QTL Mapping in Extended Halfsib Families

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QTL Mapping in Extended Halfsib Families
ADSA/ASAS Annual Meeting, Phoenix, AZ, June
22-26, 2003

• Natascha Vukasinovic, Monsanto, Animal AG
• Mario Martinez, CGNLP/Embrapa, Brazil

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QTL search in outbred populations
Daughter design
Independent halfsib families
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QTL search in outbred populations
In reality Sires are related
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QTL search

• Halfsib analysis
• Independent families (often small)
• Imprecise estimates of QTL parameters
• Low power
• General pedigree analysis
• Considers relationships among all animals
• Can this provide better estimates and higher
  power?

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Simulation study

• 1 sire ? 1 dam ? 3 sons
• Each son ? 4 dams ? 12 grandsons
• Each grandson ? 25 dams ? 300 daughters
• 12 related halfsib families, 25 daughters each
• Available for analysis Sire and daughter
  genotypes, daughter phenotypes.

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Full Pedigree
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Simulation details

• 60 cM chromosomal segment, 5 markers, 15 cM
  apart
• with 6 alleles each (polymorphic)
• with 2 alleles each (biallelic)
• 1 QTL with 5 alleles
• at 20 cM
• at 40 cM
• QTL accounts for
• 25 trait variance
• 5 trait variance
• h20.50, 50 replicates

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Statistical model

• Phenotypic value
• yij m QTLij polyij errorij
• Phenotypic variance
• Var (yij) s2 s2QTL s2poly s2error
• Covariance between two relatives j and j
• Cov (yij, yij) s2QTL rjj s2poly
• proportion of alleles IBD shared at
  QTL (IBD probability)
• rjj coefficient of polygenic
  relationship between j and j

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Estimating pq Halfsib families

• Linear regression (Fulker Cardon, 1994)
• uses information on IBD proportion at two
  flanking markers
• E (pq p M1 p M2) a b1 p M1
  b2 p M2
• p M1, p M2 - IBD proportions at 2 flanking
  markers
• b1, b2 - weights obtained as a function of
  recombination between markers and putative QTL
• Uninformative markers use average p ( r)

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Estimating pq General pedigrees

• Recursive deterministic method to calculate IBD
  proportions (IBD probabilities) between
  ancestors and descendants (Pong-Wong et al. ,
  2001).
• Requires known linkage phases (parental AND
  grandparental origin of each marker allele)
• Uses closest informative marker bracket.
• Uninformative markers skipped.

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Estimating pq General pedigrees

• IBD probabilities calculated separately for
  paternal and maternal allele, for each
  chromosomal position.
• Linear transformation of gametic IBD
  probabilities into individual IBD probabilities.
• If no informative markers, IBD probs r.

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Data analysis

• ML method
• maximize likelihood function (w.r.t. unknown
  parameters) for each position
• obtain likelihood ratio (LR) test statistics
• position the highest LR ? most likely QTL
  position.
• Note Only offspring phenotypes and IBDs used in
  actual analysis

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Results Polymorphic markers, h2QTL 0.25
QTL at 20 cM
QTL at 40 cM
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Results Polymorphic markers, h2QTL 0.05
QTL at 20 cM
QTL at 40 cM
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Results Biallelic markers, h2QTL 0.25
QTL at 20 cM
QTL at 40 cM
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Results Biallelic markers, h2QTL 0.05
QTL at 20 cM
QTL at 40 cM
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Results h2QTL estimates
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Conclusions

• GP analysis superior to HS analysis regarding
  precision and power
• always, when QTL is large
• with polymorphic markers, when QTL is small
• GP analysis provides less biased estimates of QTL
  heritability when QTL is small.

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Final remarks

• Considering relationships among daughter groups
  (via GP analysis) could be a simple way to
  increase efficiency of QTL mapping without
  additional costs.
• GP analysis requires considerably larger
  computing resources than HS analysis.
• Need to consider better algorithms ...

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Questions? Comments? Critics? Suggestions?
Correspondence Natascha Vukasinovic
(nvukasin_at_charter.net)