President's DNA Initiative
-
Advancing Justice Through DNA Technology

DNA Analyst Training

• Home
• Glossary
• Index
• Site Map
• User Guide

Paternity Calculations

Home > Population Genetics & Statistics > Statistics > Parentage and Relatedness > Paternity Calculations

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;
• H_p is the mother and alleged father are the true parents;
• H_d is the mother and an unrelated male are the true parents;
• LR numerator is P(GC|GM, GAF, H_p);
• LR denominator is P(GC|GM, GAF, H_d).01

Likelihood Ratio and Paternity Calculation
GC	GM	GAF	Num	Denominator	LR
AiAi	AiAi	AiAi	1	pi	1/ pi
		AiAj, j≠ i	1/2	pi	1/2pi
		AjAk, k≠i, j	0	pi	0
AiAi	AiAj, i ≠ j	AiAi	1/2	pi /2	1/ pi
		AiAj, j≠i	1/4	pi /2	1/2 pi
		AjAk, k≠i, j	0	pi /2	0
AiAj, i≠j	AiAi	AjAj	1	pj	1/pj
		AjAk, k≠j	1/2	pi	1/2 pj
		AkAl, k, l≠j	0	pi	0
AiAj, i≠j	AiAj, i≠j	AiAi	1/2	(pi + pj)/2	1/(pi + pj)
		AiAj	1/2	(pi + pj)/2	1/( pi + pj)
		AjAk, k≠j	1/4	(pi+ pj)/2	1/(2(pi + pj))
		AkAl, k, l≠i, j	0	(pi + pj)/2	0
AiAj, i≠j	AiAk, k≠i, j	AjAj	1/2	pj/2	1/ p j
		AjAl, l≠j	1/4	pj/2	1/2 pj
		AkAl, k, l≠j	0	pj /2	0

Example:

Locus	Mother	Child	Alleged Father
D3S1358	16	16	15, 16
vWA	17, 18	17, 18	18, 20
FGA	25, 27	23, 25	21, 23
D18S51	14, 18	18	18, 20

The following frequencies were used:

Locus	Allele	Frequency	Allele	Frequency
D3S1358	16	0.2315
vWA	17	0.2627	18	0.2219
FGA	23	0.1581
D18S51	18	0.0918

• 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.

Click here to watch a video on paternity calculations presented by Greggory LaBerge.

< Previous Page  ::  Next Page >