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 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.

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

Background Quantitative Inheritance will not follow the same pattern as a simple monohybrid cross monohybrid However, it can be explained as monohybrid cross at multiple loci resulting in a trait that is normally distributed. Bb BBBbB bBbbb

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 chromosomesDNA trait chromosomes Typically, QTLs underlie continuous traitstraits 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.

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)

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.

My understanding as a Bayesnet Z S1 P Q2 Q1 Y S2G1G2 Trait Data Marker Data 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 Polygenic value Query: Prob(Z|Y,Q1,Q2)=?

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

Experiments (Pedigrees)

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

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

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

Two-dimensional LOD scores for 2Q+P

Profile LOD scores for all models Strong QTLs

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

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

LOD scores Various QTL spacings

Strong QTLs

LOD scores Various QTL spacings Weak QTLs