Bruce Budowle and Keith L. Monson
Forensic Science Research and Training Center, Laboratory Division, FBI Academy, Quantico, Virginia 22135, USA

× Ø × Ø × Ø × Ø × Ø × Ø × Ø × Ø × Ø × Ø × Ø × Ø × Ø × Ø × Ø

The use of highly polymorphic loci to characterize biological evidence is well established for forensic identity testing. Hypervariable loci provide a high probability of excluding an individual who has been falsely associated with a biological sample. When multiple locus DNA profiles from an evidence sample and a known individual are sufficiently similar, the probability of a coincidental match is expected to be small.

The National Research Council (NRC) recently published its second report on forensic DNA applications (1996), concentrating on the conclusions which should be drawn from a coincidental match. This second report (or NRC II Report)

1. evaluated extant data and made recommendations for the application of statistics for determining the rarity of a DNA profile
   
2. corrected errors or erroneous interpretations in the first NRC Report (1992) on forensic applications, and
   
3. addressed misapplications of the recommendations of the first NRC Report (1992).

In general, the NRC II Report (1996) affirms the validity of the analytical and statistical procedures which are standard practice in the forensic community:

"The technology for DNA profiling and the methods for estimating frequencies and related statistics have progressed to the point where the reliability and validity of properly collected and analyzed DNA data should not be in doubt." (Introduction and O-28)

The NRC II Report (1996) focuses on the meaning which should properly be inferred from a match between the DNA profile of a suspect and that developed from the evidence. The appendix to this paper contains several quotations from the NRC II Report, supportive of current forensic practices, that address arguments centered on:

1. general acceptance
2. fixed bins
3. the product rule
4. confidence limits
5. databases
6. the ceiling principle
   

Since space does not permit discussion on all topics in the NRC II Report (1996), three areas that are the bases for many of the NRC II Report recommendations are reviewed here. These are:

1. whether to select the larger frequency fixed bin or to merge adjacent fixed bins when a DNA fragment resides near the boundary of a bin,
   
2. the presence and impact of null alleles (or pseudohomozygotes) on assumptions of independence and statistical estimates, and
   
3. evaluation of the FBI’s Worldwide Population Study and the support that the study lends to database selection and the assumptions of independence. The application of a small correction for inbreeding to profile frequencies of PCR-based systems, which was recommended in the NRC II Report (1996), will also be discussed.
   

After considering the issues and the wealth of data to support use of DNA profiling, as well as the supporting recommendations of the NRC II Report (1996), the reader will appreciate that DNA typing of forensic samples is a robust and reliable methodology that has withstood the scientific and legal challenges in the United States courtroom arena.

The current, widely used approach for estimating DNA profile frequencies for the general forensic case is to apply the product rule to allele frequencies derived from major (or general reference) population groups. The frequency of a given multiple locus DNA profile is estimated for each of several general reference population groups. Although the DNA fragments of VNTR loci, derived by restriction fragment length polymorphism (RFLP) analysis, are truly discrete, the fragment size distributions tend to be quasi-continuous. To accommodate the measurement error and resolution limitations of RFLP analysis, fragment sizes are grouped into categories, i.e., bins, either with fixed or floating boundaries.

The majority of forensic laboratories in North America employ the fixed bin approach and the assumptions of independence for estimating the likelihood of occurrence of a DNA profile (Budowle et al., 1991). The conventions for forming fixed bin frequency tables are:

1. all fragment lengths in each population sample are sorted into 31 fixed bin categories with boundaries based on reference size standards;
   
2. the number of DNA fragments which fall into each bin is divided by the total number of alleles (i.e., twice the number of individuals) in the sample population to determine the frequency of each bin;
   
3. then, contiguous bins are merged (i.e., "rebinned") such that no bins contain fewer than five counts. After the bin tables are established, the frequency of an observed allele from a DNA profile case in a reference database is estimated by 1) determining in which bin(s) the fragment could reside, using a ±2.5% (or +5.0%) measurement error window (Budowle et al., 1991); 2) if the measurement error window spans a bin boundary, the frequency of the higher frequency bin is assigned to the allele; 3) the single-locus frequency of a two-band pattern is calculated using 2p_ip_j, where p_i and p_j are the estimated binned allele frequencies for each VNTR band of a heterozygote, while the frequency of occurrence of a single-band pattern is estimated using 2p;
   
4. the frequency of occurrence of a profile composed of multiple single-locus profiles is calculated as the product of the single-locus frequencies.

