Why Track the Origin of an Allele Copy?
Two relatives can carry alleles with the same observed state without inheriting them from the same ancestor. For example, both might have an allele recorded as \(G\), even though each inherited it from a different ancestral copy. Conversely, a pedigree can show that copies descend from the same ancestral copy, which is information about their origin, not just their observed state. Identity by descent gives a precise way to describe that origin at a particular genetic locus.
The distinction matters because a genotype records which allele states an individual has, whereas a pedigree records possible paths of inheritance. Genotype data alone do not always reveal those paths. To discuss identity by descent, first specify the locus and track the ancestry of each allele copy through the pedigree.
Copies, States, and Ancestral Labels
For a diploid individual, there are two allele copies at an autosomal locus, one on each homologous chromosome. An allele's state is its observed form at that locus, such as \(G\) or \(A\). Its ancestral-copy label identifies the ancestral allele copy from which it descends. The label is a bookkeeping device for lineage; it does not mean that the same physical DNA molecule remains intact through generations.
For example, suppose an individual has one copy with state \(G\) descended from ancestral copy \(M_1\), and one copy with state \(T\) descended from ancestral copy \(P_1\). We can record the individual's copies as \((M_1,G)\) and \((P_1,T)\). A descendant who inherits the first copy has ancestry label \(M_1\) at this locus. Under Mendelian transmission, a parent passes one of its two copies at the locus to each offspring.
The basic examples below use a specified pedigree, a diploid autosomal locus, Mendelian transmission, and no mutation between the ancestral and observed copies. Founder allele copies are treated as distinct unless a shared ancestor is represented in the pedigree. This is the usual pedigree-boundary assumption: ancestry outside the recorded pedigree is not counted as a shared origin unless it is specified. If that assumption is unsuitable, the pedigree or founder model must be expanded.
The count describes a particular pair of individuals and a particular set of inheritance paths. When the paths are not known, the IBD status may be uncertain. The count itself is not a probability: probabilities require a model for the possible transmissions.
Worked Example: A Parent and an Offspring
Worked Example: A Parent and an Offspring
At a locus with no mutation, suppose parent \(A\) has copies \((U_1,G)\) and \((U_2,T)\). The child inherits \(U_1\) from \(A\), and inherits \((V_1,C)\) from the other parent. Find the number of IBD copies shared by \(A\) and the child.
The parent's label set is \(\mathcal{L}_A=\{U_1,U_2\}\). The child's label set is \(\mathcal{L}_C=\{U_1,V_1\}\). Therefore, $$ S_{\mathrm{IBD}}(A,C) =\left|\{U_1,U_2\}\cap\{U_1,V_1\}\right| =|\{U_1\}| =1. $$
They share one ancestral copy, \(U_1\), so this pair is IBD for one of its two copies. The copy with state \(G\) in each individual is IBD because both descend from \(U_1\). The child's other copy has label \(V_1\), not \(U_2\), and is not a second IBD match to the parent's untransmitted copy.
IBD States at a Locus
For a pair of diploid individuals in the setting above, their IBD state is often summarized by the number of shared ancestral copies: 0, 1, or 2. This is a count of shared origins, not a count of equal-looking allele states. The possible counts have direct pedigree interpretations:
| Shared-copy count | Meaning at the locus | What it does not establish |
|---|---|---|
| 0 | No ancestral allele-copy origin is shared between the pair. | It does not mean their allele states must differ. |
| 1 | One ancestral allele-copy origin is shared. | It does not mean the pair has only one matching allele state. |
| 2 | Two ancestral allele-copy origins are shared. | It is not inferred merely because both genotypes look the same. |
To determine a state, follow each copy's transmission path at the locus and compare ancestral labels. Do not infer IBD just by comparing genotype letters. A parent may pass either homolog at a locus, so a relationship alone does not identify which copy was transmitted in a particular inheritance realization.
Worked Example: Siblings Sharing One Parental Copy
Suppose one parent has copies \((M_1,G)\) and \((M_2,A)\), and the other has \((P_1,C)\) and \((P_2,T)\). In one hypothetical transmission, sibling \(X\) inherits \(M_1\) and \(P_1\), while sibling \(Y\) inherits \(M_1\) and \(P_2\). Find their shared-copy count.
