Last updated: 2022-07-25

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Before you begin:

  • Make sure that R is installed on your computer
  • For this lab, we will use the following R libraries:
require(data.table)
require(dplyr)
require(tidyr)
require(bigsnpr)
require(ggplot2)

Population Structure Inference

Introduction

We will be working with a subset of the genotype data from the Human Genome Diversity Panel (HGDP) and HapMap.

The file “YRI_CEU_ASW_MEX_NAM.bed” is a binary file in PLINK BED format with accompanying BIM and FAM files. It contains genotype data at autosomal SNPs for:

  • Native American samples from HGDP (NAM)
  • Four population samples from HapMap:
    • Yoruba in Ibadan, Nigeria (YRI)
    • Utah residents with ancestry from Northern and Western Europe (CEU)
    • Mexican Americans in Los Angeles, California (MXL)
    • African Americans from the south-western United States (ASW)

Exercises

Here are some things to look at:

  1. Examine the dataset:
  • How many samples are present?
famfile <- fread("/data/SISG2022M15/data/YRI_CEU_ASW_MEX_NAM.fam", header = FALSE)
famfile %>% head
     V1        V2 V3 V4 V5 V6
1: 1432 HGDP00702  0  0  2 -9
2: 1433 HGDP00703  0  0  1 -9
3: 1434 HGDP00704  0  0  2 -9
4: 1436 HGDP00706  0  0  2 -9
5: 1438 HGDP00708  0  0  2 -9
6: 1440 HGDP00710  0  0  1 -9
famfile %>% nrow
[1] 604
  • How many SNPs?
bimfile <- fread("/data/SISG2022M15/data/YRI_CEU_ASW_MEX_NAM.bim", header = FALSE)
bimfile %>% head
   V1        V2 V3      V4 V5 V6
1:  1 rs9442372  0 1008567  1  2
2:  1 rs2887286  0 1145994  1  2
3:  1 rs3813199  0 1148140  1  2
4:  1 rs6685064  0 1201155  1  2
5:  1 rs9439462  0 1452629  1  2
6:  1 rs3820011  0 1878053  1  2
bimfile %>% nrow
[1] 150872
  • What is the number of samples in each population?
pop_info <- fread("/data/SISG2022M15/data/Population_Sample_Info.txt", header = TRUE)
head(pop_info)
    FID       IID Population
1: 1432 HGDP00702        NAM
2: 1433 HGDP00703        NAM
3: 1434 HGDP00704        NAM
4: 1436 HGDP00706        NAM
5: 1438 HGDP00708        NAM
6: 1440 HGDP00710        NAM
# join with fam file
fam_pop_info <- left_join(famfile, pop_info, by = c("V1" = "FID", "V2" = "IID"))
fam_pop_info %>% select(Population) %>% table
Population
ASW CEU MXL NAM YRI 
 87 165  86  63 203
  1. Get the first 10 principal components (PCs) in PLINK using all SNPs.
system("/data/SISG2022M15/exe/plink2 --bfile /data/SISG2022M15/data/YRI_CEU_ASW_MEX_NAM --pca 10 --out tmp/pca_out")
  • Make a scatterplot of the first two PCs with each point colored by population membership.
pcs <- left_join(fam_pop_info, fread("tmp/pca_out.eigenvec"), by = c("V1" = "#FID", "V2" = "IID"))
pcs %>%
  ggplot(aes(x=PC1, y=PC2, color = Population)) +
  geom_point()

Version Author Date
99cdf2f Joelle Mbatchou 2022-07-25
  • Interpret the first two PCs, what ancestries are they reflecting?
  • Make a scree plot of the eigenvalues for the first 10 PCs. Approximate the proportion of variance explained by the first two PCs.
evals.pca <- fread("tmp/pca_out.eigenval", header = FALSE)
evals.pca %>%
  ggplot(aes(x = 1:10, y = V1)) +
  geom_point() +
  geom_line() +
  scale_x_continuous(breaks = 1:10) +
  labs(x = "PC", y = "Eigenvalue")

Version Author Date
99cdf2f Joelle Mbatchou 2022-07-25 
sum(evals.pca$V1[1:2]) / sum(evals.pca$V1)
[1] 0.8308752
  1. Now redo Question 2 above using the bigsnpr R package specifying a \(r^2\) threshold of 0.2 (i.e. LD pruning) as well as a minimum minor allele count (MAC) of 20.
  • Run PCA and make a scatter plot of the first two principal components (PCs) with each point colored according to population membership.
obj.bed <- bed(bedfile = "/data/SISG2022M15/data/YRI_CEU_ASW_MEX_NAM.bed")
pca.bigsnpr <- bed_autoSVD(
  obj.bed, 
  thr.r2 = 0.2, 
  k = 10, 
  min.mac = 20
)

Phase of clumping (on MAC) at r^2 > 0.2.. keep 87127 variants.
Discarding 48 variants with MAC < 20.

