Population Genetics. Matthew B. Hamilton

21 0.0051 22 0.0026 FGA D8S1179 D5S818 D7S820 Allele freq Allele freq Allele freq Allele Freq 18 0.0306 <9 0.0179 9 0.0308 6 0.0025 19 0.0561 9 0.1020 10 0.0487 7 0.0172 20 0.1454 10 0.1020 11 0.4103 8 0.1626 20.2 0.0026 11 0.0587 12 0.3538 9 0.1478 21 0.1735 12 0.1454 13 0.1462 10 0.2906 22 0.1888 13 0.3393 14 0.0077 11 0.2020 22.2 0.0102 14 0.2015 15 0.0026 12 0.1404 23 0.1582 15 0.1097 13 0.0296 24 0.1378 16 0.0128 14 0.0074 25 0.0689 17 0.0026 26 0.0179 27 0.0102

Fortunately, we can combine the information from all three loci. To do this, we use the product rule, which states that the probability of observing multiple independent events is just the product of each individual event. We already used the product rule in the last section to calculate the expected frequency of each genotype under Hardy–Weinberg by treating each allele as an independent probability. Now, we just extend the product rule to cover multiple genotypes, under the assumption that each of the loci is independent by Mendel's second law (the assumption is justified here since each of the loci is on a separate chromosome). The expected frequency of the three‐locus genotype (sometimes called the probability of identity) is then 0.0689 × 0.0841 × 0.0084 = 0.000049 or 0.0049%. Another way to express this probability is as an odds ratio, or the reciprocal of the probability (an approximation that holds when the probability is very small). Here, the odds ratio is 1/0.000049 = 20 408, meaning that we would expect to observe the three locus DNA profile once in 20 408 Caucasian Americans.

      Product rule: The probability of two (or more) independent events occurring simultaneously is the product of their individual probabilities.

Now, we can return to the question of whether two unrelated individuals are likely to share an identical three‐locus DNA profile by chance. One out of every 20 408 Caucasian Americans is expected to have the genotype in Table 2.2. Although the three‐locus DNA profile is considerably less frequent than a genotype for a single locus, it still does not approach a unique, individual identifier. Therefore, there is a finite chance that a suspect will match an evidence DNA profile by chance alone. Such DNA profile matches, or “inclusions,” require additional evidence to ascertain guilt or innocence. In fact, the term prosecutor's fallacy was coined to describe failure to recognize the difference between a DNA match and guilt (for example, a person can be present at a location and not involved in a crime). Only when DNA profiles do not match, called an “exclusion,” can a suspect be unambiguously and absolutely ruled out as the source of a biological sample at a crime scene.

      Current forensic DNA profiles