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A genetic genetic carrier has one disease-associated recessive allele and one normal allele at a genetic locus, and is unaffected under a fully penetrant recessive model. Two genetic carriers have affected-offspring probability $1/4$ under Mendelian segregation; a genetic carrier and an individual with no disease allele have affected-offspring probability zero under that same mutation-free model.

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

Sibling recurrence risk is the conditional probability that another child has the disease, given an affected sibling. For unaffected parents, complete penetrance and a single recessive disease allele, the affected child identifies both parents as genetic carriers. Independent Mendelian segregation then gives recurrence probability $1/4$, whether or not the parents are related. Incomplete penetrance, phenocopies, different causal loci or affected parents change this calculation.

// Target: biology.bigb