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