MEMORANDUM OPINION

Two men wearing masks and gloves broke into the Londonderry, branch of the First New Hampshire Bank about an hour after closing on August 4, 1995. One of the robbers apparently cut himself when he entered the building, as bloodstains were discovered inside the bank and in a stolen minivan believed to have been used as a getaway vehicle.

The government later charged Anthony Shea with the robbery and proposed to base its case in part on expert testimony comparing Shea's DNA with DNA extracted from several of the bloodstains. The government's expert, a forensic scientist employed by the FBI, used a method of DNA analysis known as Polymerase Chain Reaction ("PCR"), in determining that Shea has the same DNA profile as the person who left several of the blood stains at the crime scene and in the getaway vehicle. The expert also concluded that the probability of finding a similar profile match if a DNA sample were drawn randomly from the Caucasian population is 1 in 200,000.

Shea moved to exclude the DNA evidence prior to trial. Although he conceded that the scientific principles underlying PCR are generally accepted in the fields of molecular biology and forensic science, he argued that the evidence is inadmissible pursuant to Fed. R. Evid. 702 because the FBI's PCR methods are unreliable. He also challenged the government's random match probability estimate for similar reasons. Finally, he argued that evidence of a random match probability is barred by Fed. R. Evid. 403 because the risk that the jury would be misled by the evidence substantially outweighs its probative value.

After holding an evidentiary hearing and carefully considering Shea's arguments, I denied his motion to exclude. Shea subseguently was convicted of attempted bank robbery and several related charges. In this opinion, I explain why I admitted the DNA evidence.

I. In order to appreciate Shea's contentions, one must understand certain generally accepted principles and methodologies used in the fields of molecular biology and population genetics. Accordingly, I begin by describing several basic concepts used in human genetics, the DNA typing methodology at issue in this case, and the statistical methods the government's expert used in attempting to determine the probability of a random match.^[1] A. Some Basic Concepts Used in Human Genetics DNA, an acronym for deoxyribonucleic acid, is the chemical blueprint for life. Most human cells other than reproductive cells contain identical copies of a person's DNA. Although 99.9% of human DNA does not vary from person to person, no two persons other than identical twins have the same DNA. NRC II, supra, at 63.

Human DNA is organized into 23 pairs of chromosomes and each chromosome contains a DNA molecule. DNA molecules have a double stranded helical structure that can be envisioned as a spiral staircase. NRC I, supra, at 2. See Figure 1. Running between the two sugar-phosphate strands forming the handrails of the staircase are millions of steps comprised of two loosely bound nitrogen bases. Each step is referred to as a base pair. There are four types of bases: adenine (A), thymine (T), guanine (G) , and cytosine (C). A's ordinarily pair only with T's, and C's ordinarily pair only with G's. Thus, if the seguence of bases on one side of a DNA molecule is known, the corresponding seguence of bases on the other side can be deduced. The arrangement of base pairs in chromosomal DNA comprises the genetic code that differentiates humans from non-humans and makes every person unigue. Mange, supra, at 19-20.

In total, the DNA molecules in the 23 pairs of human chromosomes contain approximately 3.3 billion base pairs. Most of the base pairs are arranged in the same sequence in all humans. NRC II, supra, at 62-63. However, every DNA molecule has regions known as polymorphic sites where variability is found in the human population.^[2] Each possible arrangement of base pairs that occurs at a polymorphic site is referred to as an allele. Alleles can result from differences in a single base pair, differences in multiple base pairs, or differences in the number of base pairs that comprise a site.

The combination of alleles from corresponding sites on a chromosome pair is sometimes referred to as the site's genotype.^[3] NRC II, supra, at 216. One allele for each single locus genotype is inherited from each parent. If both parents contribute the same type of allele, the child's genotype is considered to be homozygous. If each parent contributes a different type of allele, the child's genotype is considered to be heterozygous. To illustrate, if only two alleles for a locus are found in the population, A and a, two homozygous genotypes, AA and aa, and one heterozygous genotype, Aa, will be found in the population. Although an individual's genotype consists of either two copies of the same allele or one copy of each of two different alleles, many different alleles may be found in the population for a single locus. NRC II, supra, at 15.

