# Coefficient of Inbreeding

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Inbreeding occurs when relatives unite to produce children. The degree of inbreeding can be measured by the coefficient of inbreeding^{[1]}, which is defined as:

(1)

where

- is the coefficient of inbreeding of the individual;
- is the number of common ancestors of the individual's parents;
- indexes the common ancestors;
- is the number of generations from the father to common ancestor ;
- is the number of generations from the mother to common ancestor ; and
- is the coefficient of inbreeding of common ancestor .

Equation (1) is hard to compute and has been criticised by more recent writers. The coefficient of inbreeding of the children of unrelated but inbred parents is set to zero. Therefore, **at Familypedia we use the following coefficient**:

(2)

where

- is the Familypedia coefficient of inbreeding for ; and
- is the Wright coefficient of inbreeding of the parents as defined by Equation (1) for .

Equation (2) is easy to compute as it only uses information about the parents and their relationship. The Wright coefficients can be seen from Table 1.

**Table 1. Wright coefficient of inbreeding for selected cases**

Relationship between parents | Coefficient of inbreeding |
---|---|

Parent/child | 0.500000000 |

Grandparent/grandchild | 0.250000000 |

Siblings | 0.250000000 |

Great-grandparent/great-grandchild | 0.125000000 |

Half-siblings | 0.125000000 |

Aunt/nephew, Uncle/niece | 0.125000000 |

Double first cousins | 0.125000000 |

First cousins | 0.062500000 |

First cousins once removed | 0.031250000 |

First cousins twice removed | 0.015625000 |

Second cousins | 0.015625000 |

Second cousins once removed | 0.007812500 |

Second cousins twice removed | 0.003906250 |

Third cousins | 0.003906250 |

Third cousins once removed | 0.001953125 |

Fourth cousins | 0.000976563 |

## See alsoEdit

## ReferencesEdit

- ^ Sewall Wright (1922), 'Coefficients of Inbreeding and Relationship',
*The American Naturalist*,**56**(645), 330-338.

## External linksEdit

- Wikipedia:Coefficient of relationship
- CoI on Supanet - includes worked examples and evaluations of the Wright coefficient