Homozygosity mapping

Homozygosity mapping searches for shared homozygous marker regions in individuals with a rare recessive condition, often in an inbred pedigree. Under a single ancestral disease copy, affected individuals inherit two copies identical by descent. Marker homozygosity alone gives identity by state, so founder haplotype frequencies matter. If a particular haplotype has founder frequency $p$ and $K$ distinct founder chromosome copies underlie all selected descendant copies, their marker-pattern probability is $E[p^K]$. For complete linkage and a single disease copy, the affected-only numerator is $p$, yielding a LOD score ${\log }_{10}(p/E[p^K])$ under linkage-equilibrium founder assumptions.