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Attaching statistical weight to DNA test results 1.Single source samples 2.Relatives 3.Substructure 4.Error rates 5.Mixtures/allelic drop out 6.Database searches

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Single Source Samples If the defendant is not the source of the evidence DNA then the observed match is a coincidence. Therefore a relevant weight for the evidence is the probability of a randomly chosen person having a matching DNA profile to the evidence

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Single Source: population genetics For each locus the frequency of each genotype if computed from the Hardy- Weinberg law Homozygotes: A i A i Let freq(A i ) be p i then the HW genotype frequency is p i 2 Heterozygotes: A i A j 2p i p j

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Relatives Relatives are more likely to share alleles in common that they have inherited from their common ancestor. Full Sibs: A i A i :(1+2p i +p i 2 )/4 A i A j :(1+p i +p j +2p i p j )/4 Example: p 14 (D3) = 0.14 HW frequency= 0.02 Pr(matching sibling) = 0.32

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Population Substructure Source population p s p1p1 p2p2 p3p3 p4p4 pmpm Source population is very large Each subpopulation has N individuals, and are isolated from each other Allele frequencies in each subpopulation become different over time Populations separated t generations

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Effects of substructure In the pooled subpopulations genotype frequencies depart from the Hardy- Weinberg expectations Freq(A i A i ) = p i 2 + p i (1-p i ) Freq(A i A j ) = (1- )2p i (1-p j ) The NRCII recommendation is to correct homozygote frequencies using the first formula

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Conditional Probabilities If we assume defendant and perpetrator are likely to be form the same subpopulation different calculations are relevant

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Error Rates Use likelihood ratios, n - false negative, p false positive Prosecution hypothesis: perpetrator and suspect the same person, no false negative-{1 (1- n )} Defense hypothesis: suspect matches evidence coincidentally and no false negative, or suspect does not match evidence and a false positive- {RMP (1- n ) + (1-RMP) p }. Suppose, RMP=10 -15, n =10 -3, p =10 -4, then the LR= 0.999/[10 -15 0.999+(1-10 -15 )10 -4 ] 1/ p

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Mixtures/Drop out Combined probability of inclusion, add up all possible contributing genotype Evidence: a, b, c Possible genotypes: aa, ab, ac, bb, bc, cc This method does not require that you make any assumption about the number of contributors, or major/minor donors – but can not take into account drop out easily

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Mixtures/Likelihood ratios This requires that the number of contributors be specified These methods can take into account allelic drop out – removing these loci is not a sufficient solution Calculations can get very complicated Popstats has software to do this although it does not account for drop out.

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State Match Report Matches at both high and moderate stringency Analyst eliminates this match after an evaluation that cant be written into the computer program or the labs SOP.

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Methods for computing statistics NRC I – use one set of loci for the search and a second set to confirm NRC II – multiply the RMP by the size of the database Bayesian – gives weight to the exclusions, number is close to the RMP RMP only – based on illogic that retest of known resets case to probable cause

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Hardy Weinberg. Hardy Weinberg refers to Populations.

Hardy Weinberg. Hardy Weinberg refers to Populations.

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