Why Similar Genotypes Need Careful Interpretation
Two people can carry the same allele at a genetic marker and still have inherited their copies through different ancestral lines. This distinction matters whenever genetic data are used to describe similarity or relatedness: an observed match is a fact about the allele states recorded now, while descent concerns the historical path by which allele copies were inherited.
For example, the allele labelled \(A\) at a marker may be common in a population. Two people who each carry \(A\) could have received their copies from different parents and different ancestors. Their copies match in state, but the match alone does not reveal whether those copies have a recent common origin. To reason clearly, keep the observed allele label separate from the identity of the physical copy and its ancestry.
Allele State and Ancestral Copy Are Different Things
At a biallelic locus, the two allele states might be labelled \(A\) and \(G\). A diploid individual has two allele copies at that locus, so a genotype may be \(A/A\), \(A/G\), or \(G/G\). A genotype records the states of the two copies; by itself, it does not identify the ancestors from whom those copies came.
IBS is a comparison of states. If one person has an \(A\) copy and another person has an \(A\) copy, those copies are IBS at the locus. IBD is a comparison of descent histories. If both copies were inherited from the same ancestral \(A\) copy, they are IBD. If they arose on separate ancestral lines, they can be IBS without being IBD.
The distinction applies to copies, not just whole genotypes. Two people with genotypes \(A/G\) and \(A/A\) share an \(A\) state, but that observation does not say whether their \(A\) copies are IBD. Conversely, two relatives can inherit a particular ancestral copy even when their full genotypes differ, because the other allele copy in each person may differ.
In real data, mutations add a qualification: copies descended from the same ancestral copy can acquire different observed states if a mutation occurs along one branch. Introductory discussions commonly assume no mutation at the locus over the ancestry being considered. With that assumption, IBD implies IBS, but IBS still does not imply IBD.
Worked Example: A Common Genotype Match Is Not Evidence of a Specific Ancestor
Suppose a hypothetical population has allele frequencies \(p=0.8\) for \(A\) and \(q=0.2\) for \(G\), with \(p+q=1\). Two people are sampled independently from this population. Assume Hardy–Weinberg genotype proportions, the same allele frequencies for both people, and no dependence between their genotypes. What is the probability that their genotypes match exactly?
Under Hardy–Weinberg proportions, the probabilities for one sampled person are \(P(A/A)=p^2=0.64\), \(P(A/G)=2pq=0.32\), and \(P(G/G)=q^2=0.04\). Because the two people are independently sampled, the probability that both have \(A/A\) is \(0.64\times0.64\); the probability that both have \(A/G\) is \(0.32\times0.32\); and the probability that both have \(G/G\) is \(0.04\times0.04\).
The three matching-genotype events do not overlap, so their probabilities add:
Thus, under these assumptions, two independent sampled people have a 51.36% chance of matching genotypes at this one locus. The calculation concerns genotype states, not genealogical history. A match can therefore be quite ordinary at a locus with a common allele; it does not establish that the people share a recent ancestor.
Tracing IBD Through Inheritance
A pedigree gives information about possible routes of descent. At a locus, a parent has two allele copies and passes one of them to each child. If two children receive the same physical copy from that parent, their inherited copies are IBD, even if the children’s other copies differ. The fact that the transmitted copies have the same state is not enough on its own to identify this route; the pedigree or other evidence about descent is what establishes it.
For a simple transmission calculation, assume Mendelian inheritance: each parent’s two copies are equally likely to be transmitted, and transmissions to two children are independent conditional on the parent’s genotype. This describes the probability of inheritance under the model, not a procedure for inferring a pedigree from genotypes.
Worked Example: Two Siblings Inherit the Same Parental Copy
In a hypothetical family, the mother has genotype \(A/G\) and the father has genotype \(C/T\) at a locus. The mother transmits her \(A\) copy to each of two children. The father transmits \(C\) to the first child and \(T\) to the second. The children’s genotypes are therefore \(A/C\) and \(A/T\).
The children have different genotypes, but each carries the very same maternal \(A\) copy: the mother had only one \(A\) copy, and both children inherited it. Their maternal copies are IBD. The children also share the allele state \(A\), so those two copies are IBS under the no-mutation assumption.
The probability that the mother transmits \(A\) to both children is \(1/2\times1/2=1/4\), because each child independently receives either of her two copies with probability \(1/2\). If the paternal transmissions specified in the example are also considered, their probability is \(1/2\times1/2=1/4\). The joint probability of all four specified transmissions is therefore \(1/4\times1/4=1/16\), under independent Mendelian transmissions from the two parents. The IBD conclusion in the example follows from the stated inheritance path, not merely from seeing an \(A\) in each genotype.
The example also shows why “same genotype” and “same ancestral copy” are not interchangeable descriptions. Genotypes summarize pairs of states, while IBD asks whether particular copies have the same origin. A pair may share an IBD copy without having matching genotypes, and a pair may have matching genotypes without sharing a recent IBD copy.