B. PCR Amplification and Typing

PCR and Restriction Fragment Length Polymorphism ("RFLP")4 are the two methods most often used in forensic DNA typing. In this case, the government relies exclusively on PCR. PCR has two aspects, amplification and allele identification.

1. PCR Amplification

PCR amplification is a process for making many copies of selected portions of a DNA sample. NRC I, supra, at 40. The process reguires the use of a primer for each end of a polymorphic site. Primers are synthetic single-stranded DNA molecules consisting of approximately 20 bases. They are arranged in a seguence that complements the bases on one strand of the double- stranded DNA molecule in a known region flanking the site at issue. Amplification is commenced by adding two corresponding primers for each end of a site, an enzyme known as DNA polymerase, and many free floating copies of the four bases (A, C, T and G) to a purified DNA sample. The double-stranded DNA molecules in the sample are then denatured. Denaturing separates double-stranded DNA molecules into single-stranded molecules with complementary base seguences. After the DNA is denatured, the primers bind with the denatured DNA at their complementary sites such that one primer binds to one strand at one end of the studied site and the other primer binds to a complementary strand at the other end of the site. Mange, supra, at 287. See Figure 2. Primers have 3 and 5 ends. The denatured DNA is replicated only from each primer's 3 end leaving the portion of a molecule on the 5 end single-stranded. Mange, supra, at 256, 287. Each step in the process after the primers are added is accomplished through carefully controlled changes in temperature in a device known as a thermal cycler. Mange, supra, at 288.

The amplification process is repeated many times. After the third cycle, some copies are produced that contain only the polymorphic region and its flanking primers. See Figure 3. The number of these copies grows exponentially with each cycle. Eventually, enough copies of the shorter segments are produced to permit the amplified alleles to be identified. Mange, supra, at 288 .

Seven different polymorphic sites were analyzed in this case. DQ Alpha; Low Density Lipoprotein Receptor (LDLR); Glycophorin A (GYPA); Hemoglobin G Gammaglobin (HBGG); D7S8; roup-Specific Component (Go); and D1S80.5 The DQ Alpha site and the five sites collectively known as the Polymarker sites (LDLR, GYPA, HBGG, D7S8 and Gc) were amplified simultaneously using a commercially available test kit known as the "AmpliType PM PCR Amplification and Typing Kit." The D1S80 site was amplified separately.

2. Identification of Amplified Alleles

Once a DNA sample is amplified, the specific polymorphic sites must be typed. The DQ Alpha and Polymarker sites are typed as follows. The amplified DNA is denatured once more and washed over strips of allele-specific probes. Each probe itself contains denatured DNA segments comprising an allele that is known to exist at the studied site.^[6] Both the DQ Alpha and The D1S80 site is typed differently because alleles for this site result from variations in the number of times that a contiguous sequence of 16 base pairs is repeated. NRC II, supra, at 74. The process used to type amplified D1S80 is known as gel electrophoresis. In this process, amplified D1S80 is deposited at one end of a thin slab of a gel material. The gel is then placed in an electric field and this field causes the amplified D1S80 to migrate through the gel. The rate at which the D1S80 segments travel through the gel depends upon the length of the amplified alleles. Shorter alleles travel further in a given time than longer alleles. After a predetermined time, the gel is removed from the electric field and the amplified D1S80 in the gel is stained. The sample can then be typed based on the distance the amplified DNA has traveled through the gel. Mange, supra, at 299-301.

PCR is a very potent process which can result in the amplification of very small amounts of DNA. Accordingly, special care must be taken to minimize the possibility that samples become contaminated though mishandling. Among the other issues that are sometimes raised when considering the PCR process are: (1) the potential that primers or probes might bind at points other than the areas flanking the site under study; (2) concerns that the process has a limited capacity to identify mixtures of more than one person's DNA; and (3) suggestions that the laboratory performing the test in a particular case might fail to detect and correct erroneous results.

C. Population Genetics

The PCR analysis conducted in this case allegedly demonstrates that Shea's DNA matches DNA extracted from several of the bloodstains at seven studied sites. To put this finding in context, the government offered evidence that the probability of finding a similar match if a DNA sample were drawn randomly from the Caucasian population is 1 in 200,000. This random match probability essentially expresses the expected freguency of the observed DNA profile in a pertinent population.

