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The following example illustrates how to compute the “scaled population recombination rate” \(\rho_{ij}\) between SNPs \(i\) and \(j\) using HapMap genetic map.
We take six SNPs in chromosome 22 from HapMap CEU Phase 2, with the genetic map shown below. We also get the effective diploid population size \(N_e=11418\) from IMPUTE software document.
position COMBINED_rate(cM/Mb) Genetic_Map(cM)
1: 14431347 8.096992 0.00000000
2: 14432618 8.131520 0.01029128
3: 14433624 8.131967 0.01847159
4: 14433659 8.132625 0.01875620
5: 14433758 8.129606 0.01956133
6: 14434713 8.024772 0.02732511To compute recombination rates from two SNPs, we use the following formula from Li and Stephens (2003):
\[ \rho = 4 \times \text{effective diploid population size} \times \text{genetic distance}. \]
For example,
As a validation, we compare our calculations above with the results from BLIMP (Wen and Stephens, 2010).
The file rmb.ceu.ch22 lists recombination rate between all adjacent markers in the panel.
library(data.table)
genetic.map.chr22 <- data.table::fread("genetic_map_chr22.txt")
legend.ceu.chr22 <- data.table::fread("legend.ceu.ch22", header = T)
rmb.ceu.chr22 <- data.table::fread("rmb.ceu.ch22")
# locate all the snps specified by the legend file
selected.pos <- intersect(genetic.map.chr22$position, legend.ceu.chr22$position)
map.index <- which(genetic.map.chr22$position %in% selected.pos)
leg.index <- which(legend.ceu.chr22$position %in% selected.pos)
# check the location is correct
location.check <- prod(genetic.map.chr22$position[map.index] == legend.ceu.chr22$position[leg.index])
if (location.check != 1) stop('locate the snps wrongly')
# calculate the shrinking coefficient: exp(-rho_{ij}/(2*m)) for adjacent (i,j)
# general formula: rho = 4 * effective population size * genetic distance
# hapmap phase 2 ceu: effective population size (Ne)=11418, haplotype size (m)=120
num.snp <- length(map.index);
ro.coef <- rep(0, num.snp);
ro.coef[1] <- 1;
map.selected <- genetic.map.chr22[map.index, ]
rcb.selected <- map.selected[[3]]
for (i in 2:num.snp){
ro.coef[i] <- exp(-4*11418*(rcb.selected[i]/100-rcb.selected[i-1]/100)/120)
}
# compare the result with the one provided in BLIMP (Wen and Stephens, 2010)
# make sure rss compute rho in the same way as BLIMP
results <- matrix(0, nrow=num.snp, ncol=2)
results[, 1] <- unlist(rmb.ceu.chr22)
results[, 2] <- ro.coef> head(results)
[,1] [,2]
[1,] 1.0000000 1.0000000
[2,] 0.9615886 0.9615886
[3,] 0.9693454 0.9693454
[4,] 0.9989173 0.9989173
[5,] 0.9969404 0.9969404
[6,] 0.9708834 0.9708834
> tail(results)
[,1] [,2]
[34021,] 0.9963701 0.9963701
[34022,] 0.9909937 0.9909937
[34023,] 0.9986032 0.9986032
[34024,] 0.9879030 0.9879030
[34025,] 0.9962124 0.9962124
[34026,] 0.9847357 0.9847357
> max(abs(results[,1]-results[, 2]))
[1] 4.999806e-08
─ Session info ───────────────────────────────────────────────────────────────
setting value
version R version 4.0.1 (2020-06-06)
os macOS Catalina 10.15.5
system x86_64, darwin17.0
ui X11
language (EN)
collate en_US.UTF-8
ctype en_US.UTF-8
tz America/Los_Angeles
date 2020-06-23
─ Packages ───────────────────────────────────────────────────────────────────
package * version date lib source
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stringi 1.4.6 2020-02-17 [1] CRAN (R 4.0.0)
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[1] /Library/Frameworks/R.framework/Versions/4.0/Resources/library