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4 Population Genetics
Pages 89-124

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From page 89...
... If it is rare, the matching of the two DNA profiles is unlikely to be a mere coincidence; the rarer the profile, the less likely it is that the two DNA samples came from different persons. To assess the probability that DNA from a randomly selected person has the same profile as the evidence DNA, we need to know the frequency of that profile in the population.
From page 90...
... The division by 2 is because in heterozygotes only half the alleles are Do. RANDOM MATING AND HARDY-WEINBERG PROPORTIONS In the simplest population structure, mates are chosen at random.
From page 91...
... The proportion, or frequency, of ALA, homozygotes is thus pit, and the proportion of A2A3 (we do not distinguish between A2A3 and A3A2) heterozygotes is P2P3 + P3P2 = 2P2P3 According to Table 4.1, the proportions of alleles D2 and D4 in the white population are 0.109 and 0.271.
From page 92...
... Of course, exactly random mating is very unlikely, but the equations are accurate enough for many practical purposes. In Chapter 5 we give estimates of the degree of uncertainty caused by departures from random mating proportions.
From page 93...
... HW Proportions in a Large Sample The data in Table 4.1 show approximate agreement with HW expectations, but there is some discrepancy. In the black population, the deficiency of heterozygotes is about 4%, and in the white population, it is about 3%.
From page 94...
... The top two graphs in Figure 4.1 show the similar distribution in white populations in Illinois and Georgia. Companson of the black and the white populations illustrates a point often made by population geneticists namely, that differences among individuals within a race are much larger than the differences between races.
From page 95...
... Illinois white population, (B) Georgia white population, (C)
From page 96...
... As mentioned in Chapter 2, DQA data can distinguish samples from different individuals 93% of the time, clearing many innocent suspects. The overall probability that two independent persons will have the same DQA genotype is the sum of the squares of the genotype frequencies, as illustrated in Box 4.1.4 4The concept of exclusion power was initially described by Fisher (1951)
From page 97...
... Frequencies at Two VNTR Loci (D2S44 and D17S79) in US White Populationa D2S44 D17S79 BinSize Range N Prop.
From page 98...
... Within a race, there is likely to be subdivision. The blending in the melting pot is far from complete, and in the white population, for example, some groups of people reflect to a greater or lesser extent their European origins.
From page 99...
... Population Subgroups The white population of the United States is a mixture of people of venous origins, mostly European. The black and Hispanic populations also have multiple origins.
From page 100...
... Thus, to repeat, computing the frequency of a genotype from the populationaverage allele frequencies, rather than using the average of the actual subpopulation genotype frequencies, will always underestimate the frequency of homozygotes and usually overestimate the frequency of heterozygotes. As an illustrative example, consider the data in Table 4.5.
From page 101...
... POPULATION GENETICS 101 TABLE 4.5 Bin (Allele) Freauencies and Pronortions in Four Ponulatinn.c anr1 Their Weighted Averagesa ~ ~_ ~_ _ _ _ ____ ~MA_ ~ ~ ~ ~ ~^ HA ~ A^V BAA ~ _ ~^ ~ ~ ~7 ~ Canadian Swiss French Spanish Total Binnj Pinj Pinj pinj Pini Pi 10 0.0000 0.0000 0.0000 0.0000 0.000 21 0.0010 0.0001 0.0021 0.0023 0.001 31 0.0011 0.0010 0.0003 0.0055 0.002 45 0.0051 0.0013 0.0052 0.00411 0.004 58 0.00913 0.0163 0.0056 0.00430 0.011 621 0.02316 0.02010 0.0167 0.01454 0.019 735 0.03848 0.06026 0.04223 0.045132 0.046 841 0.04530 0.03724 0.03917 0.033112 0.039 9130 0.142100 0.12468 0.11052 0.102350 0.123 1078 0.08573 0.09167 0.10943 0.085261 0.092 1172 0.07967 0.08335 0.05748 0.094222 0.078 1281 0.08860 0.07543 0.07024 0.047208 0.073 1381 0.08859 0.07356 0.09150 0.098246 0.086 1423 0.02524 0.03029 0.04718 0.03594 0.033 1519 0.02138 0.04714 0.02319 0.03790 0.032 1644 0.04840 0.05027 0.04422 0.043133 0.047 1798 0.10771 0.08872 0.11761 0.120302 0.106 1869 0.07564 0.08053 0.08636 0.071222 0.078 1964 0.07061 0.07648 0.07836 0.071209 0.073 2018 0.02012 0.01510 0.01618 0.03558 0.020 2111 0.01211 0.01411 0.01813 0.02646 0.016 225 0.0057 0.0098 0.0133 0.00623 0.008 230 0.0002 0.0020 0.0000 0.0002 0.001 241 0.0012 0.0020 0.0003 0.0066 0.002 257 0.0082 0.0025 0.0080 0.00014 0.005 263 0.0032 0.0023 0.0052 0.00410 0.004 270 0.0000 0.0000 0.0000 0.0000 0.000 280 0.0000 0.0000 0.0001 0.0021 0.000 Total (2N)
From page 102...
... In empirical data, if statistical uncertainties are taken into account, ~ is almost always positive or very small. For selectively neutral loci, population values of Dij for particular genotypes may be negative only temporarily, except in highly unusual situations.
From page 103...
... We chose European populations in the example because they are likely to differ more than the US subpopulations descended from those European countries. The original differences are diminished in the United States by mixing with other groups, so we would expect ~ calculated for white populations in the United States to be smaller than ~ calculated for European and Canadian populations.
From page 104...
