed to produce valid PIs. The second and third recommendations address issues associated with population genetics (allele probabilities, Y-chromosome markers, mtDNA, and population substructuring) and special circumstances (deficiency/reconstruction and immigration cases), respectively. The fourth recommendation considers strategies regarding genetic evidence against paternity. The fifth recommendation covers necessary documentation, reporting details and assumptions underlying calculations. The PTC strongly suggests that these recommendations should be adopted by all laboratories involved in paternity testing as the basis for their biostatistical analysis.

Some mathematical problems in the DNA identification of victims in the 2004 tsunami and similar mass fatalities.

DNA is a major and essential identification tool for mass fatality incidents including the hundreds of thousands of victims of the 2004 Indian Ocean tsunami. Mathematical complications characteristic of this sort of mass fatality include prevalence of related victims, the many races represented among the victims, and various identification modalities in tandem with DNA. Four mathematical problems of interest are discussed in this paper. (1) Other quantifiable factors (i.e. geography) can be formally accounted for by including a likelihood ratio that can be thought of as reducing the "effective number of victims." (2) When a victim is found and tentatively identified as V, but then it comes to light that the victim has a relative W who is also missing, confidence in the identity is depressed. To account for the existence of W, increment the effective number of victims by the likelihood ratio supporting W as the identity of the victim. (3) When several apparently related victims are found, their mutual identities should be calculated simultaneously. Compared to one-at-a-time, serial identifications, this is both logical and may lead to much more confidence in the identities. (4) Although there may be many different population groups represented among the missing, it is generally sufficient to consider population statistics for only a few of them in deciding whether to declare an identification.