Comparison of the alleles shown by both the mother and an offspring at highly heterozygous loci can aid in the evaluation of suspected incest. Wenk et al calculated the likelihood ratios for various phenotypic patterns. If the alleles of the loci are independently inherited, then the product of the likelihood ratios can be calculated to give the total likelihood ratio.


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.



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))



• 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.


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