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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.
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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.
We introduce the concept of inheritance-generating function, defined for any pair of alleles in a descent graph based on a pedigree structure.
Simwalk2 implements a Bayesian framework using a Markov chain Monte Carlo (MCMC) algorithm to select the most likely genetic descent graph depicting inheritance patterns within pedigrees [ 36].
A descent graph (Sobel and Lange, 1996) of a pedigree consists of both the paternal and maternal allele of each individual as its vertices, and one link between each parent child pair as its edges.
A descent graph illustrates one possible inheritance pattern within a pedigree, and by definition, it does not include genotype information.
As a descent graph is a realization of one particular inheritance pattern in a pedigree, for any two alleles, there is at most one inheritance path.
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