This document explains how to prepare the data and the basic usage of the mlmm.gwas package. Use ?functionName in R console to get the complete documentation of a given function.
The pipeline can be divised in 3 main steps:
Only the additive model is presented in this document. The pipeline also supports additive+dominace, female+male and female+male+interaction models. For more information on how to make the matrices for these models, read Bonnafous et al. (2017).
This package includes a dataset with genotypes, phenotypes and kinship for different hybrids of sunflower.
library(mlmm.gwas)
data("mlmm.gwas.AD")
ls()
#> [1] "K.add" "K.dom" "Xa" "Xd"
#> [5] "floweringDateAD"
Phenotypes must be put in a named vector. Names are the individuals' names and values their phenotypes.
The trait included in the dataset is the flowering date in ??C.day.
head(floweringDateAD)
#> SF173_SF326 SF160_PNS1 SF031_SF302 SF028_SF332 SF029_SF281 RA22_SF323
#> 1187.500 1200.520 1152.476 1130.149 1254.520 1215.293
It's a n by m matrix, where n is the number of individuals, and m the number of SNPs.
Be sure to:
Xa[1:5,1:5]
#> SNP1 SNP2 SNP3 SNP4 SNP5
#> SF173_SF326 1.3055556 0.4722222 -0.1944444 -0.1388889 -0.8611111
#> SF160_PNS1 -0.6944444 0.4722222 -0.1944444 -0.1388889 -0.8611111
#> SF031_SF302 -0.6944444 0.4722222 -0.1944444 -0.1388889 0.1388889
#> SF028_SF332 -0.6944444 0.4722222 -0.1944444 -0.1388889 0.1388889
#> SF029_SF281 -0.6944444 -0.5277778 -0.1944444 -0.1388889 1.1388889
As K is normalized in the pipeline, you don't need to do it yourself.
So you can get it from centered X easily:
##You can get K from X with the following command line
##We are not doing it here because the X matrix included in data("mlmm.gwas.AD")
##is a subset of a larger matrix.
#K.add = Xa %*% t(Xa)
K.add[1:5,1:5]
#> SF173_SF326 SF160_PNS1 SF031_SF302 SF028_SF332 SF029_SF281
#> SF173_SF326 213719.258 -2470.409 3375.313 -3872.576 -30046.548
#> SF160_PNS1 -2470.409 266025.924 51606.647 22635.758 -29448.215
#> SF031_SF302 3375.313 51606.647 212842.369 16744.480 10089.508
#> SF028_SF332 -3872.576 22635.758 16744.480 225864.591 -9349.381
#> SF029_SF281 -30046.548 -29448.215 10089.508 -9349.381 191078.647
Individuals and markers must be the sames and in the same order in Y, X and K.
A genetic or physical map can be used for graphical representation of association (Manhattan plot).
It's a dataframe with 3 columns:
Missing data are allowed.
There is no map in the example dataset. We will still be alble to use the manhattan.plot function but the markers will be ordered by their line index in the X matrix, not by genetic or physical position.
The function mlmm_allmodels performs GWAS correcting for population structure while including cofactors through a forward regression approach.
Several markers may be associated to a single QTL. The mlmm_allmodels function aims to solve this problem by selecting the closest SNP to each QTL using a forward regression approach. The association p-values of the SNPs are estimated. Then, the SNP with the lowest p-value is used as fixed effect (cofactor). This is repeated, adding one SNP to the fixed effects at each step, until most of the variance is explained or until the maximum number of iterations is reached.
