For the mother, she will be heterozygous or homozygous for alleles at the gene.
The child will be:
(1) homozygous for an allele shown by the mother
(2) heterozygous for alleles, identical to the mother
(3) heterozygous for alleles, with one dissimilar to the mother
In a nonconsanguineous mating, the offspring is neither homozygous nor heterozygous identical. Its genotype is usually heterozygous dissimilar since the father transmits an allele not present in the mother.
In a consanguineous mating, the offspring is often (> 25%) homozygous or (> 25%) heterozygous identical to the mother.
|
Mother
|
Child
|
likelihood ratio of incest vs random mating
|
|
homozygous (p1p1)
|
homozygous (p1p1)
|
(0.5 + (0.5 * p1)) / p1
|
|
|
heterozygous (p1px)
|
(0.5 – (0.5 * p1)) / p1
|
|
heterozygous (p1p2)
|
homozygous (p1p1)
|
(0.25 + (0.25 * (p1 + p2))) / (0.5 * (p1 + p2))
|
|
|
heterozygous identical (p1p2)
|
(0.25 + (0.25 * (p1 + p2))) / (0.5 * (p1 + p2))
|
|
|
heterozygous dissimilar (p1px)
|
(0.5 – (0.5 * (p1 + p2))) / (1.0 – (p1 + p2))
|
where:
• p1 = allelelic frequency of first allele
• p2 = allelelic frequency of second allele
• If p1 + p2 = 1, then the likelihood ratio for the heterozygous mother and heterozygous identical offspring is 0.5.
For the heterozygous mother and homozygous offspring, the likelihood that a consanguineous mating would produce a homozygous offspring demonstrating only the observed allele versus a mating with a random man is the equivalent of the incest index:
incest index =
= (0.125 + (0.25 * p1)) / (0.5 * p1)
For independently inherited alleles, then
total likelihood ratio for consanguineous vs nonconsanguineous mating =
= PRODUCT(likelihood ratio for the loci studied)
Multiple (5 or more) loci may need to be evaluated to obtain a sufficient level of confidence in an interpretation.
NOTE: If the selected loci are highly heterozygous, then the allelic frequencies will likely be relatively small. If they were large decimal fractions, then the discriminatory ability would be poor.
