# Consanguinity and relationship

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This part explains the concepts of **consanguinity** and **relationship** used by GeneWeb and how they are computed. The algorithms of consanguinity and relationship were written by Didier Rémy, director of research at INRIA. We thank him for that.

## Consanguinity and Relationship

The genom of an individual consists of a great number of genes which, if mutations are ignored, reproduce identically. The genes can be used to measure the identity of a person. The genes are placed in precise locations named “locus”. Each individual has for each locus two genes, one transmitted by his mother, the other by his father, and transmits to his children a copy of the one of his genes.

The **Consanguinity** of an individual **x** is the probability **cg(x)** to find in a given locus two identical genes.

The **Relationship** of two individuals **x** and **y** is the probability **pr(x, y)** to find in the same locus two identical genes.

## Computations

A probability calculus shows that:

- The consanguinity
**cg(x)**is equal to the relationship**pr(px,mx)**of the parents**px**and**mx**of**x**. - If
**x..a..y**is a minimal relationship link between**x**and**y**(i.e. such as the branches**x..a**and**a..y**have just**a**in common), then it contributes to the relationship of**x**and**y**of a factor where**n**is the length (distance**x..a**+ distance**a..y**) of the relationship link**x..a..y**.

The relationship of **x** and **y** is the sum of the contributions of all their minimal relationship links.

## GeneWeb

If the parameter `show_consang=`

in .gwf allows it, GeneWeb displays the consanguinity and the relationship in the form of a percentage.

Statistically, on the great number of locuses of an individual, the consanguinity corresponds approximately to the percentage of his locuses holding identical genes.

## References

- Albert Jacquard,
*Genetic structures of the Populations*, Masson & Co, 1970.