res_mlmm = mlmm_allmodels(floweringDateAD, list(Xa), list(K.add))
#> iteration LogLik wall cpu(sec) restrained
#> 1 -47.4676 16:33:53 0 0
#> 2 -43.866 16:33:53 0 0
#> 3 -43.0839 16:33:53 0 0
#> 4 -43.0056 16:33:53 0 0
#> 5 -43.0037 16:33:53 0 0
#> 6 -43.0036 16:33:53 0 0
#> null model done! pseudo-h= 0.52
#> iteration LogLik wall cpu(sec) restrained
#> 1 -35.9468 16:33:53 0 0
#> 2 -34.9284 16:33:53 0 0
#> 3 -34.6096 16:33:53 0 0
#> 4 -34.5712 16:33:53 0 0
#> 5 -34.5702 16:33:53 0 0
#> step 1 done! pseudo-h= 0.379 model: Y ~ mu + SNP303
#> iteration LogLik wall cpu(sec) restrained
#> 1 -30.707 16:33:53 0 0
#> 2 -30.1743 16:33:53 0 0
#> 3 -29.9904 16:33:53 0 0
#> 4 -29.9655 16:33:53 0 0
#> 5 -29.9648 16:33:53 0 0
#> step 2 done! pseudo-h= 0.328 model: Y ~ mu + SNP303 + SNP317
#> iteration LogLik wall cpu(sec) restrained
#> 1 -25.8333 16:33:53 0 0
#> 2 -25.8194 16:33:53 0 0
#> 3 -25.8115 16:33:53 0 0
#> 4 -25.8089 16:33:53 0 0
#> 5 -25.8085 16:33:53 0 0
#> step 3 done! pseudo-h= 0.201 model: Y ~ mu + SNP303 + SNP317 + SNP407
#> iteration LogLik wall cpu(sec) restrained
#> 1 -21.9588 16:33:53 0 0
#> 2 -21.8936 16:33:53 0 0
#> 3 -21.8537 16:33:53 0 0
#> 4 -21.8384 16:33:53 0 0
#> 5 -21.8352 16:33:53 0 0
#> 6 -21.8345 16:33:53 0 0
#> step 4 done! pseudo-h= 0.086 model: Y ~ mu + SNP303 + SNP317 + SNP407 + SNP10
#> iteration LogLik wall cpu(sec) restrained
#> 1 -18.8393 16:33:53 0 0
#> 2 -18.6398 16:33:53 0 0
#> 3 -18.5399 16:33:53 0 0
#> 4 -18.5154 16:33:53 0 0
#> 5 -18.5133 16:33:53 0 0
#> 6 -18.5131 16:33:53 0 0
#> step 5 done! pseudo-h= 0.048 model: Y ~ mu + SNP303 + SNP317 + SNP407 + SNP10 + SNP153
#> iteration LogLik wall cpu(sec) restrained
#> 1 -14.9796 16:33:53 0 0
#> 2 -14.1825 16:33:53 0 1
#> 3 -13.7957 16:33:53 0 1
#> 4 -13.7957 16:33:53 0 1
#> step 6 done! pseudo-h= 0 model: Y ~ mu + SNP303 + SNP317 + SNP407 + SNP10 + SNP153 + SNP375
mlmm_allmodels returns a list with one element per step. Each element is a vector containing the association p-values of each marker.
These p-values can be visualized as a Manhattan plot:
manhattan.plot( res_mlmm )
It is necessary to select a model using a criterion to avoid overfitting. The criterion used here is the eBIC. The model with the lowest eBIC is selected.
sel_XX = frommlmm_toebic(list(Xa), res_mlmm)
res_eBIC = eBIC_allmodels(floweringDateAD, sel_XX, list(K.add), ncol(Xa))
res_eBIC
#> BIC ajout eBIC_0.5 LogL
#> mu 301.9261 0.000000 301.9261 -143.9123
#> SNP303 289.7766 6.214608 295.9912 -135.4873
#> SNP317 284.9296 11.734067 296.6637 -130.7136
#> SNP407 280.5870 16.846055 297.4330 -126.1920
#> SNP10 276.0085 21.668350 297.6768 -121.5525
#> SNP153 272.9082 26.265488 299.1737 -117.6522
#> SNP375 266.7063 30.678287 297.3846 -112.2010
In this example, the model with 1 fixed effect is selected.
res_threshold <- threshold_allmodels(threshold=NULL, res_mlmm)
#> [1] "No p-value below the threshold for this trait"
The selected SNPs effects can be estimated with the function Estimation_allmodels
sel_XXclass = fromeBICtoEstimation(sel_XX, res_eBIC, res_threshold)
effects = Estimation_allmodels(floweringDateAD, sel_XXclass, list(K.add))
effects
#> BLUE Tukey.Class Frequency
#> mu 1148.92349 <NA> NA
#> SNP303_00 66.52243 a 0.1090909
#> SNP303_01|10 15.96944 b 0.4818182
#> SNP303_11 0.00000 c 0.4090909
You can visualize the distributions of the phenotypes of the individuals according to their allelic class for a given SNP using the genotypes.boxplot function:
genotypes.boxplot(Xa, floweringDateAD, "SNP303", effects)
The colored symbols represent the Tukey's classes. Different symbols mean that the means are significantly different.
