Likelihood ratios for sibship and half-sibship

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.