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Yun Ju Sung Elizabeth A. Thompson and Ellen M. Wijsman

MCMC-Based Linkage Analysis for Complex Traits on General Pedigrees: Multipoint Analysis With a Two-Locus Model and a Polygenic Component. Yun Ju Sung Elizabeth A. Thompson and Ellen M. Wijsman. Motivation. Mendel law: A single locus influences a trait Complex Traits

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Yun Ju Sung Elizabeth A. Thompson and Ellen M. Wijsman

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  1. MCMC-Based Linkage Analysis for Complex Traits on GeneralPedigrees: Multipoint Analysis With a Two-Locus Modeland a Polygenic Component Yun Ju Sung Elizabeth A. Thompson and Ellen M. Wijsman

  2. Motivation • Mendel law: A single locus influences a trait • Complex Traits • multiple loci influence them • Mendel law too restrictive • Current focus: Two trait Loci • Previous approaches have restrictions on • Number of markers • Pedigree sizes • Use of MCMC makes the method scalable.

  3. Background • Quantitativeinheritance refers to inheritance of a trait that is attributable to two or more genes and their interaction with the environment • Example of Traits: • Human Skin color • Diabetes • Autism • Many genes affect these traits and so changing one gene is not enough.

  4. Quantitative Trait Locus • A quantitative trait locus (QTL) is a region of DNA that is associated with a particular trait - these QTLs are often found on different chromosomes • Typically, QTLs underlie continuous traits • E.g. Height which is continuous • Moreover, a single trait is usually determined by many genes. Consequently, many QTLs are associated with a single trait.

  5. Model • Z= Q1 + Q2 + V + E • Z: Quantitative Trait • Q1: QTL effects (discrete) • Q2: QTL effects (discrete) • V: Polygenic value (normally distributed) • E: Environmental Effects (normally distributed)

  6. Now we derive 2-D LOD score • Note that previously we were interested in LOD score of a single QTL (locus) • Now we want to derive LOD score of bi-variate QTLs.

  7. My understanding as a Bayesnet Query: Prob(Z|Y,Q1,Q2)=? Trait Data MarkerData Z Y Polygenic value P Q1 Q2 S1 S2 G1 G2 Q1 and Q2 are QTL effects S1 and S2 are segregation indicators at Q1 and Q2 G1 and G2 are genotypes of founders of Q1 and Q2

  8. Sliced and Profile LOD scores • When Two QTLs are present, we need two-dimensional lod scores • To compare these to one-dimensional LOD scores, the two dimensional LOD scroes are summarized using • Sliced LOD score • Profile LOD score

  9. Experiments (Pedigrees)

  10. Experiments (Data set) • Example 1 • 300 replicates of ped6 (300ped6) • 100 replicates of ped16 (100ped16) • 40 replicates of ped52 (40ped52) • Example 2 • 600ped6 • 100ped16

  11. Experiments • Competing schemes • 2Q+P (two QTLs + polygenic component) • 1Q+P • 1Q • VC model • Aim • Find Weak and Strong QTL

  12. Example 1 Parameters QTL1 is weaker than QTL2. Weak QTL at 15cM Strong QTL at 55cM Aim: Find the location of QTL1 and QTL2 using LOD scores

  13. Two-dimensional LOD scores for 2Q+P

  14. Profile LOD scores for all models Strong QTLs

  15. Sliced LOD scores for VC and 2Q+P Weak QTLs

  16. Example 2 paramters QTL1 is weaker than QTL2. Weak QTL at 15, 25, 35 and 45 cM Strong QTL at 55cM Determine the location of strong and weak QTL using LOD scores

  17. LOD scores Various QTL spacings

  18. LOD scores Various QTL spacings Strong QTLs

  19. LOD scores Various QTL spacings Weak QTLs

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