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 Example: Full sibs
 are expected to share 50% of their DNA on average
 may actually share 45% or 55% of their DNA because each inherits a
different mixture of chromosome segments from the two parents.
 Combine genotype and pedigree data to determine exact fractions

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 Measures of genetic similarity
 A = Expected % genes identical by descent from pedigree (Wright, 1922)
 G = Actual % of DNA shared (using genotype data)
 T = % genes shared that affect a given trait (using genotype and
phenotype)

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 Construct G from marker incidence matrix M minus allele frequencies p_{j}
 M = markers (j) inherited by animals (i)
 P contains frequency of second allele
 Z = M – P (elements of Z are –p_{j} or 1p_{j})
 G = Z Z’ / [2 ∑ p_{j}(1p_{j})]
 Construct T using similar math, but all QTL that affect a trait not
observable

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 BLUP equations for marker effects, then sum to get EBV
 u^ = Z [Z’R^{1}Z + I k]^{1} Z’R^{1}(y – Xb)
 k = var(u) / var(m) = 2 ∑ p_{j}(1p_{j})
 Selection index equations for EBV
 u^ = Z Z’ [Z Z’ + R]^{1} (y – Xb)
 R has diagonals = (1 / Reliability)  1
 Equivalent model from Garrick (2007)
 u^ = [(Z Z’)^{1 }+ R^{1}]^{1} R^{1}
(y – Xb)

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 Daughter equivalents
 DE_{Total} = DE_{PA} + DE_{Prog} + DE_{YD}
+ DE_{G}
 DE_{G} is additional DE from genotype
 Reliability = DE_{total} / (DE_{Total} + k)
 Gains in reliability
 DE_{G} could be about 15 for Net Merit
 More for traits with low heritability
 Less for traits with high heritability

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 Relationships can be defined as:
 A = expected genes in common
 G = actual fraction of DNA in common
 T = QTL alleles in common for a
trait
 Full sibs share 50% ± 3.5% of DNA
 Genomic (G) or nonlinear models can better approximate QTL
relationships (T) and increase reliability as compared to traditional
relationships (A)
