Genetic relationship matrix
Siming Zhao
2026-04-13
Last updated: 2024-01-23
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Knit directory: QBS-statsgen/
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Before the class
- Download data
Download from here: https://rcweb.dartmouth.edu/Szhao/QBS148-statsgen/e2/.
- Plink
We have used plink in our first exercise class.
- R packages
Install ggplot2, data.table,
tidyverse if you don’t have them.
Data used in this analysis
- Genotype data The genotype data is given plink1 format:
oz.fam,oz.bim,oz.bed
Pay attention to the .fam file
head data/e2/oz.fam1400 1400t1 0 0 1 -9
1400 1400t2 0 0 2 -9
570 570t1 0 0 1 -9
570 570t2 0 0 1 -9
3413 3413t1 0 0 2 -9
3413 3413t2 0 0 1 -9
1911 1911t1 0 0 2 -9
1911 1911t2 0 0 2 -9
1403 1403t1 0 0 2 -9
1403 1403t2 0 0 1 -9The .fam file has 6 columns: Family ID, Individual ID, Fathers ID (0=missing), Mothers ID (0=missing), Sex (1=M, 2=F), Phenotype (-9=missing).
Now we can see there are related individuals in this cohort.
Get and plot GRM
Use plink to get GRM
plink --bfile data/e2/oz --make-grm-gz --out output/ozThis will generate oz.grm.gz and
oz.grm.id files in the output folder. Note:
you will need to create the output folder first if you
don’t have one.
To visualize this:
library("tidyverse")── Attaching packages ─────────────────────────────────────── tidyverse 1.3.1 ──✔ ggplot2 3.3.5 ✔ purrr 0.3.4
✔ tibble 3.1.2 ✔ dplyr 1.0.7
✔ tidyr 1.1.3 ✔ stringr 1.4.0
✔ readr 1.4.0 ✔ forcats 0.5.1── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag() masks stats::lag()# these are plot functions:
tileplot <- function(mat)
{
mat = data.frame(mat)
mat$Var1 = factor(rownames(mat), levels=rownames(mat)) ## preserve rowname order
melted_mat <- pivot_longer(mat, cols=-Var1, names_to="Var2", values_to="value")
melted_mat$Var2 = factor(melted_mat$Var2, levels=colnames(mat)) ## preserve colname order
rango = range(melted_mat$value)
pp <- ggplot(melted_mat,aes(x=Var1,y=Var2,fill=value)) + geom_tile() ##+scale_fill_gradientn(colours = c("#C00000", "#FF0000", "#FF8080", "#FFC0C0", "#FFFFFF", "#C0C0FF", "#8080FF", "#0000FF", "#0000C0"), limit = c(-1,1))
pp
}
grmgz2mat = function(grmhead)
{
## given plink like header, it reads thd grm file and returns matrix of grm
grm = read.table(paste0(grmhead,".grm.gz"),header=F)
grmid = read.table(paste0(grmhead,".grm.id"),header=F)
grmat = matrix(0,max(grm$V1),max(grm$V2))
rownames(grmat) = grmid$V2
colnames(grmat) = grmid$V2
## fill lower matrix of GRM
grmat[upper.tri(grmat,diag=TRUE)]= grm$V4
## make upper = lower, need to subtract diag
grmat + t(grmat) - diag(diag(grmat))
}## read grm calculated in plink into R matrix
grmat = grmgz2mat("output/oz")We can look at the distribution of diagonal values (ie the covariation of a person with themselves) using the following code. Usually we would expect the values to be close to 1. This teaching example only includes ~10,000 snps so there is more variation here than we would usually expect.
hist(diag(grmat), breaks=100)
For off diagnal values, plot distribution. The off-diagonal elements of the GRM are two times the kinship coefficient. Related samples are inferred based on the range of estimated kinship coefficients = : >0.354, 0.354-0.177, 0.177-0.0884, and 0.0884-0.0442 that corresponds to duplicate/MZ twin, 1st-degree, 2nd-degree, and 3rd-degree relationships, respectively.
