Attribution

DNA evidence can be infuriating, particularly if you're a criminal defendant.

(Henry Lee and Frank Tirnady, Blood Evidence, 2003)

It would not be scientifically justifiable to speak of a match as proof of identity in the absence of underlying data that permit some reasonable estimate of how rare the matching characteristics actually are.

When a match is observed between an evidence sample (the 'unknown' or question sample - Q) and a reference sample (the 'known' - K), then statistical methods are typically invoked to provide information regarding the relevance of this match. The prosecution advocates to the court that the Q and K samples have a common source while the defense typically argues that the samples happen to match by chance. The possibility of another unrelated individual pulled at random from the population possessing an identical genotype can be determined by calculating the frequency with which the observed genotype occurs in a representative population database (see Chapter 20). When a DNA profile is fairly common, then it is easier to imagine that the suspect might not be connected to the crime scene. If on the other hand, the genotype is found to be extremely rare, then the evidence is stronger that the suspect contributed the crime scene sample in question.

As described in Chapter 20, a number of population databases have been generated in recent years to which a DNA profile may be compared (e.g., Budowle et al. 2001). The U.S. population data shown in Appendix II (Butler et al. 2003) will be used throughout this chapter to illustrate the values for various allele frequencies. For calculations performed in one's own laboratory, a relevant population database, usually specific to possible populations in one's local area, would be used instead.

It is important to keep in mind that methods for reporting DNA evidence vary between laboratories. Some laboratories present random match probabilities that are based on genotype frequency estimates. Another approach is to report likelihood ratios to convey relative support for the weight of DNA evidence under the hypothesis that the defendant is the source of the DNA profile versus an unrelated individual from the population at large. The Federal Bureau of Investigation (FBI) Laboratory has opted for a source attribution approach when random match probabilities are sufficiently rare. In this chapter, we will discuss the issues surrounding each approach and go through the statistical calculations performed with each method.

FREQUENCY ESTIMATE CALCULATIONS

DNA profile frequency estimates are calculated by first considering the genotype frequency for each locus and then multiplying the frequencies across all loci. The most effective method to understand how the probability of a random match is calculated is to work through an example. The frequency for any DNA profile can be calculated with knowledge of the alleles from the DNA profile and allele frequencies seen in a population database. Of course a different size database or one with different allele frequencies can result in a different expected genotype frequency for each tested locus and hence a different DNA profile frequency. It is therefore important that the database used is large enough and representative of the population of the suspect(s).

In Table 21.1 the DNA profile frequencies for three short tandem repeat (STR) loci are determined using allele frequencies from two different databases. One database contains 302 U.S. Caucasians or 604 measured alleles (Table 21.1a) and the other contains 140 U.S. Hispanics or 280 measured alleles (Table 21.1b). Both a paternal and a maternal allele are counted when considering autosomal markers (see Chapter 2). The DNA profile in question contains the following alleles: 11 and 14 at D13S317 (heterozygous), 6 at TH01 (homozygous), and 14 and 16 at D18S51 (heterozygous).

In the population sample of 604 alleles (302 U.S. Caucasian individuals), allele 11 for D13S317 was observed 205 times or 34% of the time (Table 21.1a). (Note that in Appendix II, allele 11 for D13S317 is listed as 0.33940. Thus, the number of significant figures has been reduced for this example.) The frequency of allele 11 for D13S317 can therefore be recorded as p = 0.34. In other words, we can assume that there is a 34% chance that any particular D13S317 allele selected at random from an unrelated individual will be an 11. In the same manner, the chance for observing an allele 14 is q = 0.05 since this allele was seen 29 times in 604 allele measurements (in Appendix II this value is listed as 0.04801).

If the individual with the 11,14 D13S317 genotype received these alleles at random from each of his parents, then the chance to receive an 11 from his mother and a 14 from his father is pq and to receive the 14 from his mother and the 11 from his father is another pq. With either combination possible, the probability to be 11,14 by chance is pq + pq or 2pq. Plugging the frequency

(a)

DNA Profile

Allele Frequency from Database

Genotype Frequency

for Locus

Locus Alleles

Times Allele Size of Frequency

Formula Number

Observed Database

D13S317 11 14

205 29

0.03

TH01

0.05

D18S51

14 16

0.04

Profile Frequency = 0.000060 1 in 17 000

Table 21.1

Example calculation of the DNA profile frequency or random match probability using alleles from three STR loci.(a) The database used in this case involves 302 U.S. Caucasian individuals or 604 measured alleles (Appendix II). (b) The database used in this case involves 140 U.S. Hispanic individuals or 280 measured alleles (Appendix II).

(b)

DNA Profile

Allele Frequency from Database

Genotype Frequency

for Locus

Locus Alleles

Times Allele Size of Frequency

Formula Number

Observed Database

D13S317 11 14

66 13

0.02

TH01

0.04

D18S51

14 16

39 38

0.04

Profile Frequency = 0.000032 1 in 31 000

p values of p = 0.34 and q = 0.05 into the formula 2pq (2 X 0.34 X 0.05) results in an estimated genotype frequency of 0.034 or in other words approximately 3% of people from a Caucasian population are expected to have an 11,14 genotype at the D13S317 locus. Conducting the same analysis with a U.S. Hispanic database will result in a similar genotype frequency of 0.02 or 2% (Table 21.1b).

With the TH01 locus, a homozygous allele 6 was observed (Table 21.1). The same comparison of the profile's observed allele to a measured allele frequency in a population database is performed with TH01 but in this case the combined probability of inheriting allele 6 from both parents is pp or p2 (see Chapter 19). Since allele 6 was observed 140 times out of 604 allele measurements in U.S. Caucasians, p = 0.23 and p2 = 0.05 (Table 21.1a). Likewise, in the U.S. Hispanic population, p = 0.21 and p2 = 0.04 (Table 21.1b).

Since these two STR loci are on separate chromosomes (e.g., chromosome 13 for D13S317 and chromosome 11 for TH01, see Table 5.2), they will segregate independently during meiosis allowing the genotype frequencies to be multiplied. In the case of a U.S. Caucasian population, the chance of a person having the combined genotype of 11,14 at D13S317 and 6,6 at TH01 is 5% of 3% (i.e., 0.05 X 0.03) or 0.15%. Similar calculations for the D18S51 locus with alleles 14 and 16 result in an estimated genotype frequency of 4% (Table 21.1a). The combined profile frequency with these three loci thus becomes 0.000060 - the product of the three individual genotype frequencies (0.03 X 0.05 X 0.04) or about 1 in 17 000. Note that when using the Hispanic database, the DNA profile frequency in this example drops to 0.000032 (0.02 X 0.04 X 0.04) or about 1 in 31 000 individuals (Table 21.1b).

As more and more loci match during a Q and K sample comparison, it becomes less and less likely that an unrelated, random person in the population contributed the crime scene sample. Thus, either the suspect contributed the evidence or a very unlikely coincidence happened. Later in this chapter and also in Chapter 23 we will consider the impact of a related individual on the DNA profile frequency estimate calculations.

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