Efficient Precision Mapping of QTL With Dense Marker Maps

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Efficient Precision Mapping of QTL With Dense
Marker Maps
Joint Statistical Meetings, San Francisco, CA,
August 3-7, 2003 Session 28 Analysis of
Quantitative Trait Loci

• Natascha Vukasinovic, Fengxing Du
• Animal Genomics,
• Monsanto Company,
• Chesterfield, MO
• natascha.vukasinovic_at_monsanto.com
• http//www.math.usu.edu/vukasino

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Linkage vs. Linkage Disequilibrium

• Linkage

• focuses on a locus

• results from recombination events in the last
  2-3 generations

• measures co-segregation in a pedigree

• Linkage Disequilibrium

• focuses on an allele

• results from much earlier, ancestral
  recombination events

• measures co-segregation in a population

Source http//linkage.rockefeller.edu/wli/lld.htm
l
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Mapping QTL

• Linkage Analysis (LA)
• in pedigrees (individuals 2-3 generations of
  ancestors)
• uses info on recombinations in gametes
  transmitted from parents to offspring
• locates QTL within 20-40cM
• Linkage Disequilibrium (LD)
• in population (huge pedigree)
• uses info on historical recombinations
• locates QTL within lt 1cM

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Objectives

• Our study investigates
• suitability of LA- and LD-based QTL mapping
  under different conditions (marker map density,
  population size, QTL location )
• robustness of LA- and LD-based QTL mapping in
  real life situations (violated assumptions,
  missing markers )
• Todays talk
• Methodology for LD mapping
• Preliminary results

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Simulation Study

• Assumptions
• LA previously located QTL within a 20cM region
• region covered by 10 evenly spaced markers
• QTL allele mutation occurred 100 generations ago
• closed population, no selection

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Population History

• Base population 100 individuals
• Each founder individual assigned 2 unique QTL
  alleles (200 QTL alleles)
• 10 linked biallelic markers, QTL between markers
  5 and 6
• Random mating during 100 generations
• 100 offspring per generation
• Mendelian inheritance of markers and QTL alleles

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Mapping Population

• Phenotypes assigned to offspring of the final
  (100th) generation
• One survivor QTL allele with frequency gt 0.1
  randomly chosen as mutant QTL allele
• phenotype QTL allele effect error
• QTL allele effect
• error N(0,1) s2q 0.1 s2e 1.0

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Estimation of QTL effects

• Haplotype-based method
• y Xb Zh e
• y ? vector of phenotypes
• b ? vector of fixed effects (mean)
• h ? vector of random effects of marker haplotypes
  
• X, Z ? incidence matrices
• e ? vector of random error terms

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Estimation of QTL effects

• Var (h) Hps2h
• Var (e) Rs2e

• Var (y) V ZHpZs2h Rs2e

Hp - matrix of (co)variances among marker
haps at position p R - identity matrix
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Construction of Hp

• Cov (hi, hj) P (QTL is IBDmarker haplotypes)
  ? s2h
• P (QTL is IBDmarker haplotypes) PIBD ?
• Genedropping method
• Simulation of a base population and 100
  generations of random mating (genedrops)
• Final generation marker haplotypes sharing same
  alleles are more likely to share same QTL allele

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Construction of Hp

• Marker haps having same number of alleles IBS
  (identical-by-state) to the left and to the right
  from QTL position have same PIBD.
• Marker haps clustered in categories NL,NR
• NL - marker alleles IBS left of QTL
• NR - marker alleles IBS right of QTL
• haps in a NL,NR cluster where
  QTL is IBD
• PIBD
• total haps in a NL,NR
  cluster
• across large number of replicates

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REML Analysis

• L(Hp,s2h, s2e ) ?
• - 0.5lnV - lnX V-1 X - (y-Xb)
  V-1(y-Xb)
• LR (likelihood ratio) -2 (L0 - L)

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Preliminary results
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Outlook

• Questions left to answer
• Should we use LA or LD mapping in a particular
  situation?
• How sensitive is LD mapping to violation of
  assumptions about population history?
• How does combined LA/LD analysis compare with
  these methods?