Inbreeding

Inbreeding is reproduction between genetically related individuals. It increases the chance that an offspring's maternal and paternal copies at a locus are identical by descent. Such homozygosity by descent is autozygosity.

Reduced reproductive or survival performance associated with mating among relatives or self-fertilization in the relevant comparison. Measuring seed set alone can miss later offspring costs.

The inbreeding coefficient is the probability that the two allele copies at a locus within an individual are identical by descent. It equals the kinship coefficient of the individual's parents. It concerns ancestral identity, rather than merely homozygosity of observed allelic states.

// Target: biology.bigb

For a biallelic locus with frequencies $p=1-q$ and $q$, and inbreeding coefficient $F$, ancestral-copy identity with probability $F$ gives genotype probabilities $P(AA)=p^2+Fpq$, $P(Aa)=2pq(1-F)$ and $P(aa)=q^2+Fpq$. In the IBD component both copies equal a single ancestral draw; in the remaining component the two ancestral alleles are independent population draws. A fully penetrant recessive disease therefore has risk $q^2+Fq(1-q)$.

// Target: biology.bigb

For an otherwise outbred pedigree, each of the two shared grandparents contributes $(1/2{)}^{2+2+1}=1/32$ to the kinship coefficient of first cousins. Thus their child has inbreeding coefficient $1/16$. Equivalently, cousin kinship is one quarter of the $1/4$ kinship of their sibling parents.

// Target: biology.bigb