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Genomic Measures of Relationship and Inbreeding in Pedigree Analysis

Explore the calculation of relatedness using genomic and traditional pedigrees, haplotypes, and genotypes, determining shared alleles and relationship matrices. Learn about linear and non-linear models for genetic similarities and reliabilities, enhancing the accuracy of trait inheritance predictions.

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Genomic Measures of Relationship and Inbreeding in Pedigree Analysis

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  1. Genomic Measures of Relationship and Inbreeding

  2. Traditional Pedigree

  3. Genomic Pedigree

  4. Haplotype Pedigree atagatcgatcg ctgtagcgatcg ctgtagcttagg agatctagatcg agggcgcgcagt cgatctagatcg ctgtctagatcg atgtcgcgcagt cggtagatcagt agagatcgcagt agagatcgatct atgtcgctcacg atggcgcgaacg ctatcgctcagg

  5. Genotype PedigreeCount number of second allele 0 = homozygous for first allele (alphabetically) 1 = heterozygous 2 = homozygous for second allele (alphabetically)

  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 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

  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 ∑ 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)

  11. Non-linear vs Linear Models

  12. Marker Effect Prior DistributionNonlinear Model

  13. Reliability from Full Sibs50,000 markers, 1000 QTLs, sib REL = 99% A = traditional additive relationships, G = genomic relationships

  14. 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

  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)

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