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Understanding Match Probability Dependencies in Forensic Genetics

Explore the complexities of match probabilities in forensic genetics, considering multi-locus dependencies and the implications for identifying individuals. Discuss how match probabilities decrease with more loci and the challenges of assuming independence. Learn about likelihood ratios, sample allele frequencies, and empirical and theoretical dependencies. Examine how different scenarios and population structures affect match probabilities across loci. Considerations include mutation rates, identity disequilibrium, and the importance of larger databases for empirical studies.

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Understanding Match Probability Dependencies in Forensic Genetics

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  1. Multi-locusMatchProbabilityDependencies BruceWeirandEdwardZhaoUniversityofWashingtonbsweir@uw.edu 2018NIJR&DSymposium SupportedinpartbyNIJ2017-DN-BX-0136.

  2. Whatarematchprobabilities? [Vallone:https://www.nist.gov/document-7351]

  3. Willmatchprobabilitieskeepdecreasing? [Geetal,InvestigativeGenetics3:1-14,2012]

  4. Willmatchprobabilitieskeepdecreasing? HowdotheseDonnelly: match probabilities address theobservationof “aftertheobservationofmatchesatsomeloci,itisrel-ativelymuchmorelikelythattheindividualsinvolvedarerelated(preciselybecausematchesbetweenunrelatedin-dividualsareunusual)inwhichcasematchesobservedatsubsequentlociwillbelesssurprising.Thatis,knowl-edgeofmatchesatsomelociwillincreasethechancesofmatchesatsubsequentloci,incontrasttotheinde-pendenceassumption.” [Donnelly,Heredity75:26-64.1995]

  5. Arematchprobabilitiesindependentoverloci? Istheproblemthatwekeeponmultiplyingmatchprobabilitiesoverlociundertheassumptiontheyareindependent?Canwe eventestthatassumptionfor10ormoreloci? Orisourstandard“randommatchprobability”nottheappro-priatestatistictobereportingincasework?Isitactuallyappro-priatetoreportstatementssuchas Theapproximateincidenceofthisprofileis1in810quin-tillionCaucasians,1in4.9sextillionAfricanAmericansand1in410quadrillionHispanics.

  6. Putting“match”backin“matchprobability” Let’sreserve“match”forastatementwemakeabouttwopro-filesandtake“matchprobability”tomeantheprobabilitythattwoprofilesmatch.Thisrequirescalculationsaboutpairsofprofiles. Ifthesourceofanevidenceprofileisunknown(e.g.isnotthepersonofinterest),thenthematchprobabilityistheprobabilitythisunknownpersonhastheprofilealreadyseeninthePOI.Notwoprofilesaretrulyindependent,andtheirdependenceaffectsmatchprobabilitiesacrossloci.

  7. Likelihoodratiosusematchprobabilities Aswithmanyotherissuesonforensicgenetics,theissueofmulti-locusmatchprobabilitydependenciesisbestaddressedbycom-paringtheprobabilitiesoftheevidenceunderalternativepropo-sitions: Hp:thepersonofinterestisthesourceoftheevidenceDNAprofile. Hd:anunknownpersonisthesourceoftheevidenceDNAprofile. WritetheprofilesofthePOIandthesourceoftheevidenceas GsandGc.TheevidenceisthepairofprofilesGc,Gc.

  8. Likelihoodratiosusematchprobabilities Thelikelihoodratiois Pr(E|Hp) LR= Pr(E|Hd) Pr(Gc,Gs|Hp) = Pr(Gc,Gs|Hd) 1 = Pr(Gc|Gs,Hd) 1 = Matchprobability providingGc=GsunderHp.ThematchprobabilityisthechanceanunknownpersonhastheevidenceprofilegiventhatthePOIhastheprofile:thisisnottheprofileprobability.

  9. SpecialCases:UseofSampleAlleleFrequencies Thematchprobabilityisusuallyestimatedusingallelefrequen-ciesfromadatabaserepresentingsomebroadclassofpeople,suchas“Caucasian”or“AfricanAmerican”or“Hispanic.” Thepopulationrelevantforaparticularcrimemaybeanarrowerclassofpeople.Thereispopulationstructure.Ifparetheallelefrequenciesinthedatabase,thematchprobabilitiesare estimatedas [3θ+(1−θ)pA][2θ+(1−θ)pA] Pr(AA|AA)= Pr(AB|AB)= (1+θ)(1+2θ) 2[θ+(1−θ)pA][θ+(1−θ)pB] (1+θ)(1+2θ) Canthesebemultipliedoverloci?

  10. Empiricaldependencies: 284920-locusprofiles

  11. Empiricaldependencies: Y-STRprofiles

  12. Theoreticaldependencies:Nomutation TheprobabilityanindividualishomozygousAABBatlociA,B is whereηistheidentitydisequilibrium. Itcannon-zeroevenfor pairsoflocithatareunlinkedand/orinlinkageequilibrium. Samplingamongparentsorgametesand/ortheinclusionofrandomelementsintheunitinggametesleadstoacorrelationinidentitybydescentevenbetweenunlinkedlocibecausegenesatbothlociareofnecessityincludedineachgamete. [Weir&Cockerham,Genetics63:711-742,1969.]

  13. Theoreticaldependencies: Mutation [Laurie&Weir,TheoreticalPopulationBiology63:207-219,2003.]

  14. Theoreticaldependencies:Mutation “Between-locusdependenciesinfinitepopulationscanleadtounder-estimatesofgenotypicmatchprobabilitieswhenusingtheproductrule,evenforunlinkedloci. Thethree-locusratioisgreaterthanoneandisgreaterthanthecorrespondingtwo-locusratioforlargemutationrates.Theseresultsprovideevidencethatbetween-locusdependencyeffectsaremagnifiedwhenconsideringmoreloci. Highmutationratesmeanthatspecificmutantsarelikelytoberecentandrare.Hence,iftwoindividualsshareallelesatonelocus,theyaremorelikelytoberelatedthroughrecentpedigree,andhencemorelikelytoshareallelesatasecondlocus.” [Laurie&Weir,TheoreticalPopulationBiology63:207-219,2003.]

  15. Onepopulationsimulateddata:θ=0

  16. Onepopulationsimulateddata: θ=0.001

  17. Onepopulationsimulateddata: θ=0.01

  18. 2849USprofiles θ=0 θ=0.001 θ=0.01

  19. 15,000AustralianProfiles Theta=0.00 Theta=0.01 Theta=0.03 300 300 300 Expected Expected Expected 150 150 150 0 0 0 050150250350 Observed 050150250350 Observed 050150250350 Observed Numbersoffive-locusmatchesamongnine-locusprofiles. [Weir,JournalofForensicSciences49:1009-1014,2004.]

  20. Conclusions • Profileprobabilitiesdecreaseatthesamerateasnumberoflociincreases. • Matchprobabilitiesarenotprofileprobabilities. • Matchprobabilitiesdecreasemoreslowlyasnumberofloci increases. • “Thetacorrection”dencies. mayaccommodate multi-locusdepen- • Empiricalstudiesneedmuchlargerdatabases.

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