The fixed bin widths in the FBI protocol range from +3.0% to +9.4% of the midpoints for each of the 31 bins (Chakraborty et al., 1993). When the 31 bin format is rebinned the average size of a fixed bin is greater than +5.0%. Since the empirically determined measurement error between 640 and 10,000 base pairs for the FBI Laboratory is +2.5% and the larger frequency of adjacent bins is used for an allele frequency, DNA profile frequency estimates using fixed bin frequencies are conservative (Budowle et al., 1991).

The NRC I Report (1992) questioned the practice of applying the larger bin frequency to the DNA profile frequency estimation when a band, after correction using the laboratory’s measurement error window, spans a fixed bin boundary. Without any supporting data, the NRC I Report (1992) states that "All bin frequencies must be added; it is not enough to take the largest bin frequencies." Presumably, the concern was based on a belief that arbitrary fixed bin boundaries could bisect a single allele peak and result in a lower frequency in each bin than the true value for that allele (the same could occur theoretically for floating bins, but this situation will not be considered here). This could occur when a peak in a population distribution of alleles is due entirely to fragment measurements from the same allele. If the boundary of a bin bisects the peak, it is entirely possible to assign a smaller allele frequency to a DNA fragment than actually occurs in the sample population.

Two studies demonstrate that the proposal to sum adjacent bins is unwarranted and that the fixed bin approach provides larger estimates of allele frequencies than those derived from the laboratory’s quantitative matching criterion, even if alleles lie near a bin boundary. Chakraborty et al. (1993) observed, that in more than 19,000 simulations, no example could be found where a DNA fragment yielded a +2.5% floating bin frequency estimate that was larger than the fixed bin estimate for the VNTR loci D1S7, D2S44, D4S139, D10S28 and D17S79. In fact, the comparison study demonstrated that the fixed bin approach provides allele frequencies that are generally more than twice that of +2.5% floating bins. Even if a few cases could be found where the opposite were true (i.e., a DNA fragment yields a frequency estimate using a +2.5% floating bin that is larger than a fixed bin estimate), there is little concern for wrongful bias in a DNA profile estimate. DNA profile estimates are based on several alleles at multiple loci. Any situation where an allele might possibly be underestimated by the fixed bin approach would be more than compensated by the estimates obtained for the other alleles.

Monson and Budowle (1993) confirmed the findings of Chakraborty et al. (1993) by using an empirical approach to compare the performance of the fixed bin method with that of the floating bin approach. Frequency estimates for 2,046 multiple locus DNA profiles from four reference population groups were compared using the fixed bin approach for assigning allele frequencies and either a +2.5% or a +5.0% floating window. Regardless of the reference population database, the fixed bin approach never yielded a DNA profile frequency estimate that was more rare than the +2.5% floating bin approach. This observation is significant because the FBI Laboratory’s quantitative measurement error window is +2.5%. In fact, on average, the fixed bin method was more conservative than a +5.0% floating window method. When the fixed bin method yielded a DNA profile estimate that was smaller than a +5.0% floating bin approach, it was rare to find a difference in multiple locus estimates that exceeded one order of magnitude.

These studies demonstrate that there is no need to sum adjacent bins to derive an allele frequency and the data support the contention of the NRC II Report (1996) to use the larger frequency bin. There is no real evidence for alleles clustering solely at bin boundaries. The fixed bin procedure is conservative, generally yielding allele frequencies that are twice those derived from the quantitative measurement error of the FBI Laboratory.

One could argue that a +5.0% floating window (i.e., twice the quantitative measurement error of the FBI Laboratory) might be more appropriate than a +2.5% floating window for estimating allele frequencies in a database. This approach is extremely conservative in that it would include DNA fragments for an allele frequency with sizes that would not be considered a match under the quantitative match criterion. That is, the difference in some of the fragment sizes included in an allele class would be greater than a total of 5%. The same already holds true for fixed bin classifications. Moreover, the fixed bin approach, on average, still results in DNA profile frequencies that are larger than the +5.0% floating bin approach.

