BLUPs were plotted on the pedigree graph grouping all tested parents using Pedimap software [ 39].
This produces a pedigree graph with exactly 5| G| + | I | individuals and 8| G| + | E| edges.
First we create the pedigree graph for the new haplotype instance, and later we construct the required haplotype observations from the genotype data.
A plausible pedigree graph is given in b of Fig. 1, which also contains two un-genotyped animals, U1 and U2, and where arrows indicate direction from parent to offspring.
The generating function actually explicitly lists the numbers of paths of any lengths over all possible descent graphs of a pedigree.
Simultaneous sampling of the pedigree was achieved by sampling descent graphs using the Metropolis-Hastings algorithm.
Notice that there are only finite number of descent graphs for a given pedigree; therefore, there are only finite number of inheritance paths between two alleles and the summation only has finite number of terms.
Figure 1 shows a pedigree and one of its many possible descent graphs.
Note that for a pedigree with n non-founders there are 22 n descent graphs, since there is a binary choice of genetic material twice for every person that is not a founder.
A chain of length l in a pedigree translates to a set of 2 l edges in the potential descent graph of the pedigree connecting the maternal and paternal nodes of person v i to the paternal node of person v i +1 when v i is a male, and connecting them to the maternal node of v i +1 when v i is a female.
That is, given a descent graph of a pedigree and an assignments of alleles a = (a1,…, a2 f ) to the maternal and paternal variables of its f founders, every maternal and paternal variable is assigned a specific founding allele.
