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For first cousins in an otherwise outbred pedigree, compare the copies transmitted from their related parents, who are full siblings. These transmissions trace to the same shared grandparent with probability $1/2$ and then to the same homologous copy of that grandparent with probability $1/2$, giving $k_1=1/4$. The unrelated parental contributions cannot match, so two shared copies have probability zero. Selecting one random copy from each cousin chooses those two potentially shared copies with probability $1/4$, giving kinship coefficient $k_1/4=1/16$.

Let $J$ be the largest number of chromosome copies that can be paired across the two full siblings as identical by descent, counting repeated copies when a child is autozygous. For offspring of otherwise outbred first cousins, with probability $3/4$ the parental copies have no common ancestral origin, giving ordinary sibling sharing $(1/4,1/2,1/4)$. With probability $1/4$, write the parental copies as $(A,B)$ and $(A,C)$ with three distinct origins. Each child independently has one of $AA,AB,AC,BC$, equally likely. Among sixteen ordered child pairs, two share no copy, ten share one, and four share two. The mixture gives the displayed probabilities. These three numbers do not determine all Jacquard identity coefficients; the formula $\varphi =\mathbb{E}[J]/4$ is restricted to noninbred individuals and fails here.

For two individuals carrying labelled copies $(a,b)$ and $(c,d)$, condensed identity coefficients give the probabilities of nine identity by descent patterns, identifying states that differ only by exchanging the two homologues within either individual. They retain within-individual autozygosity, which three ordinary outbred sharing coefficients omit. One convention isEach block consists of copies identical by descent, and different blocks have distinct ancestral origins. For siblings whose parents are otherwise outbred first cousins, these coefficients are $(1,0,2,1,2,1,15,30,12)/64$. This follows by conditioning on whether the parents share one ancestral copy and enumerating the four independent Mendelian segregation choices to their two children. The kinship coefficient is ${\Delta }_1+({\Delta }_3+{\Delta }_5+{\Delta }_7)/2+{\Delta }_8/4$, here $9/32$. Weir's discussion of identity states uses this convention.

For otherwise outbred opposite-sex first cousins, the probability that the mother's randomly transmitted X copy matches the father's X by descent depends on which of their parents are siblings. It is zero when the male cousin is related through his father, $1/8$ when the female cousin is related through her father and the male through his mother, and $3/16$ when their mothers are sisters. Daughters can be X-autozygous; sons have one X and a Y and are not homozygous for a paired X chromosome. Recombination and pseudoautosomal regions require a locus-based formulation instead of whole-chromosome blocks.