One of the bases which has been cited as evidence of substantial population substructure in VNTR databases was the detection of an excess of observed homozygotes. This observation could indicate a departure from expectations of independence within and between loci due to the existence of appreciable genetically different subpopulations in the database. Lander (1989) was one of the first to espouse in NY v. Castro that population substructure, and its effects on independence assumptions, was an issue. He detected an excess of single band patterns in the Lifecodes Hispanic database and interpreted this as "spectacular deviations from Hardy-Weinberg equilibrium." Lander (1989) believed this was a demonstration of population substructure (i.e., Wahlund effect).

Budowle et al. (1991) demonstrated that in the FBI VNTR databases there also was an excess of single-banded patterns, but did not concur that this necessarily was evidence for an excess of observed homozygotes. An excess of single-banded patterns can be caused by a number of factors other than just substructuring. Before accepting that there is evidence for substantial population substructuring that might affect a DNA profile frequency, the degree of population substructure required to produce such a pronounced excess of homozygosity should have been examined. Chakraborty and Jin (1992), using the coefficient of gene differentiation (G_ST), showed that observed deviations from Hardy-Weinberg (HW) expectations could not be due solely to subpopulation differences. In fact, the level of excess homozygosity based on single-band patterns in United States Caucasian and African American population samples was inconsistent with the ethnohistory of these groups. Chakraborty (1991) concluded that it would require 20-30 subgroups experiencing no gene flow for 40,000 years for the observed levels of excess homozygosity to be due solely to population stratification. This is an impossible scenario, since, for example, European groups could not have differentiated from each other more than 20-25,000 years ago (Nei and Roychoudhury, 1982). Further genetic mixing of groups, particularly common in the United States, would make population substructure an unlikely cause of the spectacular Hardy-Weinberg deviations detected. However, this observed excess homozygosity is consistent with some single-band patterns being pseudohomozygotes resulting from a class of null alleles (Budowle et al., 1991; Chakraborty et al., 1992; Chakraborty and Jin, 1992, Steinberger, et al., 1993). One approach to demonstrate the existence of null alleles (A_o) is to search for an A_oA_o individual. In fact, there has never been a reported case for such a VNTR genotype. A blank lane on an autoradiogram may be attributed to technical limitations, such as insufficient DNA and/or DNA degradation. Therefore, even if a blank lane were truly the result of a homozygous null profile, it most likely would not be scored. Furthermore, a modest degree of null alleles can create psuedodependence of alleles; but null alleles may be sufficiently rare so that the detection of a null homozygote is unlikely (Chakraborty et al., 1992). The sample size (n) required to detect a null homozygote with a confidence of 100(1-µ)% must satisfy the inequality, where r is the frequency of null alleles,

Chakraborty et al. (1992) demonstrated, using the above equation, that if r=0.01, then the 95% confidence minimum sample size for detecting a null homozygous individual would be 29,995. It, therefore, should not be surprising that a null homozygous individual has not been detected.

Chakraborty et al. (1992; 1994) estimated the null allele frequency for several VNTR loci, based on observed heterozygote deficiency. The estimates for null allele frequencies ranged from zero to 5.5%. Observed departures from independence were consistent with null allele frequencies greater than 1.2%. Gart and Nam (1984) described a method for testing the independence assumption within loci that also checks whether or not estimated null allele frequencies agree with the above predictions. In addition, the method developed by Brown et al. (1980) for detecting nonrandom association of alleles across loci can be used for evaluating the presence of null alleles. Brown et al.’s (1980) approach determines if the observed variance of the number of heterozygous loci from a population sample is outside its confidence interval under the assumption of independence. These tests confirm statistically the presence of null alleles (Chakraborty et al., 1994). After correcting for the presence of null alleles, Chakraborty et al. (1992; 1994) detected no departure from HW and linkage equilibrium (LE) expectations.

While these statistical explanations support that pseudohomozygotes can cause departures from HW expectations, they do not establish formally that VNTR loci carry null alleles. The process for detecting VNTR fragments by RFLP analysis should have provided intuitive insight that some single-banded patterns may be pseudohomozygotes. A labeled DNA probe that hybridizes to a repeat region of a VNTR is used to visualize the DNA profile. Since larger fragments contain more repeat sequences than smaller fragments, there are more target sites within larger DNA fragments to which the probe can bind. Therefore, larger fragments of a DNA profile tend to be more intense than smaller fragments. There could be at times small DNA fragments that contain too few repeat sequences to which hybridization of DNA probes would not be sufficient to generate a detectable signal on an autoradiogram. Moreover, some fragments may be so small that they migrate off the gel during electrophoresis and, therefore, would remain undetected. Thus, technical artifacts of the RFLP analytical system may cause some heterozygotes, where a smaller sized allele is undetected, to appear as single-banded patterns (Budowle et al., 1991; Chakraborty et al., 1992; Chakraborty and Jin, 1992; Chakraborty et al., 1994; Devlin and Risch, 1992a; Steinberger et al., 1993). Additionally, since the resolution of two closely spaced alleles may be limited by RFLP analysis, the two alleles may coalesce and appear as a homozygote (Devlin et al., 1990). Without taking these phenomena into consideration, excess observed homozygosity would be artificially inflated.