The process of calculating a random match probability begins with a determination of the allele freguencies comprising the DNA profile. An allele freguency is simply a statement of relative proportion that is customarily expressed as a decimal fraction.^[7] Genotype frequencies are calculated by squaring the frequency of the single allele comprising each homozygous genotype (P2) and by doubling the product of the two allele frequencies comprising each heterozygous genotype (2PiPj) .8 NRC I, supra, at 4; NRC II, supra, at 92. The law of genetics that permits genotype frequencies to be determined in this way under proper conditions is called the Hardy-Weinberg law.9 Mange, supra, at 408-11. Once genotype frequencies are determined, the probability of a random match of genotypes at multiple sites is calculated by multiplying the frequencies of the sample's genotypes at each site.^[10]

The rule that the joint probability of multiple independent events can be determined by multiplying the frequencies of the individual events is known as the product rule. Mange, supra, at

61. The product rule can be applied reliably in the manner described above only if the estimate of allele frequencies is reasonably accurate and the conditions in the population approximate what are known as Hardy-Weinberg equilibrium and linkage equilibrium.

(1) Accuracy of Allele Frequencies Estimates

Because it is not practical to test an entire population, allele frequencies are derived from databases of DNA samples. If these databases do not accurately reflect the distribution of alleles in the population — either because the sample size is too small or because of a bias in the way in which samples were selected for inclusion — the calculation of a random match probability may be unreliable. NRC I, supra, at 10.

(2) Hardy-Weinberg Equilibrium

Hardy-Weinberg equilibrium is the state in which genotype frequencies can be calculated reliably using the Hardy-Weinberg law. Hardy-Weinberg equilibrium will exist for a large population if there is approximately random mating within the population, a negligible amount of biased mutation occurs in the alleles comprising the genotypes under study, migration is limited and unbiased, and natural selection is insignificant. Large deviations from Hardy-Weinberg equilibrium make it difficult to reliably determine genotype frequencies from allele frequencies.^[11] Mange, supra, at 410-411.

(3) Linkage Equilibrium

The product rule can be used reliably only if the events considered in a joint probability calculation are independent.^[12] Thus, to the extent that genotypes at multiple sites are linked, it becomes more difficult to calculate a random match probability using the product rule. Linkage eguilibrium exists in a population when alleles comprising the genotypes at one site are not associated with the alleles comprising genotypes at other sites. NRC II, supra, at 106. If Hardy-Weinberg eguilibrium persists in a population over several generations, the population will approach linkage eguilibrium.^[13] NRC II, supra, at 27.

variables that were not independent. The prosecutor used individual probabilities of a man with mustache (25%) , a Negro man with beard (10%), a girl with ponytail (10%), a girl with blond hair (33%), a partly yellow automobile (10%) and an interracial couple in car (001%), and using the product rule arrived at a 1 in 12 million random match probability. Because the characteristics were not independent, the product rule yielded a drastically exaggerated result. Id. at 37.

Linkage equilibrium will be approached more quickly for sites on different chromosomes than for sites on the same chromosome, and widely spaced sites on the same chromosome will approach linkage equilibrium more quickly than sites that are close together. NRC II, supra, at 64, 106. Whereas Hardy-Weinberg equilibrium will produce alleles in Hardy-Weinberg proportions after a single generation, it takes several generations before linkage equilibrium is approached. NRC II, supra, at 106.

Hardy-Weinberg equilibrium and linkage equilibrium are rarely attained in real populations, most significantly because real populations are finite and contain subgroups that are perpetuated by non-random mating. Accordingly, debate about whether the product rule can be used reliably often focuses on the power of the statistical methods used to detect deviations from Hardy-Weinberg equilibrium and linkage equilibrium and the adequacy of the measures that are used to account for potential deviations.

U.S. 579, 590 (1993). Rule 702 thus establishes a standard of evidentiary reliability that focuses on the scientific validity of the expert's methods rather than the soundness of his specific conclusions.^[15] United States v. Bonds, 12 F.3d 540, 566 (6th Cir. 1993). Moreover, each logical step in the expert's analysis must be scientifically valid because, as the Supreme Court observed in Daubert, "scientific validity for one purpose is not necessarily scientific validity for other, unrelated purposes." 509 U.S. at 591; see also In Re Paoli R.R. PCB Litiq., 35 F.3d 717, 743 (3d Cir. 1994) ("Paoli II") , cert, denied, 115 S. C t . 1253 (1995). In Daubert, the Supreme Court described this consideration as "fit."16 Daubert, 509 U.S. at 591.

