Pedigree Kinship Coefficients As Benchmarks

Why Pedigree Benchmarks Matter

A pair of relatives can share alleles because they inherited copies from a common ancestor. Pedigree kinship coefficients provide reference expectations for that sharing under a specified family tree. These values are useful benchmarks, but they are not direct measurements of the alleles observed in a particular pair, and they depend on the pedigree assumptions.

A frequent source of confusion is that two relatedness scales are used in practice. The kinship coefficient is the probability that one allele sampled from each of two people is identical by descent. A commonly used relatedness scale is twice that coefficient. Thus, parent–offspring kinship is conventionally \(1/4\), whereas their relatedness on the doubled scale is \(1/2\). Keeping the scale explicit prevents an apparently simple benchmark from being reported incorrectly.

The probability concerns a pair of sampled allele copies, one from each person. It is not the probability that the two people have identical genotypes, nor does it mean that a fixed proportion of their entire genomes must match exactly. In the conventional outbred pedigree examples below, \(r_{ij}\) is interpreted as the expected fraction of alleles in one individual that are IBD with alleles in the other.

Assumptions Behind the Familiar Values

Unless a case says otherwise, use the following conventional assumptions: the pedigree is autosomal; the relevant founders are unrelated to one another and non-inbred; there are no unrecorded ancestral connections; and inheritance is Mendelian. A non-inbred individual has two homologous allele copies that are not themselves IBD by pedigree. For an individual \(i\), write \(F_i\) for the probability that the individual's two homologous copies are IBD, the inbreeding coefficient. For distinct unrelated founders, \(\phi_{ij}=0\); each founder can be non-inbred while also having zero kinship with another founder.

The standard benchmark table follows under these assumptions. “First cousins” means cousins whose parents are siblings, with no additional pedigree connections.

For two individuals who are themselves the same person, the kinship coefficient is \(\phi_{ii}=(1+F_i)/2\), not the unrelated-pair value. This diagonal case is distinct from the pairwise benchmarks in the table.

Deriving Parent–Offspring Kinship

The parent–offspring benchmark illustrates both the definition and the role of assumptions. Let \(P\) be a parent and \(C\) the child. Sample one allele copy from \(P\) and one from \(C\). Assume the child’s other parent is unrelated to \(P\), so an allele inherited from that other parent contributes no IBD probability with the sampled allele from \(P\).

The child’s sampled allele comes from \(P\) with probability \(1/2\). Conditional on that event, it is a uniformly transmitted copy from \(P\). The sampled allele from \(P\) is the same homologous copy with probability \(1/2\), giving IBD with certainty. It is the other homolog with probability \(1/2\), and those two homologs are IBD with probability \(F_P\). Therefore:

If \(P\) is non-inbred, \(F_P=0\), so \(\phi_{PC}=1/4\) and \(r_{PC}=1/2\). If the parent is inbred, the conventional \(1/4\) value does not apply: the probability rises with \(F_P\). If the child’s other parent is related to \(P\), there can also be IBD when the child’s allele came from that other parent, so the unrelated-other-parent assumption matters as well.

Sibling and More Distant-Relative Benchmarks

For full siblings, each child inherits one allele copy from each parent. To see the kinship benchmark, sample one allele from each sibling. There is probability \(1/4\) that both sampled alleles are maternal; conditional on this, the two transmissions are IBD with probability \(1/2\) when the mother is non-inbred. The paternal–paternal case contributes another \(1/4 \times 1/2\). Under unrelated, non-inbred parents, the two cross-parent cases contribute zero. The total is \(1/8+1/8=1/4\), so \(r=1/2\).

This calculation also shows why “full siblings share one-half” needs a scale attached: it is their conventional doubled relatedness, while their kinship coefficient is \(1/4\). Half siblings share only one parent. With unrelated, non-inbred founders, the probability that both sampled alleles came from that shared parent is \(1/4\), and the two transmitted copies are IBD with probability \(1/2\). The result is \(\phi=1/8\), or \(r=1/4\).

For more distant relationships, a useful rule for a simple pedigree with unrelated, non-inbred founders is to add the contribution from each common ancestor. If the paths from the two individuals to a particular common ancestor contain \(n_1\) and \(n_2\) parent–offspring links, that ancestor contributes \(2^{-(n_1+n_2+1)}\) to kinship. This rule applies when the pedigree paths are distinct and there are no additional shared ancestors or loops; otherwise, contributions and pedigree structure must be handled with care.

A grandparent and grandchild have one common ancestor with path lengths 0 and 2 if the grandparent is counted as the common ancestor, giving \(2^{-3}=1/8\). An aunt or uncle and a niece or nephew have two common grandparents; each contributes \(1/16\), for a total kinship of \(1/8\). First cousins have two common grandparents, each reached by paths of length 2 from both cousins. Each contributes \(2^{-5}=1/32\), so their total is \(1/16\).

When Benchmarks Change and Why They Matter

Pedigree values are reference expectations, not universal constants that apply regardless of family structure. The parent–offspring derivation shows explicitly that a parent’s inbreeding can change the coefficient. Likewise, if the parents of full siblings are related or inbred, their kinship need not equal the simple \(1/4\) benchmark. Additional shared ancestors can raise the coefficient for any pair. A pedigree should therefore be checked for inbreeding and extra connections before a conventional value is used as an expectation.

These benchmarks help describe the scale of a relationship and provide a conceptual reference when considering relatedness estimates. They do not determine a particular pair’s observed sharing at each locus: inheritance is random, and realized sharing can differ from its pedigree expectation. Later analyses may estimate relatedness from genotype data, but the pedigree coefficients themselves are defined by inheritance probabilities, not by a calculation from observed genotype codes.

Common mistake: “Parent–offspring kinship is \(1/2\), because a child inherits half of its genome from each parent.” This uses the doubled relatedness scale while labeling it kinship. The correction is to state the scale: under the standard non-inbred, unrelated-parent assumptions, \(\phi=1/4\) and \(r=2\phi=1/2\). A second related pitfall is to apply \(1/4\) to every parent–offspring pair without checking parental inbreeding or the relationship between the parents.