The DNA fragments for the FBI RFLP system are generated by digestion of genomic DNA with the restriction enzyme Hae III (a four-base cutter). The presence of null alleles appear to be more prevalent at the VNTR loci D2S44 and D17S79. By analyzing DNA samples using a restriction enzyme that generates larger DNA fragments than Hae III for these loci, the presence of small undetected Hae III alleles may be confirmed. Therefore, the genomic DNA from a number of single-banded individuals at the loci D2S44 and D17S79 was reanalyzed, but by digestion with Pvu II (a six-base cutter). The study empirically confirmed the presence of Hae III null alleles, and the null allele frequencies ranged from 3.0% to 6.5% for D17S79 and 0.3% to 2.7% for D2S44 (Chakraborty et al., 1994). The empirically-derived null allele frequencies compared favorably with those predicted by Chakraborty et al. (1992; 1994) and those estimated by Devlin and Risch (1992a).

One might ask, "would the presence of null alleles result in fixed bin frequencies that are underestimated?" If null alleles are the primary source of an excess of observed homozygotes (which is evident), then the gene counting method for bin frequency estimates is conservative (Chakraborty et al., 1992). The frequency of a heterozygote under HW expectations is 2p_ip_j, where p_i and p_j are bin frequencies. However, with the presence of undetected alleles, the heterozygote frequency estimate, based on allele count data on conditional frequencies, where r = null allele frequency and n = number of individuals in the database, is

Rearranging,

Thus, the frequency of a heterozygote, when there are null alleles in a database, is overestimated.

For single band patterns, Budowle et al. (1991) suggested using 2p_i to estimate the frequency.

Since

single band profile frequencies also will always be overestimated.

On a practical level, an additional buffer is placed on establishing bin frequency estimates. Since single band patterns cannot be distinguished from true homozygotes, the practice is to place two allelic counts in the bin that contains the single band (Budowle, et al. 1991). Thus, if any of the single band patterns are pseudohomozygotes, then the bin frequencies will be overestimated.

However, the bin containing the smallest DNA fragments (which would include the null alleles) would be underestimated. To avoid a potential wrongful bias, no statistical estimates are made for a single locus DNA profile that contains a DNA fragment residing in the smallest size bin class.

The NRC II Report (1996) clearly supports the notion that null alleles can affect tests of independence and the 2p rule for estimating single-banded profile frequencies is appropriate. It is sufficiently conservative and more than compensates for inbreeding effects.

Several investigators, after considering the technical limitations of RFLP typing, have provided tests that demonstrate that RFLP-VNTR databases used in forensics meet HWE and LE (Chakraborty et al., 1992; Chakraborty et al., 1994; Devlin and Risch, 1992b; Devlin et al., 1992; Risch and Devlin, 1992; Weir, 1992). Even before these tests were published, the statistical tests for HWE and LE were assailed as "virtually meaningless" as indicators of population substructure by Lander (1991) and Lewontin and Hartl (1991). Even if the subgroups contained within a reference database had different allele frequencies, the effect of departures from HWE and LE would, in practice, be of little consequence particularly for forensic applications. Regardless, Lewontin and Hartl (1991) and Lander (1991) asserted that the only effective way to avoid a potential wrongful bias was to develop subgroup or ethnic databases and then to estimate the DNA profile frequencies using each of the various subgroup databases.

