Evaluating mixed stains with contributors of different ethnic groups under the NRC-II Recommendation 4.1

In countries with multiple racial or ethnic groups, it is not uncommon that contributors to a mixed stain or a DNA mixture belong to different ethnic origins. This paper derives a general formula for evaluating the likelihood ratio in such situations based on the commonly adopted Recommendation 4.1 of the U.S. Second National Research Council Report on the evaluation of DNA evidence. The restrictive Hardy-Weinberg assumption is not taken in this paper. Our formula generalizes the results of Fung and Hu for a single ethnic group, and of Weir et al. under the Hardy-Weinberg law for a single, and Fukshansky and Bär for multiple ethnic groups. The effect of different ethnic groups of contributors to the interpretation of mixtures is illustrated through the analysis of the Simpson case.