The label sets are \(\mathcal{L}_X=\{M_1,P_1\}\) and \(\mathcal{L}_Y=\{M_1,P_2\}\). Thus, $$ S_{\mathrm{IBD}}(X,Y) =\left|\{M_1,P_1\}\cap\{M_1,P_2\}\right| =|\{M_1\}| =1. $$
The siblings share the maternal ancestral copy \(M_1\), so they are IBD for one copy. Their states are \(G,C\) and \(G,T\); the matching \(G\) copies are IBD because both trace to \(M_1\). The paternal copies differ in ancestral label, so they do not form a second IBD match.
Worked Example: Matching Genotypes Without Shared Descent
Consider two individuals treated as unrelated founders under the stated pedigree-boundary assumption. Individual \(R\) has copies \((R_1,A)\) and \((R_2,G)\); individual \(S\) has copies \((S_1,A)\) and \((S_2,G)\). Assume all four founder copies have distinct origins. Calculate the shared-copy count.
Here \(\mathcal{L}_R=\{R_1,R_2\}\) and \(\mathcal{L}_S=\{S_1,S_2\}\). Therefore, $$ S_{\mathrm{IBD}}(R,S) =\left|\{R_1,R_2\}\cap\{S_1,S_2\}\right| =|\varnothing| =0. $$
Both individuals have the same genotype states, \(A\) and \(G\), but neither allele-copy origin is shared under this model. Their matching states are IBS, not IBD. If the individuals actually share an unrecorded ancestor, the pedigree-boundary assumption would not describe that ancestry; the result would need to be reconsidered using an appropriate pedigree.
Why IBD Usually Implies a Matching State—and Its Limit
Under the no-mutation assumption used in the examples, two copies descending from the same ancestral copy have the same state. The justification is direct: at the starting point, both lineages have the state of their common ancestral copy; each transmission passes on that state unchanged under the no-mutation assumption. Following either lineage therefore preserves the state, so the two descendant states match.
The converse does not follow. Distinct founder copies can independently have the same state, as in the preceding example. Thus, observing a match is not enough to establish a common ancestral copy. Also, the no-mutation assumption is important: if a mutation occurs along one lineage, two copies can share an ancestral origin yet have different observed states. Their IBD status concerns descent; their observed states concern what is present at the locus.
Common Mistakes and Practical Interpretation
- Calling every matching allele IBD. The wrong reasoning is, “Both relatives have \(G\), so they inherited the same \(G\).” The correction is to trace copy labels: matching states from different ancestral copies are IBS, not IBD.
- Treating IBD as a property of a letter. A state such as \(G\) does not itself carry an IBD label. IBD describes the relationship between copies at a specified locus.
- Assuming a pedigree reveals the realized transmissions. A known relationship may leave multiple possible copies that could have been transmitted. If the realized inheritance is unknown, distinguish a possible IBD state from a state established by the available information.
- Ignoring the pedigree boundary. If founder copies are assumed distinct, unrecorded shared ancestry is excluded by the model. That is an assumption about the pedigree, not proof that the individuals have no shared ancestry in the wider population.
- Confusing ancestry with physical identity. Copies in descendants are not the same physical molecules as the ancestral copy. “Descent from the same copy” is a statement about the line of inheritance.
IBD is useful because it separates genealogical sharing from coincidental similarity in allele state. That distinction is essential when interpreting genetic data in a pedigree: a genotype match can be compatible with shared descent, but it does not by itself demonstrate it. The pedigree and the transmission paths supply the origin information.
Check Your Understanding
For each question, distinguish allele state from ancestral-copy origin.
- Two relatives both have an allele with state \(A\). What additional information would establish whether those copies are IBD?
- A parent has copies labeled \(Q_1\) and \(Q_2\), and a child inherits \(Q_2\). What is the shared-copy count for that transmitted copy, and why is the parent's \(Q_1\) not an additional match?
- Two unrelated founders have matching genotype states, but all their founder-copy labels are distinct. What is their IBD count under that pedigree-boundary assumption?
- Can two copies be IBD but have different observed states? State the assumption under which your answer holds.
- Why is an IBD count not automatically a probability?