Given a pedigree, the matrix of coefficients of fraternity are returned - the D matrix. Note, no inbreeding must be assumed. Will return the inverse of the D matrix by default, otherwise this operation can be skipped if desired.

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`pedigree ` |
A pedigree with columns organized: ID, Dam, Sire |

`invertD ` |
A logical indicating whether or not to invert the D matrix |

Missing parents (e.g., base population) should be denoted by either 'NA' or '0'.

There exists no convenient method of obtaining the inverse of the dominance genetic relatedness matrix (or the D matrix itself) directly from a pedigree (such as for the inverse of A, i.e., Quaas (1995)). Therefore, this function computes the coefficient of fraternity (Lynch and Walsh, 1998) for every individual in the pedigree with a non-zero additive genetic relatedness. Note, the construction of the D matrix is more computationally demanding (in time and space) than is the construction of A.

`A ` |
the A matrix in sparse matrix form |

`D ` |
the D matrix in sparse matrix form |

`logDet ` |
the log determinant of the D matrix |

`Dinv ` |
the inverse of the D matrix in sparse matrix form |

`listDinv ` |
the three column form of the non-zero elements for the inverse of the D matrix |

Quaas, R.L. 1995. Fx algorithms. An unpublished note.

Lynch M., & Walsh, B. 1998. Genetics and Analysis of Quantitative Traits. Sinauer, Sunderland, Massachusetts.

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