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Formulas for paternity situations
Posers in forensic mathematics
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The formulas below were derived with the help of the Symbolic Kinship Program
The triple proportion F:H:U is listed, where F, H, and U are the likelihoods of the genetic types assuming full-shipship*, half-sibship, and unrelated respectively.
From these proportions all likelihood ratios can quickly be written. For example, the likelihood ratio comparing full to half-sibship would be F/H.
|Children share two alleles (both are pq)||(1+p+q+2pq) : (p+q+4pq) : 8pq|
|Share two alleles doubly (both are pp)||(1+p)2 : 2p(1+p) : (2p)2|
|Share one allele doubly (they are pp and pq) note||(1+p) : (1+2p) : 4p|
|Share one allele (both heterozygous, pq and pr) note||(1+2p) : (1+4p) : 8p|
|Share no alleles (pq or pp vs. rs or rr)||1 : 2 : 4|