Pedigrees - pedigree representation and extractors

Pedigree representation

A pedigree is represented as a Julia type constructed from two integer vectors, sire and dam. A parent not in the pedigree is coded as 0.

By default the Pedigreeconstructor reorders the pedigree according to the "longest ancestral path" for each animal. This guarantees that parents in the pedigree occur before their offspring, because the longest ancestral path of the offspring is greater than that of either parent. The permutation is stored in the Pedigree object.

Additive relationship matrix

An important tool in fitting models that take into account genetic relationships is the additive relationship matrix, usually written A, for a pedigree. (See R.A. Mrode, Linear Models for the Prediction of Animal Breeding Values, 2nd edition, 2004, chapter 2).

In practice, the Cholesky factor, L, which is a lower triangular matrix with positive diagonal elements and satisfying A = LL' is more useful. The Ltrans function in this package evaluates the transpose of L as a sparse matrix. The reason for evaluating L' and not L is because the result is in the SparseMatrixCSC format and it is the rows of L that are easier to evaluate than the columns. In other words, a column-oriented format is more suitable for L'.

The inbreeding function evaluates both the inbreeding coefficients and L'.