The stated need for establishing these ethnic databases, instead of only general population databases (i.e., Caucasian, African American, Hispanic, etc.), was based on the erroneous notion that there is more genetic diversity among subgroups within a race than between races (Lander, 1991; Lewontin and Hartl, 1991; NRC I Report, 1992). Prior to the generation of any DNA databases that position was refuted (Latter, 1980; Mitton, 1977, 1978; Nei and Roychoudhury, 1982; Smouse et al., 1982). Moreover, since gene flow generally occurs more readily among subgroups of a major racial group (e.g. Swiss and French) than between major groups, it should have been apparent that subgroups within a major population category would yield more similar statistical estimates. The hypothetical contention by Lewontin and Hartl (1991), Lander (1991), and the NRC I Report (1992), that ethnic subgroup databases could yield estimates that would vary to such a degree as to create a wrongfully biased forensic estimate, is unsubstantiated. The NRC II Report (1996) does not espouse the hypothetical contention either.

The main concern for calculating estimates of DNA profile frequencies in forensic analyses is whether or not there can be a substantial underestimation of the rarity of a DNA profile. In other words, as Lewontin and Hartl (1991) have proposed, could the use of a general United States Caucasian database in lieu of, for example, a Spanish database result in a DNA profile being considered more rare than it should be? While several studies have attempted to answer this question by statistical inferences on general reference databases (Brookfield, 1992; Chakraborty and Kidd, 1991; Chakraborty and Jin, 1992; Devlin and Risch, 1992b; Devlin et al., 1992; Risch and Devlin, 1992), an empirical analysis of forensic implications was meaningful.

Budowle et al. (1994a; 1994b) demonstrated that for the VNTR loci employed in forensic DNA analyses, the concern for forensic statistical applications raised by Lewontin and Hartl (1991), Lander (1991) and the NRC I Report (1992) is unfounded. VNTR population data from approximately 100 geographic and ethnic databases, generated by the forensic community using the restriction endonuclease Hae III or Hinf I, were compiled. Thus, sufficient population data were available to determine whether or not substantial differences in DNA profile frequency estimates might occur when using different population databases. Based on the data in these studies, subdivision within a major population group, either by ethnic group or by United States geographic region, does not substantially affect forensic estimates of the likelihood of occurrence of a DNA profile. A profile would be considered rare whether it has an estimated frequency of 1/5,000,000, 1/50,000,000, or 1/500,000,000. Obviously, the difference in the rarity of such estimates would have little consequence in a forensic context. In the Budowle et al. (1994a; 1994b) study, there were very few examples of an order of magnitude difference for a DNA profile estimate comparison between two within major group databases when the estimate was more common than 1/1,000,000, even though there was no attempt to correct for sampling variance in the databases and measurement biases among laboratories. Those examples of DNA profile estimate comparisons that tended to vary by more than one order of magnitude occurred when the target profiles were derived from different racial categories than the reference databases. Thus, the recommendation of the NRC II Report (1996) to use confidence (or better stated "tolerance") limits of one order of magnitude for the uncertainty of a DNA profile frequency estimate is well-founded.

As expected, the greatest variation in statistical estimates occurs across major population groups. Therefore, estimates of the likelihood of occurrence of a DNA profile using major population group databases (e.g., Caucasian, Black, and Hispanic) provide a greater range of frequencies than would estimates from subgroups of a major population category. The data support that comparisons across major population groups provide valid estimates of DNA profile frequencies without forensically significant consequences. Since using general reference databases can provide reliable forensic estimates, there is no need to invoke ad hoc procedures, such as the ceiling principle approach (NRC I Report, 1992), for deriving statistical estimates of DNA profile frequencies. The NRC II Report (1996) has taken the same position.

Although of little impact on DNA profile frequency estimates, the only notable difference in practice between the forensic community and the recommendations of the NRC II Report (1996) is the application of q (an inbreeding coefficient): "For systems in which exact genotypes can be determined, p² + p(1-p)q should be used for the frequency at such a locus instead of p²." The 2p_i2p_j formula should still be used for estimating heterozygous frequencies. The NRC II Report (1996) also recommends a conservative value of q of 0.01 for the U.S. population and for some small, isolated populations, a value of 0.03 may be more appropriate. Budowle (1995) demonstrated that values of q for African Americans, Asians, and U.S. Caucasians for the PCR-based loci HLA-DQA1, LDLR, GYPA, HBGG, D7S8, and Gc are on average well below 0.01. Thus, a q value of 0.01 is generally a conservative upper bound.

The forensic community will move quickly to accommodate the NRC II Report (1996) recommendation for applying q. In fact, the FBI Laboratory will estimate homozygote frequencies using a q value of 0.01 for most population database estimates, except for Native Americans where 0.03 will be used.

