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

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 environment

Example of Traits: Human Skin color Diabetes Autism

Many genes affect these traits and so changing one gene is not enough.

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.

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

Q2Q1

Y

S2 G1 G2

Trait Data

MarkerData

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 1 300 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

LOD scores Various QTL spacings

Strong QTLs

LOD scores Various QTL spacings

Weak QTLs