The 1996 NAS Report
James F. Crow
Genetics Department, University of Wisconsin, Madison, WI 53706
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The new report, "The Evaluation of Forensic DNA Evidence" (NRC 1996), took longer than any of us anticipated. I was appointed to chair the Committee in September 1993. The members were not selected until the fall of 1994, the delay being caused mainly by the Academys not having the necessary funds in hand. Eventually, the study was supported by The National Institute of Justice, the State Justice Institute, the National Science Foundation, the National Institutes of Health, and the Department of Energy. We had four meetings in late 1994 and early 1995; one was public, with comments invited. We had a draft report prepared in May 1995. The long process of editing, receiving and responding to reviews, and revising took another year, so that the Prepublication Copy did not appear until May 2, 1996. The final volume, which is unchanged except for minor corrections and revised wordings, is expected in mid-October. (Since the meeting I have learned that the expected date is now mid-November.)
Generally, the response to the report and its recommendations has been favorable, both from the official reviewers and those who have commented on the document after its publication. Some thought the report too technical; others wanted more technical details. We obviously cannot satisfy both. One reviewer said we had not given enough attention to the latest literature, meaning, I think, some of the reviewers papers. We have received strong criticism from a Bayesian statistician, who wanted the report couched in Bayesian terms. But whatever the statistical merits of the Bayesian philosophy, I believe it is not acceptable in American courts. One critic charged that we were "bought" by the Department of Justice. I can only respond that if we are for sale our price is remarkably low, for we were not paid for taking on this assignment. Let me add that I found the job challenging and time-consuming, but interesting. I learned a lot.
The Committee consisted of 2 human geneticists, 2 statisticians, 3 population
geneticists,
1 forensic scientist and 3 lawyers. Two members of the committee were hold-overs from the
1992 Committee and, in addition, its Chairman, Victor McKusick, served as an advisor. The
main body of the report includes 6 chapters, glossary, references, and numerical examples.
In response to those who desired a less technical report, we have provided a long
Overview, intended to be reader-friendly. Finally, for those with especially short
attention spans, we have provided a succinct Executive Summary.
COMPARISON WITH THE 1992 REPORT
In many ways our report agrees with its 1992 predecessor. In particular, the two agree in their emphasis on laboratory quality control, proper training, accreditation, and regular proficiency tests. Both emphasize the importance of retaining materials and keeping duplicate samples so that repeat tests can be made. Here I shall emphasize only those areas in which the two reports differ importantly.
Our assignment was less broad than that of the 1992 Committee. Issues such as confidentiality and security, storage of samples for possible future use, legal aspects of data banks on convicted felons, non-DNA information in data banks, availability and costs of experts, economic and ethical aspects of new DNA information, accountability and public scrutiny, and international exchange of information were not in our charge. Our report deals mainly with laboratory accuracy, population genetics and statistics.
Finally, we recognize that technical advances in this field are very rapid and that current procedures, such as VNTRs, may soon be replaced by those with fewer statistical uncertainties. We can expect future methods to be more reliable, less expensive, and less time-consuming than those currently in use. We also expect more rapid and more efficient development of population databases, often making use of DNA already in storage. For such reasons, our report is somewhat less prescriptive than the 1992 report. In a rapidly changing field, we rely on the DNA Advisory Board (DAB) and the Technical Working Group on DNA Analysis and Methods (TWGDAM) for continuous updating and revising of our recommendations as knowledge and techniques improve.
PARENTAGE TESTING
Neither the 1992 nor the 1996 report includes much about paternity testing. The basic techniques are the same as for forensic identification. Nevertheless, there are three important differences. First, mutation is a factor to be taken into account in paternity testing, but is ordinarily not a concern in forensic identification. Second, paternity testing involves analysis of genetic relationships of child, mother, putative father, and perhaps others; crime investigations involve the genetically simpler problem of determining whether two DNA samples came from the same person. Third, in paternity cases, for such things as child support and custody, the law gives the different parties roughly equal weight, whereas in criminal cases a much higher standard of proof is required. The 1992 report's recommendation of conservative population and statistical procedures was motivated by the legal requirement for proof beyond reasonable doubt. Therefore, the recommendations are inappropriate in civil cases. In particular, the ceiling principles were not intended for paternity testing and their use in civil parentage disputes is contrary to the intent of the 1992 Committee. Likewise, our recommendations are intended to apply to criminal forensic tests, not civil cases.
