LD Decay Analysis
Costa, W. G.
2025-07-29
Last updated: 2025-07-29
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Importance-of-markers-for-QTL-detection-by-machine-learning-methods/
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LD Decay Analysis
This document provides a detailed analysis of Linkage Disequilibrium (LD) decay across different linkage groups using genotype and map data. The analysis includes the following steps:
Data
The analysis uses genotype data from a text file and map data from an RDS file. The genotype data contains marker information, while the map data provides the positions and linkage group identifiers for these markers.
Load genotype data
The genotype data is loaded from a text file named “GEN.txt”. The first few columns of the data are displayed to give an overview of the structure.
V1 V2 V3 V4 V5
1 0 0 0 0 0
2 0 0 0 0 0
3 0 0 0 0 0
4 -1 -1 -1 -1 -1
5 0 0 0 0 0
6 0 0 0 0 0Load and prepare map data
The map data is loaded from an RDS file named “map.rds”. The data is then transformed to create a new column for locus names, convert positions to numeric, and ensure linkage group identifiers are integers. The structure and summary of the map data are displayed.
mapCP <- readRDS("data/map.rds") %>%
mutate(
Locus = paste0("V", 1:n()),
Position = as.numeric(Tamanho),
LG = as.integer(GL)
) %>%
dplyr::select(Locus, Position, LG)
str(mapCP)'data.frame': 4010 obs. of 3 variables:
$ Locus : chr "V1" "V2" "V3" "V4" ...
$ Position: num 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 ...
$ LG : int 1 1 1 1 1 1 1 1 1 1 ... Locus Position LG
Length:4010 Min. : 0 Min. : 1.0
Class :character 1st Qu.: 50 1st Qu.: 3.0
Mode :character Median :100 Median : 5.5
Mean :100 Mean : 5.5
3rd Qu.:150 3rd Qu.: 8.0
Max. :200 Max. :10.0 LD Decay Analysis
This section performs the LD decay analysis for each linkage group in the genotype data.
Run LD decay analysis for each linkage group
The analysis is performed in several steps:
Step 1: Obtain a sorted list of unique linkage groups from the map data.
Step 2: Apply a function to each linkage group using lapply.
Step 2a: For each linkage group, extract the corresponding marker names from the map data. Step 2b: Perform Linkage Disequilibrium (LD) decay analysis on the genotype data for these markers. Step 2c: Filter the LD results to include only significant marker pairs after Bonferroni correction. Step 2d: Check if there are any significant marker pairs. If so, create a data frame including the linkage group identifier and the filtered LD decay results; otherwise, return NULL for that linkage group.
res <- lapply(unique_LGs, function(lg) {
# Step 2a: For the current linkage group 'lg', extract the corresponding marker names
markers <- mapCP %>%
filter(LG == lg) %>% # Filter the map data to include only rows where LG equals the current linkage group
pull(Locus) # Extract the 'Locus' column, which contains marker names
# Step 2b: Perform Linkage Disequilibrium (LD) decay analysis on the genotype data for these markers
LDDecay <- LD.decay(CPgeno[, markers], # Subset the genotype matrix to include only the columns for the current markers
mapCP %>% filter(LG == lg)) # Subset the map data to include only the current linkage group
# Step 2c: Filter the LD results to include only significant marker pairs after Bonferroni correction
A <- LDDecay$all.LG %>% # Access the LD results for all marker pairs
filter(p < 0.05 / choose(length(markers), 2)) # Apply Bonferroni correction to adjust the p-value threshold
# Step 2d: Check if there are any significant marker pairs
if (nrow(A) > 0) {
# If significant pairs exist, create a data frame including the linkage group identifier
data.frame(GL = paste0("lg", lg), # Add a column 'GL' with the linkage group name (e.g., 'lg1', 'lg2', etc.)
A) # Include the filtered LD decay results
} else {
# If no significant pairs are found, return NULL for this linkage group
NULL
}
}) | | | 0% | |======================================================================| 100% | | | 0% | |======================================================================| 100% | | | 0% | |======================================================================| 100% | | | 0% | |======================================================================| 100% | | | 0% | |======================================================================| 100% | | | 0% | |======================================================================| 100% | | | 0% | |======================================================================| 100% | | | 0% | |======================================================================| 100% | | | 0% | |======================================================================| 100% | | | 0% | |======================================================================| 100%Combine results from all linkage groups
The results from the LD decay analysis for all linkage groups are combined into a single data frame. The linkage group identifier is converted to a factor for further analysis.
