The lack of population structuring with allele frequencies in HardyWeinberg equilibrium and linkage equilibrium (see Chapter 20)justifies the assumption that genotypes are independent at unlinked loci. With the assumption of independence, it then becomes possible to equate the overall match probability with the product of the locusspecific match probabilities. This combination of locusspecific match probabilities is referred to as the product rule. In other words, the match probability for the STR locus D13S317 can be combined with additional STR loci such as TH01 and D18S51 to decrease the odds of a random match to an unrelated individual.
Table 21.2 calculates the match probabilities for all 13 CODIS loci with the same STR profile using the three different U.S. population databases contained in Appendix II. Since the STR profile used for these examples is from a Caucasian and is present in the Appendix II allele frequency database, the Caucasian population is expected to provide the most common frequency estimate. This turns out to be the case where the calculated STR profile frequency estimates are 1.20 X 1015 using the Caucasian allele frequencies and 6.04X 1017 and 5.57 X 1017 using the AfricanAmerican and Hispanics allele frequencies, respectively (Table 21.2). As noted by Weir (2003), focusing on a suspect's racial group in the calculations has an element of conservativeness.
Table 21.2 Random match probabilities with all 13 CODIS loci
Often the rarity of a calculated DNA profile goes beyond one in billions (109) or trillions (1012) to numbers that are not frequently used because they are so large. A list of some big number names is contained in Table 21.3 to aid in verbal descriptions of rare DNA profiles. For example, the inverted value of 1.20x 1015 is 1 in 8.37x 1014 or 0.84x 1015 (one in 0.84 quadrillion).
A1 
A2 
Allele 1 freq (p) 
Allele 2 freq (q) 
Expected genotype freq  
From U.S. Caucasian (N 
= 302); Appendix II 
 sample in database  
D13S317 
11 
14 
0.33940 
0.04801 
2pq 
0.0326  
TH01 
6 
6 
0.23179 
P2 
0.0537  
D18S51 
14 
16 
0.13742 
0.13907 
2pq 
0.0382  
28 
30 
0.15894 
0.27815 
2pq 
0.0884  
16 
17 
0.25331 
0.21523 
2pq 
0.1090  
12 
13 
0.38411 
0.14073 
2pq 
0.1081  
D7S820 
9 
9 
0.17715 
p2 
0.0314  
D8S1179 
12 
14 
0.18543 
0.16556 
2pq 
0.0614  
CSF1PO 
10 
10 
0.21689 
p2 
0.0470  
FGA 
21 
22 
0.18543 
0.21854 
2pq 
0.0810  
D16S539 
9 
11 
0.11258 
0.32119 
2pq 
0.0723  
TPOX 
8 
8 
0.53477 
p2 
0.2860  
VWA 
17 
18 
0.28146 
0.20033 
2pq 
0.1128  
AMEL 
X 
Y 
Combined Frequency 1 in 1.20E15 Combined Frequency From AfricanAmerican (N = 258); Appendix II  sample not in database; wrong population
Expected genotype freq From AfricanAmerican (N = 258); Appendix II  sample not in database; wrong population DBS818 D7S820 D8S1179 CSF1PO D16SB39 TPOX VWA AMEL 17 X 13 9 14 10 22 11 0.3B271 0.108B3 0.14147 0.2B681 0.11628 0.19B74 0.37209 0.2422B 0.23837 0.30039 0.19B74 0.31783 0.1BB04 2pq p2 2pq p2 2pq 2pq p2 2pq 1 in 0.1682 0.0118 0.08B0 0.0660 0.04BB 0.1244 0.138B 0.07B1 6.04E17 Product Rule Combined Frequency From Hispanic (N = 140); Appendix II  sample not in database; wrong population D13S317 11 CSF1PO FGA D16SB39 TPOX VWA AMEL 14 28 TH01 D18SB1 D21S11 D3S13B8 16 DBS818 12 D7S820 D8S1179 12 17 X 14 6 16 30 13 9 14 10 22 11 18 Y 0.23B71 0.21429 0.13929 0.09643 0.28B71 0.3B000 0.11071 0.14286 0.23214 0.16786 0.13929 0.47143 0.21786 0.04643 0.13B71 0.26071 0.203B7 0.12B00 0.2B000 0.1B00G 0.26071 0.17143 2pq p2 0.0219 0.04B9 2pq 0.0378 2pq 0.0B03 2pq 0.1163 2pq 0.087B 0.0123 2pq 0.0714 0.0B39 2pq 0.0B04 2pq 0.0726 p2 0.2222 2pq 0.0747 5.57E17 Product Rule Combined Frequency Table 21.3 Names of big numbers with their corresponding scientific notation. From http://www.gomath.com/ htdocs/ToGoSheet/Algebra /bignumber.html.

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