ADMISSIBILITY
Much of the litigation in the past has been over the admissibility of DNA evidence. We believe and hope that this can become a thing of the past. Our report says: "The state of the profiling technology and the methods for estimating frequencies and related statistics have progressed to the point where the admissibility of properly collected and analyzed DNA data should not be in doubt."
Of course there is always room for differences of interpretation of the evidence, but the discussion, we believe, should be on the weight of the evidence, not its admissibility.
TYPICAL PROBLEMS
The DNAs Match
In a typical case, a sample of DNA from a suspect matches that from the crime scene. There are three possibilities:
The DNAs Do Not Match
If the DNAs do not match, either they came from different persons or an error has been made. Typically, a non-match is regarded as decisive evidence that the two DNAs came from different persons. No profile frequency estimates or statistical interpretations of match probabilities are needed.
According to the FBI data compilation, about one third of prime suspects in rape cases are wrongly accused. A prompt exclusion of innocent suspects can save a great deal of time and money, to say nothing of human anguish.
MAINTENANCE OF HIGH LABORATORY STANDARDS
It is of utmost importance that the highest standards of care and objectivity be maintained throughout the whole process, from gathering the sample at the crime scene to final analysis and presentation in court. The highest standards of quality control and quality assurance are a must.
We recommend: (1) adherence to high standards; (2) regular audits, internal and external; (3) accreditation; and (4) proficiency tests. The report makes specific suggestions for detecting and eliminating faulty equipment or technique, for dealing with possible evidence contamination, and possible conscious or unconscious analyst bias.
We believe that some of the proficiency tests should be blind. We recognize, however, that the logistics of conducting a convincing blind proficiency test are very difficult. It is likely that laboratory personnel will be astute enough to guess that a sample to be analyzed is in fact a blind test. The most important argument for blind tests, we believe, is that they are a way of keeping a laboratory on its toes. We emphatically believe, however, that blind tests should not be used as a way of estimating the laboratory error rate. The cost in money and time of the number of such tests needed to provide useful numerical data make this out of the question.
Some observers have advocated that the estimated laboratory error rate be combined with match probabilities. We reject this suggestion. Laboratory errors in the past are a poor indicator of the present rate, for past errors often lead to a correction of the faulty procedure or circumstance. We offer a better alternative, namely the opportunity for repeat tests.
Specifically, our Recommendation 3.3 reads: "Whenever feasible, forensic samples should be divided into two or more parts at the earliest practicable stage and the unused parts retained to permit additional tests. The used and saved portions should be stored and handled separately. Any additional tests should be performed independently of the first by personnel not involved in the first test and preferably in a different laboratory."
In short, the best protection that an innocent suspect has against a false accusation is the opportunity for a duplicate test.
CONVENIENCE SAMPLES
In principle, population samples should be chosen by some kind of random process. This permits the standard statistical methods of analysis. In practice, random samples are impractical, and not necessarily desirable. The requisite machinery to guarantee a random sample is cumbersome at best, and probably unrealistic. And if we want a random sample, what population do we sample from? Do we want a random sample of the whole population? Or would we prefer to sample those in the age group most likely to be involved in crimes? Should it be local or national? Should we restrict the sample to males?
In practice, we rely on convenience samples to provide the database. These data come from paternity testing laboratories, blood banks, hospitals, genetics laboratories, law enforcement staff, and persons charged with crimes. Loci chosen for forensic databases are usually not functional genes. VNTRs, for example, have no phenotype and are probably selectively neutral or very close to it. Loci that are associated with functional genes, such as some STRs, can be tested for randomness. In any case, the markers chosen for forensic use have no overt phenotype and obviously are not the basis for mate choice. Furthermore, there are no consistent differences between data from different sources. We concluded that such convenience samples are entirely appropriate and that, to a satisfactory approximation, can be treated statistically as if they were random.
In our analysis of data from different geographical and ethnic groups, we found the differences to be small, although there are somewhat larger differences between the major races. We find such agreement more convincing than the theoretical arguments against any but random samples. So, in our report, we made full use of convenience samples.
POPULATION GENETICS
The frequency of any multi-locus profile is usually so small that it is almost never found in any database. One is forced to deal with the zero frequencies in some arbitrary way. But, instead we can use population genetics theory to calculate profile frequencies from the frequencies of the constituent alleles.
