by straightforward counting have the virtue that they do not depend on theoretical assumptions, but simply on the samples having been randomly drawn from the appropriate population. However, such estimates do not take advantage of the full potential of the genetic approach.

In contrast, population frequencies often quoted for DNA typing analyses are based not on actual counting, but on theoretical models based on the principles of population genetics. Each matching allele is assumed to provide statistically independent evidence, and the frequencies of the individual alleles are multiplied together to calculate a frequency of the complete DNA pattern. Although a databank might contain only 500 people, multiplying the frequencies of enough separate events might result in an estimated frequency of their all occurring in a given person of 1 in a billion. Of course, the scientific validity of the multiplication rule depends on whether the events (i.e., the matches at each allele) are actually statistically independent.

Because it is impossible or impractical to draw a large enough population to test directly calculated frequencies of any particular DNA profile much below 1 in 1,000, there is not a sufficient body of empirical data on which to base a claim that such frequency calculations are reliable or valid. The assumption of independence must be strictly scrutinized and estimation procedures appropriately adjusted if possible. (The rarity of all the genotypes represented in the databank can be demonstrated by pairwise comparisons, however. Thus, in a recently reported analysis of the FBI databank, no exactly matching pairs were found in five-locus DNA profiles, and the closest match was a single three-locus match among 7.6 million pairwise comparisons.)

The multiplication rule has been routinely applied to blood-group frequencies in the forensic setting. However, that situation is substantially different. Because conventional genetic markers are only modestly polymorphic (with the exception of human leukocyte antigen, HLA, which usually cannot be typed in forensic specimens), the multilocus genotype frequencies are often about 1 in 100. Such estimates have been tested by simple empirical counting. Pairwise comparisons of allele frequencies have not revealed any correlation across loci. Hence, the multiplication rule does not appear to lead to the risk of extrapolating beyond the available data for conventional markers. But highly polymorphic DNA markers exceed the informative power of protein markers and so multiplication of their estimated frequencies leads to estimates that are far less than the reciprocal of the size of the databanks, i.e., 1/N, N being the number of entries in the databank.

The multiplication rule is based on the assumption that the population does not contain subpopulations with distinct allele frequencies—that each person's alleles constitute statistically independent random selections from



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