The German Stain Commission: recommendations for the interpretation of mixed stains

Abstract

In the course of forensic DNA analysis, the interpretation of DNA profiles of mixed stains, i.e. cell material from more than a single donor, has become increasingly more important. The German Stain Commission, a joint commission of Institutes of Forensic Science and Legal Medicine, has therefore developed guidelines aiming to harmonize the evaluation of mixed stains in German criminal cases.

Appendix

Examples of the calculations of P _I and P _E

The probability of inclusion P _I is calculated from the sum of all genotypes of possible stain contributors. In a stain case, where a, b, and c denote the alleles of a DNA system detected in the mixture, the sum of all relevant genotypes can be calculated as follows (assuming that allele frequency data conform to Hardy–Weinberg equilibrium):

$$P_{\text{I}} = a^2 + b^2 + c^2 + 2ab + 2bc + 2ac$$

This term can be simplified using the formula for the binominal distribution:

$$a^2 + b^2 + c^2 + 2ab + 2bc + 2ac = (a + b + c)^2 $$

Assuming a frequency of 0.1 for alleles a, b, and c, the following result is obtained:

$$P_{\text{I}} = 0.3^2 = 0.09$$

Thus, it is expected that 9% of a group of randomly selected persons will not be excluded as stain contributors. This is equivalent to one out of 11 randomly selected persons (=RMNE). The probability of exclusion is calculated from the difference

$$P_{\text{E}} = 1 - P_{\text{I}} = 1 - 0.09 = 0.91$$

Thus, it is expected that 91% of a group of randomly selected persons will be excluded as stain contributors. For several DNA systems, S ₁, S ₂,…, S _n , which are genetically unlinked (i.e., in linkage equilibrium), the general expression of P _E(S ₁, S ₂,…, S _n ) can be derived from the product of the individual inclusion probabilities P(S _j ) as follows:

$$P_{\text{E}} (S_1 ,S_2 , \ldots ,S_n ) = 1 - \left[ {P_{\text{I}} \left( {S_1 } \right) \cdot P_{\text{I}} \left( {S_2 } \right) \cdot \ldots \cdot P_{\text{I}} \left( {S_n } \right)} \right]$$

Examples for the calculation of the LR

Simple scenario

Consider a case with a mixed stain M with three alleles, a, b, and c, composed from a victim and a perpetrator. The victim V has the genotype AB, and the suspect S has the genotype BC. The hypotheses can be given as follows:

• H _p: The stain M originates from the victim V and the suspect S.

• H _d: The stain M originates from the victim V and from an unknown person unrelated to the suspect.

Let us first derive the numerator of the LR. The prosecution claims that the stain can be explained by a combination of the genotypes of the victim and the suspect, as there are no unaccounted alleles. Hence, the numerator results as

$$L(M|H_{\text{p}} ) = L(M|G_{\text{v}} ,G_{\text{s}} ) = 1$$

The defense, however, claims that the suspect has not contributed to the stain. The genotype of the suspect is not relevant since the presence of allele c in the mixture must be explained by the contribution of an unknown person. As allele c may have been contributed either by a person homozygous for allele c or from a person heterozygous for c in combination with allele a or b, the denominator is as follows:

$$L(M|H_{\text{d}} ) = L(M|G_{\text{v}} ,G_{\text{u}} ) = 2ac + 2bc + c^2 $$

And, thus, the entire expression is given as

$${\text{LR}} = \frac{1}{{2ac + 2ab + c^2 }}$$

Assuming a frequency of 0.1 for alleles a, b, and c, the following result is obtained:

$${\text{LR}} = \frac{1}{{0.02 + 0.02 + 0.01}} = \frac{1}{{0.05}} = 20$$

The result can be described by the following statement: It is 20 times more likely to observe the DNA profile if the mixed stain originated from the victim and the suspect than if it originated from the victim and an unknown person (who is unrelated to the suspect³).

Complex scenario

Let us consider a case with a mixed stain M with four alleles a, b, c, and d found on the victim’s clothes. The victim’s genotype is EF and, hence, the corresponding alleles e and f are not observed in the stain. Suspect S has genotype AB, but there is no known second person who may have contributed the alleles c and d. The hypotheses can be given as follows:

• H _p: Stain M originates from suspect S and an unknown person U.

• H _d: Stain M originates from two unknown persons U1 and U2.

The prosecution claims that the stain can be explained by a combination of the suspect’s genotype and a second person with the genotype CD. Hence, the numerator results as

$$L(M|H_{\text{p}} ) = L(M|G_{\text{s}} ,G_{\text{u}} ) = 2cd$$

The defense claims that no genotypes of the contributors are known. Thus, the sum of all possible genotype combinations from two persons U1 and U2 must be considered for the denominator:

Genotypes		Combined frequency
U1	U2	U2
AB	CD	2ab × 2cd = 4abcd
AC	BD	4abcd
AD	BC	4abcd
BC	AD	4abcd
BD	AC	4abcd
CD	AB	4abcd
$L\left( {M|H_{\text{d}} } \right) = L\left( {M|G_{U1} ,G_{U2} } \right) =$		24abcd

After reducing the term and by assuming a frequency of 0.1 for alleles a, b, c, and d, the following result is obtained:

$${\text{LR}} = \frac{{2cd}}{{24abcd}} = \frac{1}{{12ab}} = \frac{1}{{0.12}} = 8.3$$

Thus, it is eight times more likely to observe the DNA profile if the mixed stain originated from the suspect and an unknown person than if it originated from two unknown persons. If two suspects S1 and S2 with the genotypes AB and CD are considered for the same mixed stain scenario, the hypotheses and, hence, the LR change, as no unknown person remains for H _p:

• H _p: Stain M originates from the suspects S1 and S2.

• H _d: Stain M originates from two unknown persons U1 and U2.

Thus, the numerator of the LR is, again, 1. The term cannot be reduced further and the resulting LR is as follows:

$${\text{LR}} = \frac{1}{{24abcd}} = \frac{1}{{0.0024}} = 416.7$$

Thus, it is 416 times more likely to observe the DNA profile if the mixed stain originated from suspects S1 and S2 than if it originated from two unknown persons.

We give the following caveat: Additional hypotheses, which are not discussed here, can be formulated. Depending on the precise scenario, such additional hypotheses may be highly relevant in a given case, such as (a) H _p: the stain originates from S1 and S2; H _d: the stain originates from B1 and U, or (b) H _p: the stain originates from S1 and S2; H _d: the stain originates from S2 and U. Depending on the genotype frequencies of S1 and S2, the resulting LRs may differ significantly.