Reply to Weir (2001), by Fung and Hu (Forensic Science Communications, January 2001)
January 2001 - Volume 3 - Number 1
Comments and Replies
Reply to Weir (2001)
Wing K. Fung
Department of Statistics and Actuarial Science
University of Hong Kong
Department of Mathematics
It was not the intention of Fung and Hu (2000a) to perform calculations for stains having multiple contributors with the use of the profile probability in NRC II formula 4.4a "because of its simplicity," and we wrote in the Introduction that "Recommendation 4.1 of the NRC II is the most popular procedure for single source samples, and many laboratories have adopted it because of its simplicity." It was an attempt to extend the usage of Recommendation 4.1, as was stated in the Abstract that "Recommendation 4.1 of the NRC II is the most commonly used approach for dealing with these departures (from Hardy–Weinberg proportions) for single-source problems. However, this recommendation has not been applied to the mixed stain problem, and it is worthwhile to extend the recommendation to such a problem." This theme was reiterated in the Conclusion and Discussion Section of Fung and Hu (2000a).
We are aware that individuals are somehow related and their alleles exhibit dependence, albeit to a very small extent. We have already written explicitly, "Simplification also occurs because there are no between-person correlations under the model implied in Recommendation 4.1, or at least these are not taken into account." Because our aim is to use Recommendation 4.1 to deal with mixed stain problems, it is sensible that the calculations be based on the genetic model underlying that Recommendation. Actually, Recommendation 4.1 uses the profile probability for evaluating the match probability that the suspect has the profile when it is known that the perpetrator has the profile. Some workers may have a strong preference for using formula 4.10 pertaining to Recommendation 4.2 to tackle the mixed stain problem and it is fine, but our method is correct and totally legitimate on the basis of Recommendation 4.1. Actually, we did perform the mixture calculations by taking dependencies into account, as indicated by Dr. Weir, which gave the same results as Curran et al. (1999) and were reported elsewhere (Fung and Hu, 2000b).
On the comment about our handling of the issue of relatives, we feel that clear indications have been given on when our equation can be applied in writing "our result in Equation 4 can only be used when the same kinship coefficient is used across the victim, the suspect and the perpetrator." There was no claim that it could be used to deal with all sorts of mixture cases involving relatives.
One last point we want to emphasize is that calculations on mixture cases proposed so far have all been based on assumptions: Weir et al. (1997) on the Hardy–Weinberg assumption, Fung and Hu (2000a) on the assumption underlying Recommendation 4.1, and Curran et al. (1999) and Fung and Hu (2000b) on the assumption of the theory of population substructure such as evolutionary equilibrium, and so forth, which forms the basis for NRC II Recommendation 4.2. The NRC II Committee gives reasons to suggest Recommendation 4.1 in preference to 4.2 for handling general situations. If Dr. Weir can show that the "population genetic theory" underlying Recommendation 4.2, which he advocates, is exact and has no "errors" in describing the real-world situation, we think the forensic community will be interested in learning his proof.
Curran, J. M., Triggs, C. M., Buckleton, J. S., and Weir, B. S. Interpreting DNA mixtures in structured populations, Journal of Forensic Sciences (1999) 44:987–995.
Fung, W. K. and Hu, Y-Q. Interpreting DNA mixtures based on the NRC-II Recommendation 4.1, Forensic Science Communications (October 2000a). Available at: http://www.fbi.gov/programs/lab/fsc/backissu/oct2000/fung.htm
Fung, W. K. and Hu, Y-Q. Interpreting forensic DNA mixtures: Allowing for uncertainty in population substructure and dependence, Journal of Royal Statistical Society, Series A, (2000b) 163:241–254.
National Research Council (NRC II). The Evaluation of Forensic DNA Evidence. National Academy Press, Washington, DC, 1996.
Weir, B. S. DNA match and profile probabilities: Comment on Budowle et al. (2000) and Fung and Hu (2000), Forensic Science Communications (January 2001). Available at: http://www.fbi.gov/programs/lab/fsc/current/weir.htm
Weir, B. S., Triggs, C. M., Starling, L., Stowell, L. I., Walsh, K. A. J., and Buckleton, J. Interpreting DNA mixtures, Journal of Forensic Sciences (1997) 42:213–222.