Letters to the Editor References Budowle B, Giusti, AM, WayeJS, Baechtel FS, Fourney RM, Adams DE, Presley LA, et al (1991) Fixed-bin analysis for statistical evaluation of continuous distributions of allelic data from VNTR loci, for use in forensic comparisons. Am J Hum Genet 48:841-855

Lander ES (1991) Research on DNA typing catching up with courtroom application. Am J Hum Genet 48:819-823 US Congress Office of Technology Assessment (OTA) (1990) Genetic witness: forensic uses of DNA tests. Publication OTA-BA-438. US Government Printing Office, Washington DC i 1991 by The American Society of Human Genetics. All rights reserved. 0002-9297/91 /4904-0025$02.00

Am. J. Hum. Genet. 49:895-897, 1991

Statistical Interpertation of DNA Typing Data To The Editor: Both the invited editorial by Lander (1991) and similar earlier commentaries on the subject of courtroom applications of DNA typing data have led to numerous arguments that simply defy well-known human population-genetic principles. In such criticisms, the authors employ a logic that may be called "reverse logic," whose mathematical validity is highly questionable. It is true that population substructure leads to genotypic proportions that deviate from Hardy-Weinberg expectations (HWE). Population substructure also produces gametic (as well as nongametic) disequilibria. These are well-known population-genetic principles. But Lander (1989a, 1989b, 1991) and others (e.g., see Cohen 1990) fail to recognize that there are other factors, particularly relevant to the RFLP analysis of DNA typing, which may produce these end results. Therefore, from the observed deviation from HWE and from an observed linkage disequilibrium, one cannot necessarily infer population substructure. It is unfortunate that in the peer-reviewed journals the above-mentioned authors have been allowed to make this inference without validating whether other associated features of DNA typing data conform to the substructuring hypothesis. First, one might note that deviations from HWE, in

the direction of deficiency of overall proportions of heterozygotes, have been noted in the DNA typing data in binned classification of alleles (Budowle et al.

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1991). In contrast, it is demonstrated that, when we consider both the incomplete resolution of similarsized alleles and measuremental errors of allele sizing, no deviation from HWE is detected (Devlin et al. 1990). One could argue that such tests do not have sufficient statistical power for detection of deviation from HWE. To ameliorate this problem, population data from several law-enforcement agencies have been subjected to nonparametric correlation analyses to check whether alleles of different sizes aggregate in any nonrandom fashion to form DNA types of individuals. Such tests, when properly applied (considering that the paternal and materal alleles cannot be distinguished in individuals in a population data base), result in no deviation from HWE. A correlation measure, originally devised for any general continuous trait with unknown (and possibly complex-shape) distribution (Karlin 1981), has substantially more power for detection of deviation from HWE. It can also be shown that Karlin's (1981) nonparametric correlation measure applies for quasi-continuous traits such as allele sizes at VNTR loci; it is distribution free, and its expectation can be derived even if nonrandom aggregation of alleles within individauls occurs because of population substructuring. These results indicate that, even if populations such as U.S. Caucasians, U.S. blacks, or Hispanics are truly substructured, their consequence on deviations from HWE is only trivial and cannot produce effects as gross as the ones indicated in the fictitious examples given (e.g., see Cohen 1990). Furthermore, even though it is well known that in RFLP analysis by Southern blot protocol the possibility exists that certain alleles of extreme sizes may remain undetected, Lander and others pay no attention to this in explaining the observed heterozygote deficiency. There is a voluminous literature (e.g., see Skibinski et al. 1983; Gart and Namm 1984; and cited references) that deals with such issues. It can be shown that even an extent of 6%-10% overall heterozygote deficiency can be explained if the frequency of such "nondetectable" alleles is 3%-6%. Samples of quite large sizes (e.g., more than 1,5005,000 individuals/population) would be required for one to observe any single homozygote individual both of whose alleles are nondetectable. Even if this is found, there is no way to distinguish this type from those due to other vagaries of DNA typing (such as DNA degradation, insufficient DNA, etc.). Therefore, covert nondetectability of extreme-size alleles is a much simpler explanation of heterozygote deficiency of binned allele data.