... They vary with the assumptions made and the accuracy desired, but the estimates are very close to one another (Weir and Cockerham 1984; Nei 1987; Chakraborty and DankerHopfe 1991~. TAKING POPULATION STRUCTURE INTO ACCOUNT In the early days of DNA population analysis, there appeared to be a clear excess of homozygotes and a deficiency of heterozygotes (Lander 1989; Cohen 19901.
From page 105...
... It can be shown9 that if 2Pi is assigned to the frequency of a single band at the position of allele Al, then this simple formula gives an estimate that is necessarily larger than the true frequency. The upper bound always holds, but it is necessary only if some single bands represent heterozygotes.
From page 106...
... Nevertheless, to be conservative, we recommend that the HW principle, with the value 2pi for a single band at allele Al be used. MULTIPLE LOCI AND LINKAGE EQUILIBRIUM With random mating (and in the absence of selection)
From page 107...
... The main cause of linkage disequilibrium for forensic markers is incomplete mixing of different ancestral populations. We can get an idea of the extent of this in the US white population by asking what would happen in a mixed population derived from two different European countries.
From page 108...
... Risch and Devlin calculated the expected proportion of twolocus matches as the product of the match probabilities at the component loci. From 2,701,834 pairs of profiles in the FBI data involving blacks, whites, eastern Hispanics, and western Hispanics, they calculated an expected total of 95.3 two-locus matches, whereas 104 were observed not a statistically significant difference.
From page 109...
... . The cause of this difference might be the identification of single bands pairs and 176 matches, for a rate of 2.5 X 10-5.
From page 110...
... . The numbers, especially in the white population, are large enough to provide a sensitive test for departure from LE.
From page 111...
... Consider the white population frequencies in Table 4.8. Suppose that we have an evidence genotype A6-B~B~4 CioCi3 DODD, the dash indicating a single band at allele A6.
From page 112...
... chosen person from the white population matches this genotype is one in 31 million, in the black population one in 17 million, and in the Hispanic population one in 12 million. The three estimates are within about a factor of 3.
From page 113...
... Equations 4.8 and 4.9 depend on the assumption that the population is in HW proportions. Since VNTR and other forensic loci are unlinked and appear to be close to LE, the conditional probability of a multilocus genotype in a relative is the product of the pertinent single-locus conditional probabilities.
From page 114...
... 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)
From page 115...
... Two alternative assumptions are made: that the evidence profile is heterozygous (there are two clear bands) at all four loci, and that locus A has a single band at allele A6.
From page 116...
... We regard the empirical estimates of ~ from VNTRs, made either from comparison of homozygote and heterozygote frequencies (when the interpretation of single bands is not a substantial problem) or directly by comparisons among groups, as being a much better guide for forensic calculations.
From page 117...
... Table 4.10 compares VNTR loci with two PCR-based systems, STR and Polymarker.~7 The total gene diversity is the proportion of heterozygotes that would exist if the entire population were in random-mating proportions. In the table, the gene diversity within subpopulations is given as a fraction of this total 'The six STR loci represent seven populations from three races, grouped as follows (subgroups within races are in parentheses: east Asians (Chinese, Japanese, Houston Asians)
From page 118...
... (c) VNTR loci ' 31 bins D 1 S7 9 0.9470 0.995 0.005 0.001 D2S44 31 0.9342 0.985 0.007 0.009 D4S139 32 0.9103 0.989 0.005 0.006 D1OS28 33 0.9489 0.990 0.005 0.005 D17S79 38 0.8366 0.971 0.011 0.018 Mean 0.9154 0.986 0.006 0.008 STR loci CSF1R 10 4 0.751 0.987 0.005 0.008 TH01 8 4 0.781 0.905 0.011 0.084 PLA2A 9 3 0.814 0.945 0.004 0.051 F13A1 14 4 0.798 0.902 0.006 0.092 CYP19 10 4 0.723 0.947 0.007 0.046 LPL 7 4 0.656 0.956 0.006 0.038 Mean 0.708 0.939 0.007 0.054 Polymarker loci plus DQA DQA1 6 0.788 0.948 0.009 0.043 LDLR 2 0.483 0.914 0.004 0.082 GYPA 2 0.478 0.971 0.012 0.017 HBGG 3 0.539 0.876 0.003 0.121 D7S8 2 0.475 0.995 0.002 0.003 GC 3 0.654 0.909 0.003 0.088 Mean 0.571 0.934 0.006 0.060 a(a)
From page 119...
... Assuming HW proportions and LE and using the data in Table 4.10, the probability that two randomly selected individuals would have the same profile is about 10-~° for the five VNTR loci, about 10-6 for the six STR loci (using the 12 STRs mentioned in the paragraph above would lower the probability to about 10-~) , and about 10-4 for the six Polymarker loci.
From page 120...
... This value is intermediate between those that would be found in populations of first- and of second-cousin matings and is a reasonable upper limit for what might be expected. The 2p rule for VNTRs was introduced because single bands may actually come from heterozygotes.
From page 121...
... Although the mutation rates for STRs are not as high as those for VNTRs, the rates are still much higher [Qr STRs than for classical loci. A high mutation rate is desirable for forensic identification (although not for paternity testing)
From page 122...
... For systems such as VNTRs, in which a heterozygous locus can be mistaken for a homozygous one, if an upper bound on the genotypic frequency at an apparently homozygous locus (single band) is desired, then twice the allele (bin)
From page 123...
... fixation index, FIT (Ned 1977, 1987, p 159164; Chakraborty and Danker-Hopfe 1991; Chakraborty 1993J. We begin with an arbitrary mating pattern; in particular, we do not assume that random mating occurs within subpopulations, or even that distinct subpopulations occur.
From page 124...
... 2PiPi , t.d I<] First, we express the homozygote parameters Dii in terms of the heterozygote parameters Dij (i ~ j)


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