Almost any challenge to an expert's conclusions can be redefined as a dispute over methods. However, Rule 7 02's reliability requirement distinguishes between a claim that an expert's methods are unsound and a claim that scientifically sound methods have been applied improperly in a particular case. A claim that scientific methods are unsound must be addressed initially by the trial judge, while a claim that scientifically sound methods have been applied improperly ordinarily should be left for the jury to resolve unless the alleged "error negates the basis for the reliability of the principle itself." United States v. Martinez, 3 F.3d 1191, 1198 (8th Cir. 1993), cert. denied, 510 U.S. 1062 (1994).

Among the factors that a court should consider in determining whether scientific testimony is reliable are: (1) whether the expert's opinion can be or has been tested; (2) whether the theory or technique on which the opinion is based has been subjected to peer review and publication; (3) the technique's known or potential error rate; (4) the existence and maintenance of standards controlling the technique's operations; and (5) "general acceptance."17 Daubert, 509 U.S. at 592-95; Paoli II, 35 F.3d at 742. No single factor is necessarily dispositive in this analysis and other factors might also warrant consideration in the appropriate case.^[18] Daubert, 509 U.S. at 594.

B. Rule 403

Rule 403 reguires the exclusion of otherwise admissible expert testimony if the probative value of the evidence is substantially outweighed by "the danger of unfair prejudice, confusion of the issues, or misleading the jury, or by considerations of undue delay, waste of time, or needless presentation of cumulative evidence." Fed. R. Evid. 403. Expert testimony must be closely scrutinized for compliance with Rule 403 because, as the court in Daubert recognized, "[e]xpert evidence can be both powerful and guite misleading . . . ." Daubert, 509 U.S. at 595 (guoting Jack B. Weinstein, Rule 702 of the Federal Rules of Evidence is Sound; It Should Not be Amended, 138 F.R.D. 631, 632 (1991)); see also. United States v. Fosher, 590 F.2d 381, 383 (1st Cir. 1979). Nevertheless, relevant and reliable expert testimony ordinarily should be admitted notwithstanding Rule 403 unless the potential that it will be used improperly substantially outweighs any legitimate persuasive value that the evidence may have. See Paoli II, 35 F.3d at 747 (expert testimony should not be excluded simply because it is complex unless there is something about the particular technigue at issue that overwhelms the jury's ability to independently assess the evidence).

III.

Shea's challenges to the DNA evidence fall into three categories. First, he argues that the FBI's PCR testing protocols contain errors and omissions that render the methodology suspect. Second, he contends that the product rule cannot be used to calculate the probability of a random match because the databases on which the calculation is based are too small. Finally, he asserts that the government should be barred from informing the jury of the probability of a random match because it will mislead the jury. I address each class of contentions in turn.^[19]

A. PCR Typing Protocols

The PCR Typing methods used by the FBI in this case readily satisfy Rule 702's reliability reguirement. First, although PCR is a relatively new technology, it is based on sound scientific methods and it has guickly become a generally accepted technigue in both forensic and non-forensic settings. Perhaps the strongest evidence on this point is the conclusion reached by the National Research Council's Committee on Forensic DNA Science that "the molecular technology [on which PCR is based] is thoroughly sound and . . . the results are highly reproducible when appropriate guality-control methods are followed."20 NRC II, supra, at 23; see also Mange, supra, at 287 (noting PCR's "widespread and growing applications [in the field of molecular biology]"). Second, the tests used to type each of the 7 sites examined in this case were validated in a carefully constructed series of experiments and the results were later published in peer-reviewed publications.^[21] Finally, the FBI followed detailed testing protocols and quality control procedures in this case that conform to industry standards.^[22]

Notwithstanding the considerable evidence supporting a finding that the FBI's PCR test methods are scientifically valid. Shea argues that the DNA evidence must be excluded because the FBI's PCR tests will produce an unacceptably high percentage of erroneous results even if evidence samples are properly handled and the tests are properly performed. Shea bases this argument primarily on the testimony of Dr. Donald Riley.^[23] Dr. Riley claims that the FBI's testing protocols could result in typing errors because the testing protocols specify incorrect amplification and typing temperatures. He also states that this problem is particularly significant with the amplification and typing of the DQ Alpha region. Because the control probes for both the DQ Alpha and Polymarker tests are intended to detect DQ Alpha alleles. Dr. Riley theorizes, the FBI's testing protocols could produce erroneous results on both tests.

