QTL mapping for phenotypes measured over time

and interactive graphics

Karl Broman

Biostatistics & Medical Informatics, University of Wisconsin – Madison

http://www.biostat.wisc.edu/~kbroman

Remove stickies

Inbred mice

Human vs mouse

Gravitropism

Recombinant inbred lines

Data: 162 Ler × Cvi RIL

Permutations

Single-QTL analyses

[This is a static shot; click on the image to see a dynamic version.]

The top-left plot is a “heat map” of the LOD scores for each time point at each genomic position. LOD scores are also colored to indicate the sign of the QTL effect, with red indicating that CC lines have larger phenotype values and blue indicating that LL lines have larger phenotype values. We consider only those (position, time) pairs with LOD > 1.

When you hover over a point in the top-left plot, the LOD curves for the corresponding time are shown below, and the phenotype averages and estimated QTL effect (across time) for the corresponding genomic position are shown to the right.

Click on a point to show pointwise confidence bands on the QTL effect (± 2 SE). (We require a mouse click, as otherwise the graph was painfully slow to refresh.)

code | data

Phenotypes measured over time

Consider each time point individually
Combine the results from the individual analyses
SLOD(λ) = ave_t LOD_t(λ)
MLOD(λ) = max_t LOD_t(λ)
Fit a model to each individual’s curve;
treat the coefficients as phenotypes

Results: SLOD & MLOD

Multiple-QTL models

Reduce residual variation → Increase power
Separate linked QTL
Identify interactions among QTL (epistasis)

Penalized LOD

Among additive QTL models, maximize

pLOD(γ) = LOD(γ) – T × |γ|

γ = a multiple-QTL model

|γ| = no. QTL in the model

T = significance threshold

KW Broman, TP Speed (2002) J Roy Stat Soc B 64:641-656

Penalized LOD

Among additive QTL models, maximize

pLOD_t(γ) = LOD_t(γ) – T × |γ|

γ = a multiple-QTL model

|γ| = no. QTL in the model

T = significance threshold

KW Broman, TP Speed (2002) J Roy Stat Soc B 64:641-656

Forward selection

LOD profile

Multiple-QTL analyses

code | data

Penalized LOD, extended

Among additive QTL models, maximize

pSLOD(γ) = ave_t LOD_t(γ) – T_S × |γ|

pMLOD(γ) = max_t LOD_t(γ) – T_M × |γ|

γ = a multiple-QTL model

|γ| = no. QTL in the model

T = penalties

Results: SLOD

Summary

We have focused on the simplest approaches to QTL analysis with a phenotype measured over time.

Consider each time point individually.
Combine across time by taking the average or maximum LOD.

We extended the approach for multiple-QTL models.
Interactive graphs are useful and fun.
See the related paper: Moore et al. Genetics 195:1077, 2013

Acknowledgments

Edgar Spalding		Botany, UW-Madison
Candace Moore
Logan Johnson

Il-youp Kwak		Statistics, UW-Madison

NIH: R01 GM074244