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Second, if the observed deviations from HWE were truly due to substructuring, what nature of substructuring (in terms of both the number of subpopulations and their evolutionary time of divergence) can produce such an extent of deviation can be shown. Such analyses reveal that, if we were to generate a 10% proportional heterozygote deficiency at a VNTR locus that has 90% heterozygosity, we have to invoke more than 20-30 subpopulations each of which should not have exchanged any gene among them for more than 40,000 years since their divergence from a common ancestry. This is clearly contrary to the origin and demography of the U.S. populations, where even among the orthodox religious populations the gene migration has been rather substantial (at least of the order of 10% /generation during the last century; e.g., see Kennedy 1944). Lander also fails to note that Lewontin's (1972) observation-i.e., that mean genetic difference between populations is far too small compared with genetic variation within populations -has been validated with a concept of populations that is much narrower than that of racial classification (e.g., see Chakraborty and Leimer 1986; Nei 1987). Third, although Lander and others (e.g., see Cohen 1990) claim that there are substantial linkage disequilibria among VNTR alleles of unlinked loci, no specific data has been shown to this effect. Because of the presence of multiple alleles at such loci, this is particularly important, since the methods of estimation and detection of such multiallelic disequilibria are on a relatively softer ground. Applications of a recently proposed method (Hernandez and Weir 1989) in specific case studies (for courtroom applications) reveal no disequilibria. Therefore, in the absence of any solid data on the extent of disequilibria, the claim that nonrandom aggregation of alleles of unlinked loci exists in individuals should not have been published in any peer-reviewed journal. In analogy with the departure from HWE, one can easily show that, for subpopulations that diverged from their common ancestry during the past 10,000-15,000 years (which would be the extreme for U.S. Caucasians, U.S. blacks, and U.S. Hispanics) and that exchanged genes among themselves, linkage disequilibria cannot attain any significant value at all. Cohen's (1990) numerical illustration requires linkage disequilibria that can be produced only if the subpopulations represent different species. I do not think that any human genetics will support such a statistical view! Finally, if there are technical limitations to the RFLP analysis of DNA typing that generate deviation from

the square law (HWE) or multiplication rule (linkage equilibria), the question is, Can we devise any modification to guard against biased probability calculation? The answer is yes! This is so, because, first, if there are covert nondetectable alleles, the gene-count method of estimating allele frequencies already gives overestimates of allele frequencies. Second, binning provides further cushions for allele-frequency estimates, cushions that are much larger than the expected deviations-and, when binning is used in conjunction with the use of 2p for the frequency of homozygotes (single-band patterns), this cushion is even greater. All these lead to estimations of chance occurrence of specific DNA types that can be biased only in the upward direction, establishing an objectivity in statistical interpretation of DNA typing data - an objectivity not portrayed in Lander's editorial. RANAJIT CHAKRABORTY Center for Demographic and Population Genetics University of Texas Graduate School of Biomedical Sciences Houston References Budowle B, Giusti AM, WayeJS, Baechtel FS, Fourney RM, Adams DE, Presley LA, et al (1991) Fixed-bin analysis for statistical evaluation of continuous distributions of allelic data from VNTR loci, for use in forensic comparisons. Am J Hum Genet 48:841-855 Chakraborty R, Leimer 0 (1986) Genetic variation within subdivided population. In: Ryman N, Utter F (eds) Population genetics and fishery management. Washington University Press, Seattle, pp 89-120 Cohen JE (1990) DNA fingerprinting for forensic identification: potential effects on data interpretation of subpopulation heterogeneity and band number variability. Am J Hum Genet 46:358-368 Devlin B, Risch N, Roeder K (1990) No excess of homozygosity at loci used for DNA fingerprinting. Science 249: 1416-1420 Hernandez JL, Weir BS (1989) A disequilibrium coefficient approach to Hardy-Weinberg testing. Biometrics 45:5370 GartJJ, NammJ (1984) A score test for the possible presence of recessive alleles in generalized ABO-like genetic systems. Biometrics 40:887-894 Karlin S (1981) Sibling and parent-offspring correlation estimation with variable family size. Proc Natl Acad Sci USA 78:2664-2668 Kennedy RJR (1944) Single or triple melting pot? intermarriage trends in New Haven, 1870-1940. AmJ Sociol 49: 331-339

