KINSHIP%20ANALYSIS%20BY%20DNA%20WHEN%20THERE%20ARE%20MANY%20POSSIBILITIES

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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

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Kinship analysis

• Q How are these people related?
• Genetic evidence
• Likelihood ratio
• Kinship program
• ref Brenner, CH Symbolic Kinship Program,
  Genetics 145535-542, 1997 Feb

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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

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Likelihood ratio for Paternity (PI)

• Data MotherPS, ChildPQ, ManRQ
• explanation 1 man is father
• (2ps)(2qs)(1/4) event

• LR1/(2q)
• If q1/20, data 10 times more characteristic of
  father explanation

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Paternity Index exegesis

• PI X/Y, where
• XP(genetic types manfather)
• YP(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

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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?

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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.

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Three scenarios

• Father?
• Uncle?
• Unrelated?

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Father/Uncle/Unrelated analysis
So, LR for tested man being father, vs uncle, is
53
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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.

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Many-scenario kinship cases

• missing person
• disaster
• inheritance
• immigration

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Swissair flight 111 crash
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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

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Five of the X family are lost

• 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
?
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Too many possibilities!
GF M DCE
DF M GCE
?F M ?CE
?? M DFE
?F M DCE
?C G DFE
?? M ??E
...
Note G, D, M are female F, C are male. E is
living reference.
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Bottom-up approach

• MJöelle vs. Munknown

X
X
M
M
?? M ??E
Albon
Albon
?? ? ??E
Biggest objection Doesnt use all the
information (e.g. other people similar to both
M and Albon)
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Lattice
A diagram showing that some things are better
than others.
Arrow better than
Dot hypothesis/explanation
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Kinship lattice principle of design

• heuristic assumption any consistent explanation
  is weakened when a person is removed

GF M DC
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Top-down approach
GF M DC
(?lt1)
Lattice
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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.

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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

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Acknowledgements

• Ron Fourney, George Carmody, Benoit Leclair,
  Chantal Frégeau