Plot distribution of kinship coefficient:
grmat.off <- c(grmat[upper.tri(grmat)])
hist(grmat.off[which(grmat.off>0.05)]/2, breaks=100, xlim=c(0.05,0.3))
Plot GRM for a few families:
fam = read.table("data/e2/oz.fam") # second column is IID (individual ID)
head(fam, n= 6) V1 V2 V3 V4 V5 V6
1 1400 1400t1 0 0 1 -9
2 1400 1400t2 0 0 2 -9
3 570 570t1 0 0 1 -9
4 570 570t2 0 0 1 -9
5 3413 3413t1 0 0 2 -9
6 3413 3413t2 0 0 1 -9ind = fam[1:6,2]
print(ind)[1] "1400t1" "1400t2" "570t1" "570t2" "3413t1" "3413t2"There are three families: 1400, 570, and 3413. Each family has two individuals.
tileplot(grmat[ind,ind]/2)
–> –>
Credits
GRM visualization from Haky Im: https://hakyimlab.github.io/hgen471/L8-GRM.html Data from https://www.colorado.edu/ibg/international-workshop/2022-international-statistical-genetics-workshop/syllabus/polygenic-scores
sessionInfo()R version 4.1.0 (2021-05-18)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: CentOS Linux 7 (Core)
Matrix products: default
BLAS: /software/R-4.1.0-no-openblas-el7-x86_64/lib64/R/lib/libRblas.so
LAPACK: /software/R-4.1.0-no-openblas-el7-x86_64/lib64/R/lib/libRlapack.so
locale:
[1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C LC_TIME=C
[4] LC_COLLATE=C LC_MONETARY=C LC_MESSAGES=C
[7] LC_PAPER=C LC_NAME=C LC_ADDRESS=C
[10] LC_TELEPHONE=C LC_MEASUREMENT=C LC_IDENTIFICATION=C
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] forcats_0.5.1 stringr_1.4.0 dplyr_1.0.7 purrr_0.3.4
[5] readr_1.4.0 tidyr_1.1.3 tibble_3.1.2 ggplot2_3.3.5
[9] tidyverse_1.3.1
loaded via a namespace (and not attached):
[1] Rcpp_1.0.9 lubridate_1.7.10 assertthat_0.2.1 rprojroot_2.0.2
[5] digest_0.6.27 utf8_1.2.1 R6_2.5.0 cellranger_1.1.0
[9] backports_1.2.1 reprex_2.0.0 evaluate_0.20 highr_0.9
[13] httr_1.4.2 pillar_1.6.1 rlang_1.1.0 readxl_1.3.1
[17] rstudioapi_0.13 jquerylib_0.1.4 rmarkdown_2.21 labeling_0.4.2
[21] munsell_0.5.0 broom_0.7.8 compiler_4.1.0 httpuv_1.6.1
[25] modelr_0.1.8 xfun_0.38 pkgconfig_2.0.3 htmltools_0.5.5
[29] tidyselect_1.1.1 workflowr_1.6.2 fansi_0.5.0 crayon_1.5.2
[33] dbplyr_2.1.1 withr_2.5.0 later_1.2.0 grid_4.1.0
[37] jsonlite_1.7.2 gtable_0.3.0 lifecycle_1.0.3 DBI_1.1.1
[41] git2r_0.28.0 magrittr_2.0.1 scales_1.1.1 cli_3.6.1
[45] stringi_1.6.2 cachem_1.0.5 farver_2.1.0 fs_1.6.1
[49] promises_1.2.0.1 xml2_1.3.2 bslib_0.4.2 ellipsis_0.3.2
[53] generics_0.1.0 vctrs_0.3.8 tools_4.1.0 glue_1.4.2
[57] hms_1.1.0 fastmap_1.1.0 yaml_2.2.1 colorspace_2.0-2
[61] rvest_1.0.0 knitr_1.42 haven_2.4.1 sass_0.4.0