I reject Dr. Riley's testimony for two reasons. First, although he claimed that he has tested his theory, he has not subjected his conclusions to peer review, nor has he described his test methods in sufficient detail to permit a conclusion that they are scientifically valid. Second, even if the testing protocols specify the wrong amplification and typing temperatures. Dr. Riley has offered no scientific support for his theory that this methodological flaw could produce false positive signals at the control probes on the DQ Alpha and Polymarker test strips. In the face of such poorly supported testimony, I have no difficulty in finding that the published validation studies relied on by the government persuasively establish the evidentiary reliability of the FBI's PCR testing protocols.^[24]

Shea also argues that the DNA evidence should be excluded because PCR cannot reliably detect mixtures of more than one person's DNA. The government concedes that a mixture theoretically could result in the declaration of a false match. However, Richard Guerrieri,25 one of the government's expert witnesses, testified that such errors are exceedingly unlikely because an examiner will be able to identify a mixture from observable differences in the relative strengths of the signals indicated on the PCR test strips, except in extremely unusual circumstances. I reject Shea's argument because I find Mr. Guerrieri's testimony persuasive on this point.

Shea next argues that the DNA evidence must be excluded because the government did not establish that the FBI laboratory has an acceptably low PCR error rate.^[26] Testing errors can occur either because a test has inherent limitations or because the people involved in collecting, handling or testing samples are not sufficiently skilled. See Edward J. Imwinkelried, Coming to Grips with Scientific Research in Daubert's "Brave New World": The Courts' Need to Appreciate the Evidentiary Differences Between Validity and Proficiency Studies, 61 Brook. L. Rev. 1247 (1995) (explaining the difference between a validation study which evaluates whether a test produces accurate results if performed properly and a proficiency study which evaluates a laboratory's ability to correctly perform the test) . A laboratory's error rate is a measure of its past proficiency that is of limited value in determining whether a test has methodological flaws. Since Rule 702's reliability requirement focuses on the validity of the test rather than the proficiency of the tester, the absence of a laboratory error rate will rarely be dispositive if the rest of the evidence establishes that the test has been properly validated. In this case, the government produced substantial persuasive evidence to support its claim that its PCR tests are reliable. Accordingly, the absence of a known PCR error rate for the FBI laboratory does not warrant the exclusion of the government's evidence.^[27]

Shea finally challenges the reliability of the DNA evidence by pointing to several alleged deficiencies in the FBI's evidence handling and quality control procedures. Shea contends that the FBI laboratory mishandled the evidence by packaging the dried blood samples in individual paper coin envelopes and storing them together. Dr. Riley theorizes that this practice is fatally flawed because DNA from one sample could migrate through a paper coin envelope and contaminate other similarly packaged samples. Shea also contends that the laboratory's quality control procedures are deficient because substrate control samples28 were not taken and a positive control sample29 was not tested for each possible allele. The government responds by noting that Shea failed to produce any scientific evidence to support Dr. Riley's contamination theory and by explaining that the laboratory's quality control procedures conform to industry standards.

I need not address the merits of Shea's arguments. Instead, I join the many courts that have addressed similar issues by concluding that because such arguments concern the way in which a method is applied in a particular case rather than the validity of the method, they affect the weight that should be given to the evidence rather than its admissibility.^[30] See, e.g.. United States v. Beasley, 102 F.3d 1440, 1448 (8th Cir. 1996); United States v. Hicks, 103 F.3d 837, 848 (9th Cir. 1996); United States v. Chischillv, 30 F.3d 1144, 1154 (9th Cir. 1994), cert, denied, 115 S. C t . 946 (1995); United States v. Bonds, 12 F.3d 540, 563 (6th Cir. 1993); United States v. Jakobetz, 955 F.2d 786, 800 (2d Cir.), cert, denied, 506 U.S. 834 (1992).

