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be known that the DNA came from a white person, in which case the white database is appropriate. 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. Alternatively, if a single number is preferred, one might present the calculations for the major racial group that gives the largest probability of a match. Similar procedures can be used for persons of mixed ancestry.

If it is known that the contributor of the evidence DNA and the suspect are from the same subpopulation and there are data for that subpopulation, this is clearly the set of frequencies to use to obtain the most accurate estimate of the genotype frequency in the set of possible perpetrators of the crime. Of course, the database should be large enough to be statistically reliable (at least several hundred persons), and rare alleles should be rebinned (see Chapter 5) so that no allele has a frequency less than five. The product rule is appropriate, in that departures from random mating within a subgroup are not likely to be important (and, as mentioned above, this is supported empirically). The use of the 2p rule makes the product rule conservative.

Some have argued that even if there is no direct evidence, it should be assumed for calculation purposes that the person contributing the evidence and the suspect are from the same subgroup (Balding and Nichols 1994). Even though it is not known to which subpopulation both persons belong, Balding and Nichols assume that the two are likely to be more similar than if they were chosen randomly from the population at large. In our view, that is unnecessarily conservative, and we prefer to make this assumption only when there is good reason to think it appropriate—for example, if the suspect and all the possible perpetrators are from the same small, isolated town. Most of the time, we believe, the subgroup of the suspect is irrelevant.

To continue with the assumption that the person contributing the evidence and the suspect are from the same subgroup, an appropriate procedure is to write the conditional probability of the suspect genotype, given that of the perpetrator. As before, we measure the degree of population subdivision by , although a single parameter is not sufficient to describe the situation exactly. A number of formulae have been proposed to deal with this (Morton 1992; Crow and Denniston 1993; Balding and Nichols 1994, 1995; Roeder 1994; Weir 1994). They depend on different assumptions and methods of derivation but agree very closely for realistic values of and p.15 The simplest of the more accurate formulae is due to Balding and Nichols (1994, 1995):

(4.10 a)

¹⁵ Deriving a formula for these conditional probabilities requires some assumption about the population structure. Some models that have been used are a pure random-drift model, a mutation-drift, infinite-allele model, or a mathematically identical migration-drift infinite-allele model; or

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