Fit the loess model
The loess model is fitted to the LD decay data to smooth the relationship between distance and r² values. The model is saved for later use.
Predict r² values for a sequence of distances
The model is used to predict r² values for a sequence of distances ranging from 0 to the maximum distance in the data. This allows for visualization of the LD decay curve.
Find the distance where r² is approximately 0.2
To find the distance at which the predicted r² value is approximately 0.2, we identify the index of the closest predicted value to 0.2 and extract the corresponding distance.
# Find the distance where the predicted r² is approximately 0.2
target_r2 <- 0.87
closest_index <- which.min(abs(pred - target_r2))
closest_d <- d_seq[closest_index]
# Display the closest distance and the target r² value
closest_d[1] 2.6Plot the LD decay curve
Finally, the LD decay curve is plotted, showing the relationship between distance and r² values. The plot includes points for each linkage group, a red line for the predicted values, a blue dashed line for the target r² value, and a green dashed line for the closest distance.
# Create the plot with additional adjustments
# Define a color palette for the linkage groups
color_palette <- colorRampPalette(c('black', 'gray50'))
# Create the ggplot object with the LD decay data
p <- ggplot(dados, aes(x = d, y = r2, colour = GL)) +
geom_point(pch = 21, show.legend = FALSE) +
geom_line(
data = data_pred,
aes(x = d, y = pred),
colour = 'red',
linewidth = 1
) +
geom_hline(yintercept = target_r2,
linetype = "dashed",
color = "blue") +
geom_vline(xintercept = closest_d,
linetype = "dashed",
color = "green") +
geom_point(
aes(x = closest_d, y = target_r2),
data = NULL,
color = "gold",
size = 3
) +
scale_color_manual(values = color_palette(length(unique(dados$GL)))) +
scale_y_continuous(breaks = seq(0, 1, by = 0.1)) +
scale_x_continuous(breaks = seq(0, max(dados$d), by = 10)) +
labs(x = "Distance (d)", y = expression(r^2)) +
theme_classic() +
theme(text = element_text(size = 20))
# Add text annotation for the closest distance and target r² value
p +
geom_text(
aes(
x = closest_d + 15,
y = target_r2,
label = paste("d =", round(closest_d, 2), "cM")
),
data = NULL,
nudge_y = 0.02,
color = "black",
fontface = "bold"
)
R version 4.4.1 (2024-06-14 ucrt)
Platform: x86_64-w64-mingw32/x64
Running under: Windows 11 x64 (build 26100)
Matrix products: default
locale:
[1] LC_COLLATE=Portuguese_Brazil.utf8 LC_CTYPE=Portuguese_Brazil.utf8
[3] LC_MONETARY=Portuguese_Brazil.utf8 LC_NUMERIC=C
[5] LC_TIME=Portuguese_Brazil.utf8
time zone: America/Sao_Paulo
tzcode source: internal
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] ggrepel_0.9.6 dplyr_1.1.4 ggplot2_3.5.2 sommer_4.4.2 crayon_1.5.3
[6] MASS_7.3-60.2 Matrix_1.7-0
loaded via a namespace (and not attached):
[1] gtable_0.3.6 jsonlite_2.0.0 compiler_4.4.1 promises_1.3.3
[5] tidyselect_1.2.1 Rcpp_1.1.0 stringr_1.5.1 git2r_0.36.2
[9] later_1.4.2 jquerylib_0.1.4 scales_1.4.0 yaml_2.3.10
[13] fastmap_1.2.0 lattice_0.22-7 R6_2.6.1 generics_0.1.4
[17] workflowr_1.7.1 knitr_1.50 tibble_3.3.0 rprojroot_2.0.4
[21] RColorBrewer_1.1-3 bslib_0.9.0 pillar_1.11.0 rlang_1.1.6
[25] cachem_1.1.0 stringi_1.8.7 httpuv_1.6.16 xfun_0.52
[29] fs_1.6.6 sass_0.4.10 cli_3.6.5 withr_3.0.2
[33] magrittr_2.0.3 digest_0.6.37 grid_4.4.1 rstudioapi_0.17.1
[37] lifecycle_1.0.4 vctrs_0.6.5 evaluate_1.0.4 glue_1.8.0
[41] farver_2.1.2 whisker_0.4.1 rmarkdown_2.29 tools_4.4.1
[45] pkgconfig_2.0.3 htmltools_0.5.8.1