Finding genes in families: linkage, sibling pairs and recurrence risk

Updated November 2026

Before genome-wide association studies, geneticists found disease genes by following DNA markers through families: if a marker and a disease are inherited together more often than chance allows, the gene is probably nearby. The main tools were LOD scores, affected sibling pairs and the sibling risk ratio λs.

The short version

Genetic markers are DNA variants at known positions. Genes close to a marker on the same chromosome tend to be inherited with it: they are linked.
A LOD score is the log₁₀ of a likelihood ratio: linkage versus no linkage. LOD ≥ 3 (odds of 1,000 to 1) is the classic threshold for declaring linkage.
Any two full siblings share 0, 1 or 2 copies of a stretch of DNA identical by descent (IBD) with probabilities 25%, 50%, 25%. Pairs of affected siblings who share more than that near a gene point to linkage.
λs = risk to siblings of an affected person ÷ population prevalence. It measures how strongly a condition clusters in families.
For common, complex traits, GWAS largely replaced linkage from the mid-2000s, because it can detect many variants with small effects.

Markers and linkage

When a parent makes an egg or sperm, the two copies of each chromosome swap segments by crossing over. Positions far apart, or on different chromosomes, are separated half the time; positions close together rarely are. The recombination fraction, θ (theta), is the proportion of offspring in which they are separated. It ranges from 0 (always inherited together) to 0.5 (independent, as for genes on different chromosomes). A recombination fraction of 1% corresponds to 1 centimorgan (cM) of genetic distance.

A useful marker must be polymorphic (vary between people) so you can tell which parental copy a child inherited. Early genome scans used a few hundred microsatellites (short DNA motifs repeated a variable number of times); later studies use single-nucleotide polymorphisms (SNPs).

LOD scores

For a family, you calculate how likely the observed pattern of marker and disease inheritance is if the disease gene is linked to the marker at some θ, and how likely it is if they are unlinked (θ = 0.5). The LOD score ("logarithm of the odds") is:

LOD(θ) = log₁₀ [ L(data | θ) ÷ L(data | θ = 0.5) ]

A LOD of 3 means the data are 10³ = 1,000 times more likely under linkage than under no linkage. This is a likelihood ratio, not the probability that linkage is real (see likelihood vs probability).
LODs from independent families can simply be added, because multiplying likelihoods means adding their logarithms.
The traditional threshold for declaring linkage of a single-gene (Mendelian) trait is LOD ≥ 3.0. A LOD of −2 or lower is taken as excluding linkage at that θ.
The bar is set this high because any particular marker is unlikely to be near the gene to begin with; LOD 3 corresponds roughly to a 5% chance of a false claim. When a whole genome is scanned for a complex trait, Lander and Kruglyak (1995) proposed slightly stricter thresholds, about 3.3 for genome-wide significance with LOD scores.

A famous example: in 1990, 23 families with early-onset breast cancer gave a LOD score of 5.98 for a marker on chromosome 17, leading to the gene later named BRCA1.

Classic LOD scores are "parametric": you must specify the mode of inheritance, penetrance and allele frequency, which is hard for complex conditions.

Affected sibling pairs

The affected sib-pair method avoids specifying a genetic model. It only asks: at this marker, do siblings who both have the condition share more DNA by descent than siblings normally do?

Two alleles are identical by descent (IBD) if they are copies of the same parental chromosome segment. For any position in the genome, a pair of full siblings has:

Expected IBD sharing between full siblings at any locus, with no linkage
Alleles shared IBD	Probability	Why
0	25%	Different allele from mother (½) and from father (½): ½ × ½
1	50%	Same from one parent, different from the other: 2 × ½ × ½
2	25%	Same from both parents: ½ × ½

On average siblings share half their alleles IBD. Near a gene that influences the condition, pairs who are both affected should share more often than 25/50/25 predicts. Hypothetical example: in 400 affected pairs, chance alone predicts 100, 200 and 100 pairs sharing 0, 1 and 2 alleles. If you observe 70, 190 and 140, mean sharing is (190 × 1 + 140 × 2) ÷ (400 × 2) = 470 ÷ 800 ≈ 59% instead of 50%, a sign of linkage. Real analyses then test whether such excess sharing is larger than chance allows, using genome-wide thresholds.