The simplest theory, and the starting point for any discussion, assumes that the population frequencies are equivalent to those under random mating. For a single locus this leads to the Hardy-Weinberg (HW) proportions. If pi and pj stand for the frequencies of alleles Ai and Aj the expected genotypic proportions are
AiAi : pi2 (homozygotes)
AiAj : 2pipj (heterozygotes)
For multiple loci, the simplest assumption is that the loci are in linkage equilibrium (LE). This implies that the frequency of any multi-locus genotype is the product of the individual locus expectations. This simple manner of calculation is termed the product rule or the multiplication rule.
Of course the United States population is not choosing mates at random. For one thing, persons in Oregon are much more likely to choose a person from Oregon than from Tennessee. Yet, if the allele frequencies in Oregon and Tennessee are the same, the distance is irrelevant. The important consideration is that the forensic markers not be part of the criteria by which mates are chosen. This is best assured if the markers are unknown to the person carrying them. It is also important that the marker loci not be associated with any important function; for example, a gene producing malaria resistance would be more common in persons whose ancestry is from regions where malaria is common. The most important cause of departure from the assumptions is population subdivision. The United States population is a mixture of people of various origins, and these are not thoroughly mixed. Hence, there may be regions or ethnic groups with different allele frequencies. I shall deal with this later.
An example of a good marker is the M-N blood locus. Of course, most people don't know their MN blood groups and those who do are not likely to use this as a basis of mate choice. There are only two alleles and their frequency is close to 1/2, making detection of departures from HW ratios near maximum. Table 1 shows data from New York City, totaling 6001 persons (12002) genes. These were gathered at 6 times between 1931 and 1969. The sources are patients, hospital staff, blood donors, and persons involved in paternity cases. New York whites are far from a homogeneous population, yet the deviation from expectation is very small (an excess of 0.99% heterozygotes, and a corresponding deficiency of 0.96% in homozygotes). The c2 value for the total is not significant, nor are those of any of the six samples. VNTR data are comparable.
To illustrate the close approach to LE in forensic markers, Table 2 shows data from the large compilation by TWGDAM. The single-locus match frequencies were obtained from the data, and from these the expected frequencies of two- and three-locus matches were obtained by simple multiplication. As the table shows, the observations are very close to the expectations when the numbers are large enough to provide statistical reliability. The only important departure from LE is found in the American Indians. This is not surprising, given the tribal structure of this population. This means that these populations have to be treated differently, and our recommendations consider this.
The combined TWGDAM data for 7201 whites, 4378 blacks, and 1243 Hispanics give, when paired within groups, 58 million pairs. Among these there were no five- or six-locus matches and only two matching at four loci. These are comparisons run on different gels; if they had been run in parallel columns on the same gel, the four locus matches might have been declared a visual non-match. Or there might be brothers in the database. In any event, the important point is that multiple-locus matches are exceedingly rare.
HOW ACCURATE ARE FREQUENCY ESTIMATES?
The numbers in the databases are only estimates and are subject to various inaccuracies. If it is assumed that convenience samples can be treated as random samples, we can then apply the standard statistical procedures and obtain confidence limits for multi-locus profiles. Our report discusses this and describes the calculations.
We believe, however, that this is almost certain to be an underestimate of the true uncertainty, which involves many other possibilities for error. So, instead, we resorted to empiricism. For example, the database may be from the United States as a whole whereas the crime was committed in Georgia. How large an error would be involved if the U.S. data were used instead of local data? Figure 1 shows such an example. Each dot in the scatter graph corresponds to the frequency in two populations. The abscissa is the frequency calculated from the Georgia database; the ordinate is the value from the United States database. In both cases, the product rule was used. As the graph shows, the dots fall rather close to the 45 degree line of perfect agreement. All of the points are within the two parallel lines, which represent deviations of 10 fold in either direction.
The United States white population is a collection from various European populations, certainly not completely mixed. The melting pot is a better metaphor than description of reality. Rather than compare American localities with different European origins, we have used data from Europe. The differences ought to be greater than among the American descendants, which are partially mixed. So this procedure should provide a conservative estimate of the uncertainty. Suppose the evidence sample is from a community of largely Danish ancestry. How large is the error if the database from the United States as a whole is used? Figure 2 provides such a test. Again, the uncertainty from using an inappropriate database is less than 10-fold in either direction.
