1	Genomic Measures of Relationship and Inbreeding
2	Traditional Pedigree
3	Genomic Pedigree
4	Haplotype Pedigree
5	Genotype Pedigree Count number of second allele
6	How Related are Relatives? 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
7	Alleles Shared by Sibs
8	Relationship Matrices 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)
9	Computing Relationships 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 1-p_j) G = Z Z’ / [2 ∑ p_j(1-p_j)] Construct T using similar math, but all QTL that affect a trait not observable
10	Linear Model Equations BLUP equations for marker effects, then sum to get EBV u^ = Z [Z’R^-1Z + I k]^-1 Z’R^-1(y – Xb) k = var(u) / var(m) = 2 ∑ p_j(1-p_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)
11	Non-linear vs Linear Models
12	Marker Effect Prior Distribution Nonlinear Model
13	Reliability from Full Sibs 50,000 markers, 1000 QTLs, sib REL = 99%
14	Reliability from Genotyping 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
15	Conclusions 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 non-linear models can better approximate QTL relationships (T) and increase reliability as compared to traditional relationships (A)