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					KINSHIP ANALYSIS BY DNA
 WHEN THERE ARE MANY
     POSSIBILITIES

  Charles Brenner
    – visiting Dept of Genetics, University
      of Leicester, UK
    – forensic mathematics
           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
     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
Likelihood ratio for Paternity (PI)
• Data: Mother=PS, Child=PQ, Man=RQ
  – explanation #1: man is father     PS        RQ
     • (2ps)(2qs)(1/4) event               PQ

  – explanation #2: not father; his Q is coincidence
     • (2ps)(2qs)(q/2) event        PS               RQ
                                         PQ
• LR=1/(2q)
  – If q=1/20, data 10 times more characteristic of
    ―father‖ explanation
      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
            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?
        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.
 Three scenarios —

• Father?
• Uncle?
• Unrelated?
    Father/Uncle/Unrelated analysis
Likelihoods of data, assuming man
is      Father              Uncle                  Unrelated
          X               (X + Y)/2                   Y


Likelihood ratios
   Father vs Unrelated Uncle vs Unrelated Unrelated vs Unrelated
           X/Y            (X/Y+1)/2                 1

  If for example X/Y=5,
          5       :             3        :          1

  So, LR for tested man being father, vs uncle, is 5:3
         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.‖
Many-scenario kinship cases
 • missing person
   – disaster
 • inheritance
 • immigration
Swissair flight 111 crash
    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
Five of the X— family are lost

              XX
              Sylvie Jean-L
                                                      X
                                                      Jöelle




                              XX
                              Clelia   Yves   Albon


• Living reference = Albon = E
• Body parts G,F,D,C,M share DNA with Albon
• (of which G,D,M are female, F,C are male)



               G      F                               M
                               D       C       E               ?
       Too many possibilities!
GF M         DF M              ?F M           ?? M
 DCE          GCE               ?CE            DFE


?F M         ?C G              GF ?
                                              ...
 DCE          DFE               D?E


?? M
 ??E         ...


   Note: G, D, M are female; F, C are male.
   E is living reference.
        Bottom-up approach
  • M=Jöelle              vs.      M=unknown


                  X
                  M
                                                 X
                                                 M

?? M      Albon                          Albon
                                ?? ?
 ??E
                                 ??E


 Biggest objection —
        Doesn’t use all the information
        (e.g. other people similar to both M and Albon)
Lattice
           A diagram showing
          that some things are
            better than others.

           Arrow = “better than”

    Dot = hypothesis/explanation
Kinship lattice — principle of design
 • heuristic assumption: any consistent
   explanation is weakened when a person is
   removed
                       GF M
                        DC
                                     (Obtained by
       ?F M            GF ?     MF G exchange, not by
        DC              DC       DC  removal)
?? M            ?F ?
 DC              DC

                              ?? ?
                               DC

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

                                 ?? ?
                                  ?C
                                                  “Lattice”
       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.
                       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
        Acknowledgements
• Ron Fourney, George Carmody, Benoit
  Leclair, Chantal Frégeau

				
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