B. Random Match Probability

The government's estimate of a 1 in 200,000 random match probability is based primarily on information drawn from a PCR database comprised of DNA profiles for 148 Caucasians, 145 African Americans, 94 Southeastern Hispanics, and 96 Southwestern Hispanics.^[31] Bruce Budowle, et al.. Validation and Population Studies of the Loci LDLR, GYPA, HBGG, D7S8, and Gc (PM loci). Procedure, 40 Journal of Forensic Sciences 45, 50 (1995). Shea contends that this database is simply too small to be used reliably in estimating random match probabilities with the product rule.

The government cites a study published in a peer-reviewed journal to refute Shea's claim. Id. This study analyzes the government's database using several statistical tests in an effort to identify significant departures from Hardy-Weinberg and linkage equilibrium. The study states that the distribution of the various genotypes found at the 7 loci at issue in this case meet Hardy-Weinberg expectations and exhibit little evidence of deviation from linkage equilibrium. Accordingly, it concludes that "[t]he data demonstrate that valid estimates of a multiple locus profile frequency can be derived for identity testing purposes using the product rule under the assumption of independence."32 Id. at 53.

Notwithstanding the study cited by the government, legitimate questions can be raised concerning the reliability of a random match probability that is estimated with the product rule from a database as small as the one used here. Because such databases are comprised of a limited number of samples, the possibility of random error ordinarily must be considered.^[33] Further, legitimate questions can be raised concerning the power of existing statistical methods to detect deviations from Hardy- Weinberg and linkage equilibrium when small databases are used. If random error is not accounted for and if the likely potential effects of factors such as population substructuring are not identified and addressed, a random match probability estimated with the product rule may be unreliable.

The recently released NRC II report addresses these issues by acknowledging the potential for error and suggesting several ways to conservatively account for the problem. First, the report describes alternative adjustments to the product rule to account for the systematic over-representation of homozygous genotypes that is caused by undetected population substructuring.^[34] NRC II, supra, at 99-100. If, as is the case with most PCR-based systems, the method used to identify alleles

Moore's Federal Practice: Reference Manual on Scientific Evidence 415, 466 (1994).

does not present significant ambiguity, the report recommends that homozygous freguencies be determined by using P2+P(l-P) rather than by P2 where P is the allele freguency and is the percentage of excess homozygosity that is expected because of undetected population substructuring. Id. at 122. After examining empirical data from several sources, the report concludes that a value of .01 will conservatively address the likely potential systematic effect of undetected population substructuring except for cases involving small, isolated populations, where a value of .03 may be appropriate.^[35] Id. at 122. If an allele identification system such as one based on VNTRs is used where there is a potential that a heterozygous genotype may be misidentifled as homozygous, the report recommends that homozygous genotype freguencies be calculated using 2P rather than P2. Id. at 122. The report concludes that these two methods will account in a conservative way for the likely systematic effect of undetected population substructuring. Id.

Undetected population substructuring and random error can also affect individual random match probability calculations in ways that are difficult to predict. NRC II, supra, at 112. Thus, the NRC II report also suggests a way of gualifying random match probability estimates to account for such uncertainties. After considering empirical data comparing genotype freguencies observed in a number of aggregate population databases with genotype freguencies found in known regional and ethnic subpopulation databases, the report concludes that likely uncertainties caused by random error and undetected population substructuring can be conservatively accounted for if the database used in calculating the random match probability contains samples from "at least several hundred persons" and the estimate obtained by using the product rule is gualified by stating that the true value is likely to be within a factor of 10 above or below the estimated value.^[36] Id. at 156.

The government agreed to adjust its random match probability estimate in the manner suggested in the NRC II report.^[37] Accordingly, I consider whether the method used by the government's expert in estimating the probability of a random match, when adjusted in accordance with the recommendations contained in the NRC II report, satisfies Daubert's reliability standard.

