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Population Genetics and Statistics for Forensic Analysts

Paternity Calculations

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In paternity calculations the likelihood ratio is the same as the paternity index. The three tables below show the calculations of the likelihood ratio for different possible combinations of genotypes assuming that the mother, alleged father and father are unrelated.

In the tables

  • GC is the child's genotype
  • GM is the mother's genotype
  • GAF is the alleged father's genotype
  • Hp is the mother and alleged father are the true parents
  • Hd is the mother and an unrelated male are the true parents
  • LR numerator is P(GC|GM, GAF, Hp)
  • LR denominator is P(GC|GM, GAF, Hd).01

Likelihood Ratio and Paternity Calculation

GCGMGAFNumDenominatorLR
Ai AiAi AiAi Ai1pi1/ pi
  Ai Aj, j≠ i1/2pi1/2pi
  Aj Ak, k≠i, j0pi0
Ai AiAi Aj, i ≠ jAi Ai1/2pi /21/ pi
  Ai Aj, j≠i1/4pi /21/2 pi
  Aj Ak, k≠i, j0pi /20
Ai Aj, i≠jAi AiAj Aj1pj1/pj
  Aj Ak, k≠j1/2pi1/2 pj
  Ak Al, k, l≠j0pi0
Ai Aj, i≠jAi Aj, i≠jAi Ai1/2(pi + pj)/21/(pi + pj)
  Ai Aj1/2(pi + pj)/21/( pi + pj)
  Aj Ak, k≠j1/4(pi + pj)/21/(2(pi + pj))
  Ak Al, k, l≠i, j0(pi + pj)/20
Ai Aj, i≠jAi Ak, k≠i, jAj Aj1/2pj /21/ pj
  Aj Al,l ≠j1/4pj /21/2 pj
  Ak Al, k, l≠j0pj /20

Example:

LocusMotherChildAlleged Father
D3S1358161615, 16
vWA17, 1817, 1818, 20
FGA25, 2723, 2521, 23
D18S5114, 181818, 20

The following frequencies were used:

LocusAlleleFrequencyAlleleFrequency
D3S1358160.2315  
vWA170.2627180.2219
FGA230.1581  
D18S51180.0918  

  • D3S1358 — LR = 1/2p16 = 1/(2 x 0.2315) = 2.1598
  • vWA — LR = 1/[2(p17 + p18)] = 1/[2(0.2627 + 0.2219)] = 1.0317
  • FGA — LR = 1/2p23 = 1/(2 x 0.1581) = 3.1625
  • D18S51 — LR = 1/2p18 = 1/(2 x 0.0918) = 5.4466

Therefore, LR = 2.1598 x 1.0317 x 3.1625 x 5.4466 = 38.3815

In other words, it is 38 times more likely that the child's DNA profile would be observed if the alleged father is the true father rather than an unrelated individual selected at random from the Caucasian population.

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