We conclude that, in general, a profile frequency estimate made from a database is not likely to be wrong by more than a factor of 10 in either direction. If the estimated frequency is one in 10 billion, the true value is not likely to lie outside the range one in 1 billion and one in 100 billion. We suggest that this be used as a guide to the degree of uncertainty in the calculations.
Such graphs suggest that the profiles with very small probabilities those at the upper right may deviate by a larger amount. This doesn't seem too important, however; if the estimated match probability is 10-12, it is not a matter of great moment if the error is greater than 10 fold. The uncertainty appears to be smaller near the lower left of the graph, that is with higher probabilities. These involved profiles based on small numbers of loci. Especially if these involve PCR loci, it may be that more accurate formulae could be used, but we dont discuss them. Such methods should, I believe, continue to be empirical rather than theoretical.
INBREEDING AND SUBDIVIDED POPULATIONS
One problem that sometimes arises is that there is a relative of the suspect in the pool of possible suspects. In most cases, the direct determination of the profile of the relative will answer the question. If this is not feasible, then there are formulae from population genetics that give the conditional probability of the same profile in a relative of specified relationship. I won't give the formulae here; they are in the report. A possible problem is that there may be half-brothers with the same father but different mothers in the population, and they may not know they are related. If this seems probable, the match probability can be modified to include such half-sibs, provided there is some estimate of how frequent they might be.
Despite the close approach to HW and LE proportions that I have just mentioned, there is still likely to be some structure in the population. The population is almost certain to be subdivided to some extent, although the differences between such subdivisions may be slight and the borders between subdivisions fuzzy. Individuals within a subdivision tend to be somewhat related to each other, and the population therefore somewhat inbred. To take this into account, we can rewrite the standard HW formulae as follows:
AiAi: pi2 + pi(1 - pi)q (homozygotes)
AiAj: 2pipj(1 - q) (heterozygotes)
q is a quantity that may vary in magnitude for different alleles, but which is almost always positive. It may be determined empirically, and the values usually are considerably less than 0.01. Hence, the modification makes little difference unless the allele frequencies are very small.
There may also be departures from LE, but these occur in both directions, so we do not introduce any systematic correction to the product rule.
CONSERVATIVE ADJUSTMENTS
In our legal system it is regarded as a much more serious error to convict an innocent person than to acquit a guilty one. Hence, our report followed the policy that when there are uncertainties, we should err on the conservative side that is in favor of the defendant.
Using the simple HW formula will underestimate the frequency of homozygotes (since q is positive) but will overestimate the frequency of heterozygotes. Hence a conservative adjustment is:
For homozygotes, use pi2 + pi(1 - pi)q.
For heterozygotes, use 2pipj .
A value of 0.01 is suggested for q. Some commentators have suggested that a value of 0.03 be used, and those who want to be especially conservative may opt for this.
These adjustments are appropriate for PCR systems where the genotypes are unambiguously determined. For VNTRs there can be doubt as to whether a single band represents a true homozygote or a heterozygote in which the second band is missing or not resolved. In this case, we recommend following the standard practice of using 2pi rather than pi2 for single bands.
EVIDENCE SOURCE AND SUSPECT FROM THE SAME SUBPOPULATIONS
If there is good reason to think that the source of the evidence DNA and the suspect are from the same small population, we recommend using conditional probabilities for the genotypes. The appropriate formulae are

Notice that when q = 0, these reduce to the standard HW formulae. A value of q = 0.01 is suitable, although a value of 0.03 might be used if the subpopulation is thought to be very small.
Some have suggested that such formulae always be used because of the possibility that the two sources (if different) may be from the same small subgroup without our knowing it. We believe that this is unnecessarily conservative, but this alternative is available for those who prefer such conservatism.
MATCH PROBABILITY vs. LIKELIHOOD RATIO
The likelihood ratio is the probability of the observed profile if the evidence and suspect sample came from the same person divided by the probability if the evidence and suspect samples are from two different persons.
In simple cases, the numerator is one. The possibility of laboratory error might make it slightly less than one, but this difference is swamped by the much greater uncertainty of the denominator. The denominator is the same as the match probability. Hence, the likelihood ratio is simply the reciprocal of the match probability. Stated this way, there is little reason to prefer one or the other; they contain the same information.
The likelihood ratio has a very useful property, however. According to Bayes Theorem
Posterior Odds = Prior Odds ´ Likelihood Ratio.
