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Genomic Measures of Relationship and Inbreeding. Traditional Pedigree. Genomic Pedigree. Haplotype Pedigree. atagatcgatcg. ctgtagc gatcg. ctgtagcttagg. ag atctagatcg. agggcgcgcagt. cgatctagatcg. ctgt ctagatcg. atg tcg cg cagt. cggtagatcagt. agagatcg cagt. agagatcgatct.
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Haplotype Pedigree atagatcgatcg ctgtagcgatcg ctgtagcttagg agatctagatcg agggcgcgcagt cgatctagatcg ctgtctagatcg atgtcgcgcagt cggtagatcagt agagatcgcagt agagatcgatct atgtcgctcacg atggcgcgaacg ctatcgctcagg
Genotype PedigreeCount number of second allele 0 = homozygous for first allele (alphabetically) 1 = heterozygous 2 = homozygous for second allele (alphabetically)
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
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)
Computing Relationships • Construct G from marker incidence matrix M minus allele frequencies pj • M = markers (j) inherited by animals (i) • P contains frequency of second allele • Z = M – P (elements of Z are –pj or 1-pj) • G = Z Z’ / [2 ∑ pj(1-pj)] • Construct T using similar math, but all QTL that affect a trait not observable
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 ∑ pj(1-pj) • 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)
Reliability from Full Sibs50,000 markers, 1000 QTLs, sib REL = 99% A = traditional additive relationships, G = genomic relationships
Reliability from Genotyping • Daughter equivalents • DETotal = DEPA + DEProg + DEYD + DEG • DEG is additional DE from genotype • Reliability = DEtotal / (DETotal + k) • Gains in reliability • DEG could be about 15 for Net Merit • More for traits with low heritability • Less for traits with high heritability
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)