= Recessive affected-sib-pair likelihood
{title2=$L_0=u^2,\ L_1=uv,\ L_2=v^2$}
For unaffected <genetic carriers> of a disease with complete <penetrance> and <recessive inheritance>, suppose parental marker-disease <haplotype> phases are equally likely and the marker is fully informative. Write $u=\theta(1-\theta)$ and $v=1/2-u$, where $\theta$ is the <recombination fraction>. Conditional on sharing a parental marker copy, the probability that both siblings inherit that parent's disease allele is $[(1-\theta)^2+\theta^2]/2=v$; conditional on inheriting different marker copies it is $\theta(1-\theta)=u$. Independent paternal and maternal transmissions therefore give $L_0=u^2,L_1=uv,L_2=v^2$. Conditional instead on both siblings being affected, the IBD probabilities are $s^2,2s(1-s),(1-s)^2$, where $s=2u\in[0,1/2]$.
// Target: biology.bigb
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