Shea relies primarily on the testimony of Dr. William Shields38 in claiming that the FBI's methodology for estimating the probability of a random match is unreliable even if it is adjusted to conform to the recommendations contained in the NRC II report. Dr. Shields challenged the FBI's methodology by claiming that: (1) a value of .01 is insufficient to capture the likely systematic effects of population substructuring; (2) the NRC II's recommended factor of 10 correction is based on VNTR data that cannot reliably be applied to the PCR loci at issue here; and (3) the PCR database used in this case is too small, even when judged by the standards of the NRC II report, for the factor of 10 correction to account for potential error. Rather than using the adjustment to the product rule suggested in the NRC II report. Dr. Shields proposed an alternative method of accounting for potential error.^[39] Using his method. Dr. Shields claimed that the probability of a random match should be estimated at 1 in 49,000. If, as Dr. Shields suggests, a 95% confidence interval40 is then calculated to account for the potential effect of random error, the bottom end of the range in his estimate would be 1 in 23,000, rather than the bottomrange of 1 in 20,000 proposed by the government.

The government countered Dr. Shields' testimony with testimony from Dr. Martin Tracey.^[41] Dr. Tracey (1) endorsed the use of both P2 + P(l-P) with a value of .01 and 2P as adjustments to homozygous genotypes, (2) opined that there is no reason to expect that the factor of 10 correction recommended in the NRC II report will be insufficiently conservative if it is applied to PCR loci, and (3) concluded that a database of 148 is sufficiently large to reliably permit the use of the factor of 10 correction recommended in the NRC II report.

Whether the adjustments to the product rule suggested in the NRC II report are sufficiently conservative and whether a database of 148 is of sufficient size to serve as the basis for a reliable random match probability estimate are important guestions about which population geneticists can legitimately disagree. However, Rule 702 does not reguire scientific consensus. The government has produced a peer-reviewed study using accepted statistical methods to support its position that the estimation of a random match probability from the database used in this case will produce a reliable result. It has further gualified its estimate in accordance with the recommendations of a distinguished committee of scientists and academicians that included leading population geneticists as members. Under these circumstances, the concerns raised by Dr. Shields affect the weight that should be given to the evidence rather than its admissibility. See Bonds, 12 F.3d at 564 (substructuring argument affects weight rather than admissibility); see also Jakobetz, 955 F.2d at 792.

C. Juror Confusion

Evidence that a defendant's DNA profile matches DNA extracted from an evidence sample suggests that the defendant cannot be excluded as a potential contributor, but it is of little value, standing alone, in proving the defendant's guilt. Giving the jury a random match probability estimate for the profile is one way of helping it assess the potential significance of a DNA profile match. However, because such evidence also has the potential to mislead. Rule 403 reguires that the probative value of the evidence must be carefully balanced against the danger of unfair prejudice.

Shea argues that a jury would be so overwhelmed by evidence of a random match probability that it could not properly assess the possibility that a profile match is false unless a laboratory or industry error rate is calculated and combined with the random match probability estimate. Shea bases this argument on the following reasoning: (1) a random match probability estimate is meaningless if the declared DNA profile match is false; (2) the best evidence of whether a match is false in a particular case is the laboratory's false match error rate; (3) if the laboratory's false match error rate cannot be determined, the next best evidence is the industry's false match error rate; (4) jurors cannot understand the significance of a laboratory's error rate unless it is combined with the random match probability estimate. Because the FBI laboratory does not calculate a PCR false match error rate and the government refuses to combine what Shea suggests is the industry's PCR error rate with the random match probability estimate. Shea argues that the estimate is inherently misleading.

I reject Shea's argument because it is built on several flawed premises. First, I cannot accept Shea's contention that a laboratory or industry error rate is the best evidence of whether a test was properly performed in a particular case. Juries must decide whether a particular test was performed correctly based on all of the relevant evidence. This determination can never be precisely guantified because it will often depend in part on subjective factors such as the credibility of the person who performed the test. At best, evidence of a laboratory's past proficiency should be considered as one of several factors in making this important judgment.^[42] See NRC II, supra, at 85-86 ("[t]he risk of error in any particular case depends on many variables (such as the number of samples, redundancy in testing, and analyst proficiency) , and there is no simple eguation to translate these variables into the probability that a reported match is spurious"). Shea's method for dealing with the probability of a false match is thus seriously flawed because it would deprive the jury of the opportunity to determine the probability of a false match based on all of the pertinent evidence.

