Mapping QTL in general pedigrees using the random model approach

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Mapping QTL in general pedigrees using the random
model approach
Joint Statistical Meetings, NYC, NY, August
11-15, 2002 Session 289 Evolution, Genetics, and
Genomics

• N.Vukasinovic1, M. Martinez2
• 1 Animal Genomics, Monsanto Company,
  Chesterfield, MO
• 2 EMBRAPA/CNPGL, Brazil
• natascha.vukasinovic_at_monsanto.com
• http//www.math.usu.edu/vukasino

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Introduction
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Introduction
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QTL mapping

• QTL detection
• check if QTL is present
• QTL location
• determine the position of the QTL on the
  chromosome
• QTL effect
• estimate the magnitude of allelic effect or
  variance of the QTL

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Random model approach

• Estimates variance due to QTL.
• Based on phenotypic similarity between
  relatives.
• Does not require assumptions about genetic
  model at the QTL.
• Appropriate for outbred populations.

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Statistical model

• Phenotypic value
• yij m QTLij polygenesij 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
• rjj coefficient of relationship between
  j and j

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Estimating

• Sib-pair approach
• is a linear function of proportions IBD
  shared by two sibs at linked marker loci.
• Procedures well established for unrelated full-
  and halfsib families.
• No efficient procedures for general pedigrees
• Animal pedigrees too complicated for algorithms
  used for human pedigrees.

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Estimating

• Pong-Wong et al. (2001)GSE 33453-471
• Fast, partly recursive deterministic method
  to calculate IBD shared
• between ancestors and descendants
• Recursive method for single marker
• between sibs
• Method for multiple markers
• Uses informative markers only (closest
  informative marker bracket).

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Informative marker brackets
?
?
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Informative marker brackets
a b c
a b c
?
?
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Informative marker brackets
AA BB CC
aa bb cc
?
Aa Bb Cc
aa Bb cc
?
Aa BB Cc
aa BB Cc
aa Bb Cc
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IBD between ancestors descendants
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Calculating PDQs
q1 - recombination between 1st marker and QTL q2
- recombination between QTL and 2nd marker q -
recombination between 2 flanking markers
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IBD among sibs
q1 - recombination between 1st marker and QTL q2
- recombination between QTL and 2nd marker q -
recombination between 2 flanking markers
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Using IBD in QTL mapping

• All calculations done separately for paternal and
  maternal allele
• G - gametic IBD matrix
• Order 2n
• Q - matrix of IBD at individual level
• Order n
• where

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Concerns

• G (and Q) may not be positive definite.
• The method may not work well when markers are not
  informative.
• Is the method general enough?
• What about really large pedigrees?
• What about loops and inbreeding?

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Current work

• Simulation studies to assess the performance of
  this method using
• Pedigrees of different size and complexity level
• Different marker density and informativeness
• Different size / position of QTL
• Results to be shown in the paper (JSM ProCDings,
  2002).