|email: Comments? Questions? Discussion?
Formulas for paternity situations
Posers in forensic mathematics
Go to home page of Charles H. Brenner
The formulas below were derived with the help of the Symbolic Kinship Program
The triple proportion A:B:C is listed, where A, B, and C 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 A/B.
|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|
Note: Sharing one allele is evidence that the children share at least one parent, but very little evidence that they share one parent rather than two.