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