One might argue that reconsideration should be given to previous legal proceedings where p² instead of p² + p(1-p)q was used for the frequency estimate of homozygous PCR-based loci profiles. This assertion might be based on the assumption that undue bias would result when only applying p². However, the data support that no undue bias occurs, and application of either p² instead of p² + p(1-p)q would be appropriate. First, q values for PCR-based loci used in forensic analyses in the United States are low (Budowle 1995). Thus, the slight modification has little effect on a profile frequency estimate. Second, when allele frequencies are relatively large, as they are for the loci HLA-DQA1 and Polymarker, the effect of q is marginal. Third, with highly polymorphic loci, the profile at a locus is more likely to be heterozygous and not homozygous. Thus, even for the short tandem repeat loci, the effect of applying q would still be marginal. The difference in estimates with and without application of q are shown in the scatter plots in
Figure 1. It is evident that the application of q, either at a value of 0.01 or 0.03, has little or no impact on PCR-based profile frequency estimates. Moreover, the difference in estimates is well within the order of magnitude tolerance limit advocated by the NRC II Report (1996). Thus, no undue bias was received by using p² for PCR-based homozygous profile frequency estimates.

CONCLUSION

In general, most of the recommendations of the NRC II Report (1996) already are in practice in the forensic community. The extant data, most of it derived from the forensic community, support the conclusions of the NRC II Report (1996) that :

"The technology for DNA profiling and the methods for estimating frequencies and related statistics have progressed to the point where the reliability and validity of properly collected and analyzed DNA data should not be in doubt." [See appendix for quotations regarding specific issues].

Moreover, the DNA Advisory Board (DAB) has endorsed the NRC II Report (1996) by stating:

"The DAB congratulates Professor Crow and his National Research Council Committee for their superb report on the statistical and population genetic issues surrounding forensic DNA profiling. We wholeheartedly endorse the major findings of the report in these substantive areas."

The NRC II Report (1996) will be useful in minimizing controversies in the legal setting.

Figure 1. Examples of scatter plot comparisons of the difference in estimates with and without application of q in various reference population databases. The likelihood of occurrence of N target profiles (from one to seven PCR-based locus profiles) was estimated using p² and p² + p(1-p)q for homozygous profiles and 2p_ip_j for heterozygous profiles and the product rule. The first column of scatter plots displays comparisons using a q value of 0.01; the second column of scatter plots displays comparisons using a q value of 0.03.

The technology for DNA profiling and the methods for estimating frequencies and related statistics have progressed to the point where the reliability and validity of properly collected and analyzed DNA data should not be in doubt. (Intro and O-28)

Methods of DNA profiling are firmly grounded in molecular technology. When profiling is done with appropriate care, the results are highly reproducible. In particular, the methods are almost certain to exclude an innocent suspect.

(O-28, 2-14)

Nonetheless, DNA testing provides a great opportunity for the falsely accused, and for the courts, because it permits a prompt resolution of a case before it comes to court, saving a great deal of expense and reducing unnecessary anxiety. (1-5)

Because cases in which a suspect is excluded by nonmatching DNA almost never come to court, experts from testing laboratories usually testify for the prosecution. (1-5)

Most presentations of DNA evidence use some form of grouping of alleles. Grouping reduces statistical power but facilitates computation and exposition. (5-14)

We conclude that both the procedure we recommend and that employed by the FBI provide adequate and usually conservative approximations to the correct floating-bin frequency. (5-19)

With fixed bins, some statistical power is lost, but there are computational and expository gains.
(5-18)

The fixed-bin is simpler in some ways and easier for the average laboratory to use; hence, it is more widely employed. (O-10)

If a bin in the database contains fewer than five entries, it is pooled with adjacent bins so that no bin has fewer than five. We recommend this procedure for VNTRs and for other systems in which an allele is represented fewer than five times in the database. (O-12, 5-22)

Often, two or more bins will be overlapped by the match window. When that happens, we recommend that the bin with the highest frequency be used. (The 1992 NRC report recommends taking the sum of the frequencies of all overlapped bins, but empirical studies have shown that taking the largest value more closely approximates the more accurate floating-bin method.) (O-12)

If fixed bins are employed, then the fixed bin that has the largest frequency among those overlapped by the match window should be used. (ES-6, O-32, 5-18)

