Consanguinity calculator: Wright's coefficient, inbreeding F, and recessive disease risk

Short version. Consanguinity is partnership between two individuals who share one or more recent common ancestors. It is quantified by two related coefficients: Wright's coefficient of relationship (r), the expected proportion of alleles shared identical by descent between two individuals, and the inbreeding coefficient (F), the probability that an offspring's two alleles at a locus are identical by descent from a common ancestor. For first cousins, r = 1/8 and the offspring's F = 1/16. Consanguinity raises the risk of recessive disease, with the largest relative effect for rare alleles. Clinical counselling should present absolute as well as relative risks and be culturally sensitive.

Defining consanguinity

In clinical genetics, "consanguinity" generally refers to unions between individuals related as second cousins or closer (F ≥ 1/64). Unions between more distant relatives have a diminishing effect on genotype probabilities and are not typically the focus of counselling. In population genetics, the same coefficients describe non-random mating in any structured population.

The clinical concern is straightforward: relatives share alleles inherited from common ancestors. If one of those ancestral alleles is a recessive disease allele, the probability that both partners carry it (and therefore the probability of an affected offspring) is elevated above the population baseline.

Wright's coefficient of relationship (r)

Wright's coefficient r is the expected fraction of alleles shared identical by descent between two individuals. For each step of descent along the shortest ancestral path, the allele has a 1/2 probability of being transmitted. The coefficient for two individuals connected by N links through L common ancestors is:

r = Σ(1/2)^L+1 summed over all loops through each common ancestor.

For common relationships:

Distantly related unions have F values small enough that the consanguinity contribution to disease risk is generally swamped by the baseline population risk and is not typically discussed in counselling unless a specific founder mutation or small endogamous population is at play.

The inbreeding coefficient F

F measures the probability that at a randomly chosen locus in the offspring, both alleles are identical by descent from a recent common ancestor. For simple genealogies without additional inbreeding in the ancestral line, F for the offspring is half the coefficient of relationship between the parents.

F has two useful interpretations:

• Autozygosity fraction: on average, a proportion F of the genome is expected to be homozygous by descent. Modern genomic tools (runs of homozygosity, ROH) provide an empirical estimate of autozygosity that often correlates with pedigree F but with individual-level variation.
• Recessive-risk weight: the increase in homozygous-by-descent probability at any locus, which translates directly into increased probability of autosomal recessive disease for any allele segregating in the shared ancestry.

Clinical significance: recessive disease risk

For a rare autosomal recessive allele with frequency q, the probability that an offspring is homozygous affected is approximately:

P(affected) = Fq + (1 - F)q²

For small q, the term Fq dominates. For an allele with q = 1/1000 (incidence 1 in 1,000,000 at population baseline), a first-cousin couple (F = 1/16) gives P(affected) ≈ 1/16000 — a sixty-fold relative increase, but still a low absolute probability per pregnancy.

For a common allele with q = 1/50 (incidence 1 in 2,500), a first-cousin couple gives P ≈ 1/16 × 1/50 + (15/16) × 1/2500 ≈ 1/780. The relative increase here is smaller (about three-fold) but the absolute risk is higher.

The clinical upshot: consanguinity raises the risk of any rare recessive condition in the shared ancestry. For a family with known recessive conditions in the pedigree, the risk for that specific condition is further elevated. For a family with no known conditions, an approximate "background" risk increment is often quoted as a few percent above the population baseline for a first-cousin couple's risk of serious congenital or developmental condition in offspring — but empirical estimates vary and should be presented with appropriate uncertainty.

Counselling communication

Consanguineous unions are common in several cultures and religious traditions, with historic and contemporary practice across much of the Middle East, North Africa, and South Asia, among other regions. Genetic counselling should:

• Present absolute as well as relative risks. "Three-fold increased" is much less informative to a family than "approximately 1 in 40 rather than 1 in 120."
• Distinguish family-specific from background risk. A first-cousin couple with a known recessive condition in the shared lineage is in a different risk category from a first-cousin couple with no known conditions.
• Avoid stigmatising framing. Consanguinity is a demographic and cultural fact; it is not a "mistake" to be counselled against but a context to be understood.
• Offer appropriate screening. Expanded carrier screening panels, targeted testing for conditions with known founder variants in the family's ancestry, and prenatal options (CVS, amniocentesis, NIPT where applicable) should be discussed factually.
• Acknowledge limitations. The risk increment is probabilistic; many consanguineous couples have entirely healthy children. The purpose of counselling is to inform, not to direct reproductive decisions.

Edge cases and complications

Several situations complicate the simple Fq calculation:

• Multiple loops of relatedness: a couple related through more than one common ancestor (for example, double first cousins) has F summed across each loop. Standard pedigree-tracing software computes this automatically; manual calculation is error-prone.
• Pre-existing inbreeding: in families with multiple generations of consanguinity, F is cumulative and can exceed the standard first-cousin value. Empirical autozygosity estimates are helpful.
• Small endogamous populations: baseline population structure can create meaningful F values even when no specific consanguinity is reported. Community-specific founder variants may be the dominant consideration.
• Adopted or donor-conceived relationships: social relationships are not always biological; consanguinity calculation requires biological ancestry.

How Evagene supports this

Evagene automatically detects consanguineous unions in a pedigree as it is drawn. When two partners on the canvas are connected through shared ancestors, Evagene traces the ancestral path, calculates Wright's coefficient of relationship r for the couple, and computes the inbreeding coefficient F for any offspring. Multiple loops of relatedness are handled automatically.

The coefficient is then integrated into the Mendelian inheritance calculator: autosomal recessive risk estimates for offspring of consanguineous couples are computed as Fq + (1-F)q² using family-specific allele frequency priors and ancestry-appropriate population data. For conditions catalogued in the 200+ disease library, the calculator reports the absolute per-pregnancy risk alongside the relative increase, making the distinction clear in counselling.

Ancestry can be entered manually or inferred from 23andMe SNP imports where those data are available, so population carrier frequencies are drawn from the relevant reference. The consanguinity flag is also surfaced in batch risk screening, so any condition whose risk is materially elevated by the union is highlighted. AI interpretation drafts a culturally respectful narrative around the identified consanguinity and its specific implications for this family, using your own Anthropic or OpenAI LLM key.

Frequently asked questions

Related reading

• Mendelian inheritance calculator overview
• Autosomal recessive calculator
• Carrier probability calculator
• Identifying inheritance patterns
• Clinical genetics pedigree tools
• Three-generation family history