How IBS Can Occur Without Recent IBD
Suppose allele copies are sampled from a population in which \(A\) has frequency \(0.8\) and \(G\) has frequency \(0.2\). Under independent sampling of two copies, the chance that their states match is the chance that both are \(A\) plus the chance that both are \(G\). This calculation describes IBS. It does not require the two copies to have a shared ancestor within a specified recent pedigree.
Worked Example: Matching Allele States on Separate Ancestral Lines
Consider two hypothetical allele copies sampled independently, with \(P(A)=0.8\) and \(P(G)=0.2\). For this example, the pedigree model treats the sampled copies as coming from separate founder lines, with no shared ancestor within the generations represented. What is the probability that the copies are IBS?
The copies match if both are \(A\) or both are \(G\). Under independent sampling, \(P(A,A)=0.8\times0.8=0.64\), and \(P(G,G)=0.2\times0.2=0.04\). These events are mutually exclusive, so
The probability of a state match is 68%. In this stipulated pedigree model, a match can occur even though the copies do not share a recent ancestor in the generations represented: they may simply both be \(A\), or both be \(G\). The model does not rule out a more distant common ancestor outside its stated pedigree window. The calculation demonstrates why an allele-state match cannot, by itself, establish recent IBD.
A Short Derivation: Why IBD Implies IBS Under the Basic Model
Assume that allele states are transmitted unchanged from an ancestral copy to its descendants. Let two copies be IBD, meaning they both descend from one ancestral copy. Because neither branch changes the state, each descendant copy has the state of that same ancestor. Therefore their observed states are equal, so the copies are IBS.
This implication is one-way. Observing the same state does not identify a shared ancestral copy: the \(A\) state can occur on separate lineages, particularly when \(A\) is common. If mutation is allowed, even the one-way implication needs qualification, because a mutation on one branch can make two descendants of the same ancestral copy differ in state.
For a pair of diploid individuals, there are two allele copies per person at a locus. A kinship coefficient is an ancestry-based probability: it is the probability that one allele copy chosen at random from each individual at the locus is IBD. This is different from the observed fraction of matching allele states. A state-match summary may contain information relevant to relatedness, but it is not itself the probability of IBD; interpretation depends on allele frequencies, population assumptions, and the inheritance model.
What the Distinction Does—and Does Not—Tell Us
IBS and IBD answer different questions. IBS asks, “Do these copies have the same recorded allele state here?” IBD asks, “Do these copies descend from the same ancestral copy?” The first is directly about observed genotypes. The second is about ancestry and inheritance. Neither label alone summarizes all genomic similarity across people: at different loci, the same pair may have different state matches and different descent histories.
This distinction is useful when interpreting genetic similarity in populations with common alleles or shared ancestry. Two people drawn from the same population can match at many markers because common states occur frequently, even if they are not close relatives. Conversely, relatives may fail to match at a particular copy because they inherited different ancestral copies. A single marker is especially limited: it provides only a small piece of evidence about a much larger inheritance history.
Population context matters as well. If allele frequencies differ across groups, a state match may be more or less common depending on the population being used as a reference. The earlier material on population structure and reference-panel choice motivates care in defining that context. Similarity should not be converted into a claim about recent ancestry without a model that accounts for the relevant frequencies and descent process.
Common Mistakes
- Equating a matching allele with a shared ancestor. “Both people have \(A\), so they inherited it from the same recent ancestor” is not justified. \(A\) may be common and may occur on separate lineages. The match establishes IBS, not necessarily IBD.
- Calling different genotypes proof of no shared descent. Two people can inherit the same ancestral copy but have different other copies, as in the sibling example. Compare the relevant allele copies and their inheritance paths, rather than only the full genotype labels.
- Treating IBS as a probability of relatedness. A proportion of matching states is an observed similarity summary. A kinship coefficient concerns the probability of IBD under a specified ancestry model. They are not interchangeable.
- Ignoring assumptions behind a probability calculation. A genotype-match probability calculated under Hardy–Weinberg proportions and independent sampling is conditional on those assumptions and the allele frequencies used. It is not a universal probability for every population or pair of individuals.
- Forgetting the mutation qualification. In the no-mutation model, IBD implies IBS. If mutation is possible, descendants of one ancestral copy need not retain the same observed state.
Check Your Understanding
Answer each question by distinguishing observed allele states from the ancestry of allele copies.
- At one locus, two people each carry an \(A\) allele. What does this observation establish, and what does it not establish?
- Under the no-mutation model, why does IBD imply IBS? Why does the converse fail?
- Two siblings inherit the same maternal allele copy but receive different paternal copies. Must their genotypes match? Explain.
- For allele frequencies \(P(A)=0.7\) and \(P(G)=0.3\), calculate the probability that two independently sampled allele copies are IBS.
- In one sentence, distinguish an observed genotype-match proportion from a kinship coefficient.