For convenience, all of the example command lines are compiled below:
library(mlmm.gwas)
data("mlmm.gwas.AD")
res_mlmm = mlmm_allmodels(floweringDateAD, list(Xa), list(K.add))
manhattan.plot( res_mlmm )
sel_XX = frommlmm_toebic(list(Xa), res_mlmm)
res_eBIC = eBIC_allmodels(floweringDateAD, sel_XX, list(K.add), ncol(Xa))
res_threshold <- threshold_allmodels(threshold=NULL, res_mlmm)
sel_XXclass = fromeBICtoEstimation(sel_XX, res_eBIC, res_threshold)
effects = Estimation_allmodels(floweringDateAD, sel_XXclass, list(K.add))
genotypes.boxplot(Xa, floweringDateAD, "SNP303", effects)
You can also run the entire pipeline (without the figures plots) with the function run_entire_gwas_pipeline. This function runs internally the functions mlmm_allmodels, frommlmm_toebic, eBIC_allmodels, threshold_allmodels, fromeBICtoEstimation and Estimation_allmodels and returns a list with the results of the mlmm, eBIC and effects estimation steps.
results = run_entire_gwas_pipeline(floweringDateAD, list(Xa), list(K.add), threshold=NULL)
#> iteration LogLik wall cpu(sec) restrained
#> 1 -47.4676 16:33:56 0 0
#> 2 -43.866 16:33:56 0 0
#> 3 -43.0839 16:33:56 0 0
#> 4 -43.0056 16:33:56 0 0
#> 5 -43.0037 16:33:56 0 0
#> 6 -43.0036 16:33:56 0 0
#> null model done! pseudo-h= 0.52
#> iteration LogLik wall cpu(sec) restrained
#> 1 -35.9468 16:33:56 0 0
#> 2 -34.9284 16:33:56 0 0
#> 3 -34.6096 16:33:56 0 0
#> 4 -34.5712 16:33:56 0 0
#> 5 -34.5702 16:33:56 0 0
#> step 1 done! pseudo-h= 0.379 model: Y ~ mu + SNP303
#> iteration LogLik wall cpu(sec) restrained
#> 1 -30.707 16:33:56 0 0
#> 2 -30.1743 16:33:56 0 0
#> 3 -29.9904 16:33:56 0 0
#> 4 -29.9655 16:33:56 0 0
#> 5 -29.9648 16:33:56 0 0
#> step 2 done! pseudo-h= 0.328 model: Y ~ mu + SNP303 + SNP317
#> iteration LogLik wall cpu(sec) restrained
#> 1 -25.8333 16:33:56 0 0
#> 2 -25.8194 16:33:56 0 0
#> 3 -25.8115 16:33:56 0 0
#> 4 -25.8089 16:33:56 0 0
#> 5 -25.8085 16:33:56 0 0
#> step 3 done! pseudo-h= 0.201 model: Y ~ mu + SNP303 + SNP317 + SNP407
#> iteration LogLik wall cpu(sec) restrained
#> 1 -21.9588 16:33:56 0 0
#> 2 -21.8936 16:33:56 0 0
#> 3 -21.8537 16:33:56 0 0
#> 4 -21.8384 16:33:56 0 0
#> 5 -21.8352 16:33:56 0 0
#> 6 -21.8345 16:33:56 0 0
#> step 4 done! pseudo-h= 0.086 model: Y ~ mu + SNP303 + SNP317 + SNP407 + SNP10
#> iteration LogLik wall cpu(sec) restrained
#> 1 -18.8393 16:33:57 0 0
#> 2 -18.6398 16:33:57 0 0
#> 3 -18.5399 16:33:57 0 0
#> 4 -18.5154 16:33:57 0 0
#> 5 -18.5133 16:33:57 0 0
#> 6 -18.5131 16:33:57 0 0
#> step 5 done! pseudo-h= 0.048 model: Y ~ mu + SNP303 + SNP317 + SNP407 + SNP10 + SNP153
#> iteration LogLik wall cpu(sec) restrained
#> 1 -14.9796 16:33:57 0 0
#> 2 -14.1825 16:33:57 0 1
#> 3 -13.7957 16:33:57 0 1
#> 4 -13.7957 16:33:57 0 1
#> step 6 done! pseudo-h= 0 model: Y ~ mu + SNP303 + SNP317 + SNP407 + SNP10 + SNP153 + SNP375
#> [1] "No p-value below the threshold for this trait"
names(results)
#> [1] "pval" "eBic" "threshold" "effects"