How does an inbreeding coefficient measure genetic relatedness between parents?

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consanguinity (Left) Absence of inbreeding: horizontal lines connect mates, vertical lines connect parents with their child; (right) an inbreeding loop: horizontal bar at top of loop connects brother and sister, all other lines and bars as above

The inbreeding coefficient (F) is a statistical measure used to define the probability that an individual inherits two alleles that are identical by descent—meaning they originated from the same common ancestor.1

Rather than measuring the relatedness of the parents directly, the coefficient quantifies the likelihood that their offspring will receive a pair of identical genes from a shared forebear. This probability is determined by the degree of consanguinity between the parents:1

Sibling mating: The offspring has a 1 in 4 (0.25) chance of inheriting identical alleles.1
Aunt-nephew mating: The likelihood is 1 in 8 (0.125).1
First-cousin mating: The likelihood is 1 in 16 (0.0625).1

In pedigree construction, inbreeding is represented by loops connecting the parents. The total inbreeding coefficient for an individual is the sum of the values calculated for all such loops. High values of F typically occur in small, isolated populations where members marry within the community over many generations.1