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Letters to the Editor Lander ES (1 989a) DNA fingerprinting on trial. Nature 339: 501-505 (1989b) Population genetic considerations in the forensic use of DNA typing. In: DNA technology and forensic science. Banbury rep 32. Cold Spring Harbor Laboratory, Cold Spring Harbor, NY, pp 143-156 (1991) Research on DNA typing catching up with courtroom application. Am J Hum Genet 48:819-823 Lewontin RC (1972) The apportionment of human diversity. Evol Biol 6:381-398 Nei M (1987) Molecular evolutionary genetics. Columbia University Press, New York Skibinski DOF, Beardmore JA, Cross TF (1983) Aspects of the population genetics of Mytilus (Mylilidae; Mollusca) in the British isles. Biol J Linnaean Soc 19:137-183 i 1991 by The American Society of Human Genetics. All rights reserved. 0002-9297/91 /4904-0026$02.00

Am. J. Hum. Genet. 49:897, 1991

DNA Fingerprinting To the Editor:

Lander's (1991) editorial on DNA fingerprinting may leave the casual reader with the impression that forensic applications of molecular genetics are inappropriate and ill conceived. Lander also implies that the providers and proponents of these procedures are either naive, uninformed, or Machiavellian. Many knowledgeable, thoughtful investigators would respectfully disagree with these views. The editorial reports that DNA evidence was withdrawn in one case, accepted in part in another, and rejected at an appellate level in Massachusetts. The editorial fails to note that DNA evidence has been admitted in over 450 criminal cases in the United States and that it has survived appellate review in several jurisdictions. DNA fingerprinting has also been widely accepted in European courts. The editorial claims that the two accompanying articles represent "an excellent first step" in scientific studies of DNA typing (Lander 1991, p. 820). This opinion conveniently ignores both the hundreds of technical articles already published on DNA fingerprinting in general and the score or more of technical articles discussing forensic applications of molecular genetics. It also ignores the several articles published prior to initiation of DNA casework by the Federal Bureau of Investigation (FBI), as well as the numerous public documents on the subject available at that time.

The FBI is accused in the editorial of having been pressed, prematurely, into DNA casework. A less conspiratorial view is that by early 1989 the FBI had established detailed laboratory protocols, had performed appropriate validation studies, and was more than ready to provide a valuable forensic service desperately needed by the law-enforcement community. Both in his Journal editorial and in earlier editorials, Lander has raised questions about matching criteria and frequency calculations in forensic applications of DNA fingerprinting. Readers may be left with the impression that the providers were extremely dullwitted for not having foreseen these potential difficulties. In fact, a number of workshops, symposia, and public discussions have been held to address these issues. Further, the issues have been debated in numerous trials, with extensive, publicly available documentation. It is interesting to note, without elaborating on details, that research scientists who use these procedures routinely to solve important problems in biology, medicine, and forensics feel that in most cases a "match" is visually self evident and that, whatever the intricacies of the underlying population structure, the chance of a match by coincidence alone is very remote. Constructive criticism is healthy and desirable. Lander provided a valuable service by raising these issues. Further, a balanced view of DNA fingerprinting in criminal cases would recognize that the procedures are technically demanding and that laboratory personnel are fallible. However, with intelligent protocols and rigorous oversight, these potential problems can be and have been largely avoided. Forensic use of DNA fingerprinting is an application of molecular genetics that is of great value to society. It would be tragic if the criminal justice community were denied the use of these investigative tools because of technical minutiae. STEPHEN P. DAIGER Medical Genetics Center Graduate School of Biomedical Sciences The University of Texas Health Science Center Houston

Reference Lander ES (1991) Research on DNA typing catching up with courtroom application. Am J Hum Genet 5:819-823 © 1991 by The American Society of Human Genetics. All rights reserved. 0002-9297/91 /4904-0027$02.00

Statistical interpretation of DNA typing data.

Letters to the Editor References Budowle B, Giusti, AM, WayeJS, Baechtel FS, Fourney RM, Adams DE, Presley LA, et al (1991) Fixed-bin analysis for sta...
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