Iteration 1:
Computing SVD..
The default of 'doScale' is FALSE now for stability;
  set options(mc_doScale_quiet=TRUE) to suppress this (once per session) message
0 outlier variant detected..

Converged!
plot(pca.bigsnpr, type = "scores", scores = 1:2) +
  aes(color = fam_pop_info$Population) +
  labs(color = "Population")

Version Author Date
99cdf2f Joelle Mbatchou 2022-07-25
  • Does the plot change from the one in Question 2?
  • Check the SNP loadings for the first 10 PCs.
plot(pca.bigsnpr, type = "loadings", loadings = 1:10, coeff = 0.4)

Version Author Date
99cdf2f Joelle Mbatchou 2022-07-25
  1. Predict proportional Native American and European Ancestry for the HapMap MXL from the PCA output in Question 3 using one of the principal components. (Which PC is most appropriate for this analysis?) Assume that the HapMap MXL have negligible African Ancestry.
pca.bigsnpr %>% str
List of 7
 $ d     : num [1:10] 2262 1434 553 495 474 ...
 $ u     : num [1:604, 1:10] 0.0488 0.043 0.0489 0.0489 0.0492 ...
 $ v     : num [1:87079, 1:10] -0.00229 -0.00165 -0.00315 -0.00888 0.00177 ...
 $ niter : num 7
 $ nops  : num 128
 $ center: num [1:87079] 0.818 0.914 0.233 0.827 0.432 ...
 $ scale : num [1:87079] 0.695 0.704 0.454 0.696 0.582 ...
 - attr(*, "class")= chr "big_SVD"
 - attr(*, "subset")= int [1:87079] 1 2 3 5 6 8 10 11 12 13 ...
 - attr(*, "lrldr")='data.frame':   0 obs. of  3 variables:
  ..$ Chr  : int(0) 
  ..$ Start: int(0) 
  ..$ Stop : int(0) 
ceu.mean <- pca.bigsnpr$u[fam_pop_info$Population == "CEU",2] %>% mean
nam.mean <- pca.bigsnpr$u[fam_pop_info$Population == "NAM",2] %>% mean
c(ceu.mean, nam.mean)
[1] -0.04885356  0.09084845
mxl.prop.nam <- (pca.bigsnpr$u[fam_pop_info$Population == "MXL",2] - ceu.mean) / abs(nam.mean - ceu.mean)
mxl.prop.nam %>% summary
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
0.05262 0.37780 0.48238 0.47152 0.58381 0.81709
  1. Make a barplot of the proportional ancestry estimates from question 4.
data.frame(
  ind = 1:length(mxl.prop.nam), 
  NAM = sort(mxl.prop.nam, decreasing = TRUE)
  ) %>%
  mutate(CEU = 1 - NAM) %>%
  gather(Pop, Prop, NAM, CEU) %>%
  ggplot(aes(x = ind, y = Prop, fill = factor(Pop, levels = c("NAM", "CEU")))) +
  geom_bar(position="stack", stat="identity") +
  labs(x="Sample", y = "Ancestry Proportion", fill = "Population")

Version Author Date
99cdf2f Joelle Mbatchou 2022-07-25
  1. Check if there are samples related 2nd degree or closer. If so, run PCA as in Question 3 removing these samples then project the remaining samples onto the PC space.
# check for 2nd degree relateds or closer
rel.df <- snp_plinkKINGQC(
  plink2.path = "/data/SISG2022M15/exe/plink2", 
  bedfile.in = "/data/SISG2022M15/data/YRI_CEU_ASW_MEX_NAM.bed", 
  thr.king = 2^-3.5,
  make.bed = FALSE
)
rel.df %>% str
'data.frame':   362 obs. of  8 variables:
 $ FID1   : chr  "1563" "1567" "1567" "1570" ...
 $ IID1   : chr  "HGDP00845" "HGDP00849" "HGDP00849" "HGDP00852" ...
 $ FID2   : chr  "1556" "1556" "1561" "1551" ...
 $ IID2   : chr  "HGDP00838" "HGDP00838" "HGDP00843" "HGDP00832" ...
 $ NSNP   : int  150801 150802 150832 150816 150822 150814 150819 150815 150674 150796 ...
 $ HETHET : num  0.0976 0.1069 0.1059 0.099 0.1022 ...
 $ IBS0   : num  0.0221 0.0219 0.0223 0.0219 0.0227 ...
 $ KINSHIP: num  0.104 0.126 0.13 0.118 0.118 ...
# Gets indices of samples not related (match by fid/iid)
rel.ids <- c(paste(rel.df$FID1, rel.df$IID1), paste(rel.df$FID2, rel.df$IID2))
indices.unrel <- which(!(paste(famfile$V1,famfile$V2) %in% rel.ids))
indices.unrel %>% str
 int [1:116] 1 2 3 4 5 6 8 12 15 16 ...
# Run PCA excluding relateds
pca.bigsnpr.norels <- bed_autoSVD(
  obj.bed, 
  ind.row = indices.unrel,
  thr.r2 = 0.2, 
  k = 10, 
  min.mac = 20
)

Phase of clumping (on MAC) at r^2 > 0.2.. keep 77173 variants.
Discarding 12226 variants with MAC < 20.

