Post on 21-Dec-2015
KINSHIP ANALYSIS BY DNA KINSHIP ANALYSIS BY DNA WHEN THERE ARE MANY WHEN THERE ARE MANY
POSSIBILITIESPOSSIBILITIES
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 alleleexplanations: – paternity + some coincidence– non-paternity + lots of coincidence
• Data: Mother=PS, Child=PQ, Man=RQ– explanation #1: man is father
• (2ps)(2qs)(1/4) event
Likelihood ratio for Paternity (PI)
PS RQ
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
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
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
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
• Living reference = Albon = E
?
XYvesXClelia
XJean-LXSylvie XJöelle
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
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
• 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
XMAlbon
XMAlbon?? M
??E ?? ? ??E
Lattice
A diagram showingthat some things are
better than others.
Arrow = “better than”
Dot = hypothesis/explanation
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
MF G DC
(Obtained byexchange, not byremoval)
Top-down approach
GF M DC
Goal is LR>106
GF M D?
GF M ?C
LR=3008
1010
?F M DC
10
?F ? DC
?? M DC
810 9
10
?? ? ?C
?? ? DC
910
>1?? D ?C 6
10
“Lattice”
(<1)
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