For young sires, TBV and GEBV were simulated jointly (in the GPS population) from multivariate normal distributions and conditional on parent average (EBV before including progeny information).
Because the rvTDT is conditional on the parents' data, using parental data in estimating the linear combination does not affect the validity or asymptotic distribution of the rvTDT.
Now, when a multi-trait QTL analysis is performed according to the actual phenotype causal network, detecting indirect-effect QTL is avoided by simply performing mapping analysis of each phenotype conditional on their parents (i.e., upstream phenotypes).
Notice that receiving remittances is not conditional on either parent migrating, as our data section below confirms.
Assuming the local directed Markov property that states that each variable is independent of its nondescendant variables conditional on its parent variables, we can factor the joint distribution as P (X | G ) = ∏ j = 1 p P (X j | X G j ), (A1 where X = (X 1,..., X p ) T, G j is the set of parents of j, and X G j = { X i : i ∈ G j }.
Note that as the estimation on offspring is conditional on the parental genotypes, there will be no genotypic correlations between offspring and parents and between offspring themselves.
No additional information is gained by incorporating the parent-of-origin indicator into the nuisance parameter since once the phaseknown genotypes of the parents and offspring are specified, and conditional on the fact that parent-oforigin can be deduced, parent-of-origin is also established.
In the first step we imputed a probability distribution for the genotypes of each pair of parents, conditional on the observed genotypes of all family members.
The linkage disequilibrium signal comes from the quantities ℙ(Z i (x) = z| h i) and ℙ (Q i j d (x ) = a | h i j d ) which are the probabilities of QTL alleles in the parents conditional on the surrounding marker haplotypes.
However, these grants are not conditional on anything except low parent or guardian income.