The method is model-free, but it typically needs hundreds of sib pairs and loses power quickly when each gene has only a small effect.

The sibling recurrence risk ratio, λs

λs = (risk that a sibling of an affected person is also affected) ÷ (prevalence in the general population)

Example: a condition affects 1% of people, and 10% of siblings of affected people. λs = 10% ÷ 1% = 10.
A rare dominant single-gene disorder with prevalence 1 in 10,000 and a 50% sibling risk has λs = 0.5 ÷ 0.0001 = 5,000. That is why linkage worked so well for Mendelian diseases.

Neil Risch (1990) defined this family of ratios (λR for relatives of type R) and showed that λR is the critical quantity for the power of affected-relative-pair linkage studies. Under a single-locus model, λR − 1 halves with each step further apart in relationship. He also showed that the chance an affected sib pair shares 0 alleles IBD at a disease locus is 0.25 ÷ λs for that locus: a gene contributing a λs of 2 lowers the "share nothing" fraction from 25% to 12.5%. Most genes for common traits contribute far less than that, which is why sib-pair scans for common diseases often found weak, hard-to-replicate signals.

Caution. λs measures familial clustering, not genetics alone. Siblings also share homes, diets and exposures, so shared environment can raise λs too.

How GWAS took over

A genome-wide association study (GWAS) compares the frequencies of hundreds of thousands to millions of SNPs between many people with a condition and many without (or across people with different values of a trait). It needs no families. It became practical in the mid-2000s, after the Human Genome Project (2003) and HapMap (2005); an early success linked the complement factor H gene to age-related macular degeneration.

Linkage is good at finding rare variants with large effects; association is far more powerful for common variants with small effects, which turned out to be the main architecture of most common traits. Because so many SNPs are tested, GWAS uses a strict genome-wide significance threshold, conventionally p < 5 × 10⁻⁸. An associated SNP marks a region and may simply travel with the true causal variant nearby.

Family-based linkage has not disappeared: combined with exome or genome sequencing, it is still used to find the causes of rare inherited disorders.

Memory aid

"Quarter, half, quarter — unless it matters." Siblings share 0, 1 or 2 alleles IBD in a 1 : 2 : 1 ratio, like tossing two coins (two tails, one of each, two heads). Affected siblings tip the coins toward sharing near a gene that matters.

For λs: "Sibs over all": sibling risk on top, everyone's risk below.

A verse to remember it

Tune: London Bridge Is Falling DownSisters, brothers share by chance None, one, two; none, one, two; Quarter, half, and quarter, too, By chance alone. Affected pairs share more than that Near the gene, near the gene; LOD of three: a thousand to one For linkage. Sibling risk divided by Everyone's, everyone's, Gives you lambda-s, and that's why Families matter.

Check yourself

What is the probability that two full siblings share both alleles IBD at a given locus, and what is their average sharing?

25% share both alleles; average sharing is 50% of alleles (one allele out of two).

A family gives LOD = 1.2 and a second gives LOD = 2.1 at the same θ. What is the combined LOD, and does it meet the classic threshold?

1.2 + 2.1 = 3.3, which exceeds 3.0. (For a genome-wide scan of a complex trait, about 3.3 is the stricter threshold proposed by Lander and Kruglyak.)

A disease has a prevalence of 0.5% and a sibling recurrence risk of 4%. What is λs?

4% ÷ 0.5% = 8.

Why did GWAS replace linkage for common diseases?

Common diseases are mostly influenced by many common variants with small effects. Linkage studies have little power to detect small effects, while large case–control association studies can.