2. KINSHIP ANALYSIS BY DNA WHEN THERE ARE MANY POSSIBILITIES Charles Brenner –visiting Dept of Genetics, University of Leicester, UK –forensic mathematics

3. Kinship analysis Q: How are these people related? Genetic evidence Likelihood ratio Kinship program –ref: Brenner, CH “Symbolic Kinship Program”, Genetics 145:535-542, 1997 Feb

4. What a likelihood ratio is Compares two explanations for data Example: man & child both have Q allele explanations: –paternity + some coincidence –non-paternity + lots of coincidence

5. Data: Mother=PS, Child=PQ, Man=RQ –explanation #1: man is father (2ps)(2qs)(1/4) event Likelihood ratio for Paternity (PI) PSRQ PQ PS PQ RQ –explanation #2: not father; his Q is coincidence (2ps)(2qs)(q/2) event LR=1/(2q) –If q=1/20, data 10 times more characteristic of “father” explanation

6. Paternity Index exegesis PI = X/Y, where –X=P(genetic types | man=father) –Y=P(genetic types | man not father) Interpretations: –Odds favoring paternity over non-paternity assuming all other evidence is equally divided –Evidence is PI times more characteristic of paternity

7. Kinship I (basic) paternity (Is this man the father?) avuncular (Is this man the uncle?) –(Latin “avunculus” = uncle) missing person (Is this corpse the missing relative?

8. Kinship II (advanced) More than two scenarios –Three –Many disaster inheritance immigration Can always compare two at a time. The trick is to organize the work.

9. Three scenarios — Father? Uncle? Unrelated?

10. Father/Uncle/Unrelated analysis If for example X/Y=5, 5 :3 :1 So, LR for tested man being father, vs uncle, is 5:3 Father X Uncle (X + Y)/2 Unrelated Y Likelihoods of data, assuming man is Father vs Unrelated X/Y Uncle vs Unrelated (X/Y+1)/2 Unrelated vs Unrelated 1 Likelihood ratios

11. Likelihood ratios are “multiplicative” means that if explanation “father” is 2 times better than explanation “uncle” and “uncle” is 10 times better than “unrelated” then “father” explains data 20 times better than “unrelated.”

12. Many-scenario kinship cases missing person –disaster inheritance immigration

13. Swissair flight 111 crash

14. Swissair example DNA data –crash victims (unknowns) –relatives & effects (references) Tentative families –per Benoit Leclair program Too many possibilities! Bottom-up approach Top-down approach

15. Five of the X— family are lost Living reference = Albon = E ? X Yves X Clelia X Jean-L X Sylvie X Jöelle Albon G F M D C Body parts G,F,D,C,M share DNA with Albon (of which G,D,M are female, F,C are male) E

16. Too many possibilities! Note: G, D, M are female; F, C are male. E is living reference. GF M DCE DF M GCE ?F M ?CE ?? M DFE ?F M DCE ?C G DFE ?? M ??E... GF ? D?E

17. M=Jöelle vs. M=unknown Biggest objection — Doesn’t use all the information (e.g. other people similar to both M and Albon) Bottom-up approach X M Albon X M ?? M ??E ?? ? ??E

18. Lattice A diagram showing that some things are better than others. Arrow = “better than” Dot = hypothesis/explanation

19. Kinship lattice — principle of design GF M DC heuristic assumption: any consistent explanation is weakened when a person is removed GF ? DC ?F M DC ?F ? DC ?? M DC ?? ? ?C ?? ? DC M F G DC (Obtained by exchange, not by removal)

20. Top-down approach GF M DC Goal is LR>10 6 GF M D? GF M ?C LR=300 8 10 ?F M DC 10 ?F ? DC ?? M DC 8 10 9 ?? ? ?C ?? ? DC 9 10 >1 ?? D ?C 6 10  “Lattice” (  <1)

21. X— family conclusion GF(DC)M explains the data at least ten million times better than any other arrangement of some or all of the DNA profiles G,F,D,C,M –except ?F(DC)M is only 300-fold inferior Practically speaking, the identifications are proven.

22. Summary Likelihood ratios are the way to quantify evidence Kinship with multiple scenarios: Individual likelihoods for several scenarios Lattice approach for the most complicated situations

23. Acknowledgements Ron Fourney, George Carmody, Benoit Leclair, Chantal Frégeau