In general, the calculation of a profile frequency should be made with the product rule. If the race is not known, calculations for all the racial groups to which possible suspects belong should be made. For systems such as VNTRs, in which a heterozygous locus can be mistaken for a homozygous one, if an upper bound on the frequency of the genotype at an apparently homozygous locus (single band) is desired, then twice the allele (bin) frequency, 2p, should be used instead of p². For systems in which exact genotypes can be determined, p² + p(1-p)q should be used for the frequency at such a locus instead of p². A conservative value of q for the US population is 0.01; for some small, isolated populations, a value of 0.03 may be more appropriate. For both kinds of systems, 2p_i2p_j should be used for heterozygotes. (ES-4, O-21, O-31, 4-36).

Extensive studies from a wide variety of databases show that there are indeed substantial frequency differences among the major racial and linguistic groups (Black, Hispanic, American Indian, east Asian, and white). And within these groups, there is often a statistically significant departure from random proportions. As we said earlier, those departures are usually small, and formulae based on random mating assumptions are usually quite accurate. So, the product rule, although certainly not exact for real populations, is often a very good approximation. (O-20)

4. Confidence Limits

Finally, the assumptions of HW and LE, although reasonable approximations for most populations, are not exact. We believe that it is safe to assume that the uncertainty of a profile frequency calculated by our procedures from adequate databases (at least several hundred persons) is less than a factor of about 10 in either direction. (O-20)

Confidence intervals derived from the simplifying assumptions of sampling theory do not take account of all possible sources of uncertainty that can affect the accuracy of a match probability or likelihood ratio. (5-22)

We conclude that, when several loci are used, the probability of a coincidental match is very small and that properly calculated match probabilities are correct within a factor of about 10 either way. (O-25, O-26, 5-21, 5-22, 5-23)

If the calculated profile probability is very small, the uncertainty can be larger, but even a large relative error will not change the conclusion. (5-30)

The empirical studies show that the differences between the frequencies of the individual profiles estimated by the product rule from different adequate subpopulation databases (at least several hundred persons) are within a factor of about 10 of each other, and that provides a guide to the uncertainty of the determination for a single profile. (5-34)

Match probabilities are calculated from a database. Those data are a sample from a larger population, and another sample might yield different match probabilities. (5-20)

Ideally, the reference data set from which genotype frequencies are calculated would be a simple random sample or a stratified or otherwise scientifically structured random sample from the relevant population. Several conditions make the actual situation less than ideal. One is a lack of agreement as to what the relevant population is (should it be the whole population or only young males? should it be local or national?) and the consequent need to consider several possibilities. A second is that we are forced to rely on convenience samples, chosen not at random but because of availability or cost. It is difficult, expensive, and impractical to arrange a statistically valid random-sampling scheme. The saving point is that the features in which we are interested are believed theoretically and found empirically to be essentially uncorrelated with the means by which samples are chosen. Comparison of estimated profile frequencies from different data sets shows relative insensitivity to the source of the data. (O-23, 4-22, 5-1, 5-2)

If the race is not known or if the population is of racially mixed ancestry, the calculations can be made with each of the appropriate databases and these presented to the court. (4-27)

The 1992 NRC report relied on a single study (Lewontin 1972) that appeared to support the opposite view, but that study has not been confirmed by other, more extensive ones. (5-25)

The recent compilations by the FBI, as well as numerous other studies, confirm the intuitively reasonable expectation that differences between ethnic groups within races are smaller than differences between races. (5-25, 5-28)

Within a racial group, geographic origin and ethnic composition have very little effect on the frequencies of forensic DNA profiles, although there are larger differences between major groups (races). It is probably safe to assume that within a race, the uncertainty of a value calculated from adequate databases (at least several hundred persons) by the product rule is within a factor of about 10 above and below the true value. If the calculated profile probability is very small, the uncertainty can be larger, but even a large relative error will not change the conclusion. (5-30)

Both the ceiling principle and the interim ceiling principle are unnecessary. (ES-2, ES-3, O-32, 4-30,
5-32)

We share the view of those who criticize it on practical and statistical grounds and who see no scientific justification for its use. (O-27, 5-31)

That is also a disadvantage, for it does not permit the use of well-established differences in frequencies among different races; the method is inflexible and cannot be adjusted to the circumstances of a particular case. (O-27)