Iteration 1:
Computing SVD..
0 outlier variant detected..

Converged!
# Project related samples
PCs <- matrix(NA, nrow(obj.bed), ncol(pca.bigsnpr.norels$u))
PCs[indices.unrel, ] <- predict(pca.bigsnpr.norels) # pc from model (unrels)
proj.rels <- bed_projectSelfPCA(
  pca.bigsnpr.norels, 
  obj.bed,
  ind.row = (1:nrow(famfile))[-indices.unrel]
  )
PCs[-indices.unrel, ] <- proj.rels$OADP_proj # pc from projection (rels)
data.frame(PC1 = PCs[,1], PC2 = PCs[,2], pop = fam_pop_info$Population, Type = c("Projected", "Model")[1 + (1:nrow(famfile)) %in% indices.unrel]) %>%
  ggplot(aes(x = PC1, y = PC2, color = pop, shape = Type)) +
  geom_point() +
  labs(color = "Population")

Version Author Date
99cdf2f Joelle Mbatchou 2022-07-25 

sessionInfo()
R version 4.2.1 (2022-06-23)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 22.04 LTS

Matrix products: default
BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.10.0
LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.10.0

locale:
 [1] LC_CTYPE=C.UTF-8       LC_NUMERIC=C           LC_TIME=C.UTF-8       
 [4] LC_COLLATE=C.UTF-8     LC_MONETARY=C.UTF-8    LC_MESSAGES=C.UTF-8   
 [7] LC_PAPER=C.UTF-8       LC_NAME=C              LC_ADDRESS=C          
[10] LC_TELEPHONE=C         LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C   

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] ggplot2_3.3.6     bigsnpr_1.9.11    bigstatsr_1.5.6   tidyr_1.2.0      
[5] dplyr_1.0.9       data.table_1.14.2 workflowr_1.7.0  

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.9         lattice_0.20-45    getPass_0.2-2      ps_1.7.1          
 [5] assertthat_0.2.1   rprojroot_2.0.3    digest_0.6.29      foreach_1.5.2     
 [9] utf8_1.2.2         RSpectra_0.16-1    parallelly_1.32.0  bigsparser_0.6.1  
[13] R6_2.5.1           evaluate_0.15      bigutilsr_0.3.4    highr_0.9         
[17] httr_1.4.3         pillar_1.7.0       flock_0.7          rlang_1.0.3       
[21] rstudioapi_0.13    hexbin_1.28.2      whisker_0.4        callr_3.7.0       
[25] jquerylib_0.1.4    Matrix_1.4-1       rmarkdown_2.14     labeling_0.4.2    
[29] bigparallelr_0.3.2 stringr_1.4.0      munsell_0.5.0      compiler_4.2.1    
[33] httpuv_1.6.5       xfun_0.31          pkgconfig_2.0.3    htmltools_0.5.2   
[37] tidyselect_1.1.2   tibble_3.1.7       codetools_0.2-18   viridisLite_0.4.0 
[41] fansi_1.0.3        withr_2.5.0        crayon_1.5.1       later_1.3.0       
[45] grid_4.2.1         jsonlite_1.8.0     gtable_0.3.0       lifecycle_1.0.1   
[49] DBI_1.1.3          git2r_0.30.1       magrittr_2.0.3     scales_1.2.0      
[53] cli_3.3.0          stringi_1.7.6      farver_2.1.1       fs_1.5.2          
[57] promises_1.2.0.1   doParallel_1.0.17  robustbase_0.95-0  bslib_0.3.1       
[61] ellipsis_0.3.2     generics_0.1.3     vctrs_0.4.1        cowplot_1.1.1     
[65] iterators_1.0.14   tools_4.2.1        glue_1.6.2         DEoptimR_1.0-11   
[69] purrr_0.3.4        processx_3.7.0     parallel_4.2.1     fastmap_1.1.0     
[73] yaml_2.3.5         colorspace_2.0-3   bigassertr_0.1.5   bigreadr_0.2.4    
[77] knitr_1.39         sass_0.4.1