Second, I am unconvinced by Shea's claim that a jury cannot properly assess the potential of a false match unless a false match error rate is calculated and combined with the random match probability estimate. Shea relies on testimony and research conducted by Dr. Jay Koehler43 to support this contention. Although Dr. Koehler's research suggests that jurors could become confused if evidence of a false match error rate and a random match probability estimate are presented with little or no explanation, it does not support Shea's broader contention that jurors cannot be made to understand such evidence even if it is properly explained. See NRC II, supra, at 199 (noting that "[t]he argument that jurors will make better use of a single figure for the probability that an innocent suspect would be reported to match never has been tested adeguately"). In a real trial setting, the parties are given an opportunity to explain the significance of statistical evidence through expert testimony. Further, if a trial judge concludes that jurors could be confused by statistical evidence, the judge can deliver carefully crafted instructions to insure that the evidence is properly understood. Notwithstanding Dr. Koehler's research, I am confident that the concerns Shea raises can be properly addressed through expert testimony and, if necessary, clarifying jury instructions.

Shea next argues that a random match probability estimate is inherently misleading because the jury inevitably will confuse the probability of a random match with the potentially very different probability that the defendant is not the source of the matching samples. This type of incorrect reasoning is often referred to as the fallacy of the transposed conditional, or the prosecutor's fallacy. NRC II, supra, at 133. The probability of a random match is the conditional probability of a random match given that someone other than the defendant contributed the evidence sample. The potentially different probability that someone other than the defendant contributed the sample given the existence of a match can only be determined by considering all of the evidence in the case.^[44] Shea argues, based on research conducted by Dr. Koehler, that the jury will inevitably confuse these two probabilities.

Although I acknowledge that a jury could become confused concerning the meaning and potential significance of a random match probability estimate, I am confident that the risk of confusion is acceptably small if the concept is properly explained. Moreover, because such an estimate can be extremely valuable in helping the jury appreciate the potential significance of a DNA profile match, it should not be excluded merely because the concept reguires explanation. Accordingly, I decline to exclude the government's random match probability estimate pursuant to Rule 403.

IV. After carefully considering Shea's motion to exclude the DNA evidence, I reached the following conclusions: (1) PCR is a scientifically sound technology that can be extremely helpful in resolving guestions of guilt or innocence. The theory and technigues used in PCR are sufficiently established that a court may take judicial notice of their general reliability. See Beasley, 102 F.3d at 1448 (taking judicial notice of general reliability of PCR testing) ; see also United States v. Martinez, 3 F.3d 1191, 1197 (8th Cir. 1993) (taking judicial notice of general reliability of DNA testing), cert, denied, 114 S. C t . 734 (1994); Jakobetz, 955 F.2d at 799 (taking judicial notice of reliability of DNA testing).

(2) The PCR tests used in this case readily satisfy Rule 702's reliability reguirement. Accordingly, disputes concerning the way in which the tests were conducted, while vitally important, are matters that should be left for the jury to resolve.

(3) Random match probability estimates calculated with the product rule provide an important means of placing the significance of a DNA profile match in an appropriate context. However, such estimates must be gualified to account for potential errors such as in the manner suggested by the NRC II report. The government satisfied this reguirement.

(4) When the significance of a random match probability estimate is properly explained, the probative value of the evidence is not substantially outweighed by the limited potential that jurors could be misled.

Accordingly, I denied the defendant's motion to exclude (document no. 15).

Paul Barbadoro United States District Judge March 18, 1997 cc: Bjorn Lange, Esg. Gary Milano, Esg. United States Marshal United States Probation

FIGURE 1

_____ Figure 1. "Diagram of the double-helical structure of DNA in a chromosome. The line shown in the chromosome is expanded to show the DNA structure." NRC I, supra, at 2. FIGURE 2 _____ Figure 2. "The primers used in the Polymerase Chain Reaction are chosen so that they bind to opposite ends of opposite strands of the DNA section to be amplified. In this over-simplified diagram, the primers are only 12 bases long, rather than about 20." Mange, supra, at 288. FIGURE 3 Figure 3. "The first two cycles of the Polymerase Chain Reaction." Mange, supra, at 289.