The prior odds are the odds that the suspect is the origin of the sample in the absence of the evidence provided by DNA analysis. The posterior odds are the odds when the DNA evidence is taken into account. In words: whatever you think the odds are that the suspect provided the crime-scene DNA, these odds are multiplied by the likelihood ratio when the DNA calculations are taken into account.
This way of looking at the problem is very appealing, for it answers the question we really want answered: What is the probability that the suspect is the source of the evidence? Yet the courts have been reluctant to accept this, partly because of the difficulty in determining appropriate prior odds, especially when a jury is asked to do so. One practice that has been advocated is to give the court the posterior odds for a range of prior odds. It is often the case that the likelihood ratio is large enough that reasonable alternative values of prior odds make little difference in the conclusion.
We do not necessarily advocate such a procedure. We note, however, that Bayes Theorem is routinely used in paternity analysis. Perhaps it will come into increasing use by the forensic community.
UNIQUENESS
The 1992 Report specifically stated that an expert should avoid any statement that a
profile is unique in the population. Yet, when the probability of a random match to an
evidence profile is, say,
10-10, one realizes that there is an appreciable probability that the profile
will not again be found in the world population. How should we approach this problem?
Let P be the probability of the evidence profile. The probability that this profile will fail to occur in a population of N additional profiles is (1 - P)N. Suppose N is the United States population, say 250 million, and the profile frequency is 10-10. (1 - P)N > 1 - NP, or in this case 39/40. The probability that the profile is unique then is at least 39/40.
There may be a legal or political decision that, say, a probability less than 1/10 the reciprocal of the United States population constitutes uniqueness. Our report does not define a probability level for uniqueness, but if this is defined, we show how to make the calculation. It is important, I believe, for such a decision to be in terms of match probability, not number of loci, since allele frequencies vary.
IDENTIFICATION BY DATABASE SEARCH
Increasingly, suspects are being discovered by a database search that reveals a profile matching that of the evidence sample. The 1992 report suggests that those loci used to identify the suspect not be used to determine the match probability or the likelihood ratio. There is the risk, however, that this may not leave enough markers for an adequate calculation. Of course, with the multiplication of markers, this may soon cease to be a problem.
The procedure advocated by our report is to note that if P is the frequency of the profile, then by the reasoning of the section above, the probability of finding at least one match in a database of size N is < NP. So the rule is to multiply the match probability by the number in the database searched (or divide the likelihood ratio by N).
As databases get to be larger so that NP is of the order one or greater, a more careful rule is needed. Clearly, if N is the entire population, the solution is obvious. The profile either does or does not exist in the population, and no probability calculation is needed.
This section of our report has been strongly criticized by some Bayesians. Those who wish to follow the argument may refer to the writings of David Balding and Peter Donnelly.
THE INTERIM CEILING PRINCIPLE
No part of the 1992 report generated as much discussion and criticism as the two ceiling principles. In particular, the interim ceiling has been especially controversial. (The ceiling principle argument has disappeared by default; no one has undertaken the sampling of 15-20 populations called for in the reports recommendation.) The interim ceiling principle was introduced in order to find a simple procedure that was independent of the racial origin of the profile. It says: "In applying the multiplication rule, the 95% upper confidence limit of the frequency of each allele should be calculated for separate US racial groups and the highest of these or 10% (whichever is the larger) should be used. Data on at least three major races (e.g. whites, blacks, Hispanics, east Asian, and American Indians) should be analyzed." Loci were to be used only when there was no significant departure from HW and LE.
There have been a number of criticisms: (1) The 10% value is arbitrary and has no scientific grounds. (2) Confidence limits are multiplied, which is contrary to standard statistical usage. (3) The method does not make use of all the data. (4) The method does not make use of population genetics theory. (5) The result is usually very conservative, unnecessarily so, many believe. (6) The procedure has lent itself to creative misuse by finding numbers favorable to a particular view; for example, reference populations can be selected to have the desired frequencies. (7) The method discriminates against the most reliable data, since small databases are most likely not to differ significantly from HW ratios. For these and other reasons, our Committee stated that the interim ceiling principle is not necessary.
