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1 Statistical genetics and genetical statistics Thore Egeland, Rikshospitalet and Section of Medical Statistics Joint work with P. Mostad, NR, B. Olaisen, B. Mevåg, M. Stenersen, Inst of Forensic Medicine. Grimstad 6/6/2000 www.uio.no/~thoree Grimstad 6/6/2000 www.uio.no/~thoree

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2 Contents What did we learn in school and what have we read in the papers? Erik Essen-Möller Identification problems: - origin of wine grapes (Science, 3/10/99), - wolves and dogs (Villmarksliv 3, 2000), - disasters, (Nature gen. 15/4/97), - paternity, e.g., Jefferson (Nature. 5/11/98).

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3 Peas!

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4 Nature Genetics, OJ

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5 Dispute laid to rest

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6 Tre slides på Essen-Møller

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7 On the theory and practice of Essen-Möller's W value and Gurtler's paternity index (PI). Hummel K Forensic Sci Int 1984 May;25(1):1-17

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8 H 1 : M1 father H 2 : Random man father P(data| H 1 )= P(data| H 2 )=p B Paternity index=LR=1/ p B Five independent loci, p B =0.05: LR=(1/p B ) 5 = 3 200 000 Paternity index (PI). LR A,AB,B A,B M1 F1 M2

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9 Bayes Theorem on odds form Posterior odds = LR * prior odds Essen-Möller’s W=P(H 1 |data) assuming prior odds=1

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10 Bayes theorem: Framework for merging independent data Nuclear DNA. Several independent loci mitochondrial DNA: maternally inherited All these mitochondrial DNAs stem from one woman who is postulated to have lived about 200,000 years ago, probably in Africa. Cann, Nature, 1987 Y-chromosome. Paternal

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11 Dual origins of finns

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12 Ambitions We would like to: - determine most likely family among many, - include non-DNA data (prior), e.g. age, - m odel mutations, - model kinship (departures from Hardy-Weinberg), - model measurement uncertainty.

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14 Bayesian solution Find a set of “possible” pedigrees Set up prior probabilities based on non-DNA information. Compute for each pedigree Make inferences from the posterior distribution:

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15 Example of use: The Romanov family 9 bodies found, presumed to be Tsar Nicolay II, Tsarina and his three daughters, three servants, and a doctor. Age and sex information for the bodies narrow down possible pedigrees to 4536. Our method picked among these the accepted pedigree. Mitochondrial DNA link with Prince Philip, Duke of Edinburgh.

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16 Prior distribution

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17 Modelling mutations Mutation rate varies with –Sex of parent and locus. Alleles tend to mutate to close alleles:

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18 database

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19 Kinship and uncertainty in allele frequencies Vector of allele frequencies p Dirichlet by evolutionary argument data|p ~ Multinomial Then p|data ~ Dirichlet Basis for simulation

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20 Paper challenge

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21 Alternatives to consider One extra woman and man introduced gives 1074 possible families Flat prior Three examples:

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22 w2 childwom childwom man m2 man Full sibs Incestuous Unrelated childwom man

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23 w2 childwom childwom man m2 man most probable among 1074 I II III LR (I/II) =2.1 LR(I/III) = 1.6*10^18 childwom man

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24 Further results Number reduced from 1074 to 193 disregarding incestuous pedigrees. Same result; now LR=165. Full sib alternative most likely also when allowing for larger pedigrees. Non-flat prior not needed, even so...

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25 F F F b G = 2 b I = 3 b P = 3 b G = 1 b I = 0 b P = 0 Example Prior ratio A/B= A: B: childwommanchildwomman

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26 Non-flat prior All M-parameters 0.1: same result.

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27 Literature Evett og Weir. "Interpreting DNA evidence". Sinauer, MA, USA, 1998. http://www.nr.no/familias Egeland, Mostad, Mevåg og Stenersen. "Beyond traditional paternity and identification cases. Selecting the most probable pedigree". Forensic Science International, 110(1), 2000

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