Academic journal article Forensic Science Communications

Evaluating Mixed DNA Profiles with the Presence of Relatives: Theory, Method, and Computer Software

Academic journal article Forensic Science Communications

Evaluating Mixed DNA Profiles with the Presence of Relatives: Theory, Method, and Computer Software

Article excerpt


The theory and method are provided for evaluating the evidential weight of DNA mixture in a subpopulation with the presence of related contributors. An efficient, user-friendly, Windows-based software for handing such mixture problems has been developed. The software is illustrated by analyzing a case with various relationships between the persons involved in the case. The effects of different population substructure, kinship relationships, and defense propositions are also demonstrated numerically.


The evaluation of DNA mixture is needed in many situations, such as the case of rape, in which the mixed crime stain may come from more than one person. The likelihood ratio is a useful measure commonly used to assess the weight of DNA evidence. A general formula for calculating the likelihood ratio in the mixture case was provided by Weir et al. (1997) and Fukshansky and Bar (1998) under the Hardy-Weinberg equilibrium. When all involved people come from the same subpopulation, Curran et al. (1999) and Fung and Hu (2000A) have derived formulas for evaluating the likelihood ratios. Fung and Hu (2000B) reported a general formula for calculating likelihood ratios for DNA mixtures based on Recommendation 4.1 of the second National Research Council Report (1996) on the evaluation of forensic DNA evidence.

In some situations, the interpretation of DNA evidence involves the relatives of the suspects and/or perpetrators. The assessment of the weight of DNA evidence when a relative of a suspect is involved in the pool of possible perpetrators has been discussed in the literature. Evett (1992) obtained a formula for the likelihood ratio in a case when the defense was "it was my brother." Brookfield (1994) evaluated the effect that the suspect and the contributor of the crime stain are relatives upon the likelihood ratio (see also Berlin et al. 1997; Fung et al. 2002; Sjerps and Kloosterman 1999). All these papers, however, studied the effect of a relative on the likelihood ratio for a single source DNA sample problem. With regard to DNA mixture problems, Fukshansky and Bar (2000) and Hu and Fung (2003) have developed formulas for evaluating the likelihood ratios when relatives are involved. In both works, Hardy-Weinberg equilibrium was assumed in the population to which all involved persons belong.

In this paper, the theory and method for interpreting DNA mixture, with the presence of relatives, are discussed when all involved people are of the same subpopulation origin and allele proportions are only available for total population. A general formula of match probability is provided for the case that the suspect is not available for typing but his or her relative is available or that there are two related unknown contributors.

A Windows-based computer software, which is easy to use, can handle various kinds of relationships between the relatives simultaneously, and requires only minimal input, making it less susceptible to transcriptional error, was developed to analyze this problem. The method and the software are illustrated with an example using various sets of hypotheses. It demonstrates that the software can handle common mixture problems involving unrelated persons.

Match Probability Formulas

Let M be the DNA mixture, which comprises distinct alleles, K be the genotype(s) of the typed person(s), and H be a proposition about who the contributors of the mixed stain were. Usually, some unknown and some typed persons were declared as the contributors of the mixture in hypothesis H. The weight of DNA evidence is usually measured by the likelihood ratio, which is a ratio of two probabilities like P (Evidence|H). Writing P (Evidence|H) = P (K|H)P(M|K, H) and using the fact that P (K|H) = P(K), the calculation of the likelihood ratio is then reduced to the evaluation of P (M|K, H) (Hu and Fung 2003). In order to find the weight of the DNA evidence, calculating the match probability P(M|K, H) should be done. …

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