We recognize, however, that the interim ceiling principle may continue to be used. If so, we recommend the following modifications, mostly taken from reports of TWGDAM: (1) With fixed bins, when bins are overlapped by the match window, use the frequency of the largest, not the sum. (2) Do not use American Indians or other highly subdivided groups for database frequencies. (3) Use 1.64 rather 1.96 as the 95% confidence coefficient since this is a one-tailed interval. (4) Use this only in criminal, not civil cases; in particularly the interim ceiling principle is not appropriate for parentage testing. (5) Use the method only for loci, such as VNTRs, with many alleles, such that no one is common. (6) Use all loci, not just those not departing significantly from HW ratios.
CONCLUDING REMARKS
It is now clear that our report did not give sufficient attention to PCR systems, such as STRs, which are rapidly becoming the methods of choice. In addition to technical advances, recent months have seen increasing amounts of population data, showing essentially the same agreement with HW and LE that VNTR data have shown. We emphasized in the report that loci chosen for forensic work should not be disease-causing genes or be closely linked to these. We realized, of course, that as the human chromosome map becomes more dense, almost every site will be linked to some gene. In particular, several STRs are associated with functional genes. This means that they need to be tested for agreement with HW ratios, and of course not be linked to each other. These criteria are increasingly being met. (Since this is a Promega Symposium, Ill note that the nine fluorescent STR loci described in the Technical Manual of 2/96, when combined, show close agreement with HW ratios. The average deviation in heterozygosity from the expectations is about 0.3%.)
As a rule, we have opted for the simpler procedures as long as these are good approximations. We have been conscious of the fact that our findings and recommendations are for the use of the courts, and excessive refinements would be counter-productive. We have, however, tried to be clear and understandable and to advocate procedures that are readily understood and followed. At the same time, we have tried not to distort by over-simplification.
In general, our report has not been very prescriptive, probably less so than the 1992 report. Increasingly, I am convinced that this was a wise course, for the technology changes very rapidly as does the gathering of adequate databases for the newer systems. In such a rapidly changing field many details of our report will become obsolete. But, the general principles should stand and I count on the DNA Advisory Board and TWGDAM to update our findings and recommendations continuously as the field changes. I hope there will not be a need for another NRC Report four years hence.
As I said earlier, the 1992 report was roundly criticized and statements in the report were misinterpreted, sometimes intentionally. We hoped to write a report that would not be readily misinterpreted and would lead to greater agreement, especially for quantitative estimates. I have no illusions that our report will eliminate the controversy; the adversary system guarantees its continuance. Yet, I hope and believe that we have established a solid basis for acceptable procedures that can be modified as new techniques and data require. I anticipate a time in the not-distant future when DNA analysis will be as acceptable as dermal fingerprints now are.
Finally, let me enter a disclaimer. I have tried to reflect correctly the views of the Committee and the contents of the report, but in a few cases I have introduced personal opinions. These are of course my own responsibility, as are any errors in summarizing the report.REFERENCE
NRC 1996. The Evaluation of Forensic DNA Evidence. Committee on DNA Forensic Science: An Update. National Academy Press, Washington, DC.
Table 1. MN Blood Group Frequencies in the New York City White Population (from NRC 1996)
| Genotype | Observed | Expected | % Deviation |
| MM | 1851 | 1865.6 | -0.78 |
| MN | 2990 | 2960.7 | +0.99 |
| NN | 1160 | 1174.6 | -1.24 |
| Total |
6001 |
6000.9 |
c2 = 0.74, D. F. = 1, Prob = 0.35
Table 2. Two- and Three-locus Matches in TWIGDAM Data (from NRC 1996)
Two Loci |
Three Loci |
|||
| Observed | Expected | Observed | Expected | |
| White | 33,131 | 33013 | 291 | 321 |
| Black | 5,246 | 5,137 | 39 | 35 |
| Hispanic | 1,609 | 1,568 | 25 | 18 |
| East Asian | 864 | 830 | 13 | 6 |
| American Indian | 2,320 | 1,964 | 66 | 32 |

Figure 1. A scatter plot for the U. S. black population. Each point represents a specific profile of from one to four VNTR loci. The abscissa gives the estimated frequency in the Georgia population and the ordinate that of the United States. The upper and lower lines represent values that deviate from equality by a factor of 10 (from NRC 1996; data from FBI).

Figure 2. A scatter plot for the white population. The abscissa gives estimated frequencies in the U. S. and the ordinate the frequencies of the same profiles in Denmark (from NRC 1996; data from FBI).
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