A desciptive summary of genomic relationships in wheat dataset
All Z and G matrices output are based on filtered genotype and phenotype data containing no duplicates
raw_pheno <- read_xlsx("Raw_phenotypes.xlsx")
dim(raw_pheno)[1] 11424 19raw_pheno[1:5, 1:5]# A tibble: 5 × 5
Genotype Range Row Location Year
<chr> <dbl> <dbl> <chr> <dbl>
1 AYT-O-1848 1 1 Roseworthy 2014
2 AYT-O-0974 1 2 Roseworthy 2014
3 AYT-S-0579 1 3 Roseworthy 2014
4 AYT-S-0299 1 4 Roseworthy 2014
5 AYT-S-0664 1 5 Roseworthy 2014adj_pheno <- read.csv("adj_phenotypes.csv")
adj_pheno <- adj_pheno[,-c(8:20)]
dim(adj_pheno)[1] 11424 20adj_pheno[1:5, 1:5] X ID Range Row Location
1 1 AYT-O-1848 1 1 Roseworthy
2 2 AYT-O-0974 1 2 Roseworthy
3 3 AYT-S-0579 1 3 Roseworthy
4 4 AYT-S-0299 1 4 Roseworthy
5 5 AYT-S-0664 1 5 Roseworthy#Unique phenotype
unique_pheno <- adj_pheno[!duplicated(adj_pheno$ID), ]
dim(unique_pheno)[1] 10375 20summary(unique_pheno) X ID Range Row
Min. : 1 Length:10375 Min. : 1.00 Min. : 1.0
1st Qu.: 2846 Class :character 1st Qu.: 6.00 1st Qu.:119.0
Median : 5702 Mode :character Median :12.00 Median :238.0
Mean : 5705 Mean :12.48 Mean :238.3
3rd Qu.: 8562 3rd Qu.:18.00 3rd Qu.:357.0
Max. :11423 Max. :24.00 Max. :476.0
Location Year GrowthHabit adj_NDVI
Length:10375 Min. :2014 Min. :1.000 Min. :-0.495391
Class :character 1st Qu.:2014 1st Qu.:2.000 1st Qu.:-0.048276
Mode :character Median :2014 Median :2.000 Median : 0.004227
Mean :2014 Mean :2.365 Mean :-0.000125
3rd Qu.:2014 3rd Qu.:3.000 3rd Qu.: 0.050554
Max. :2014 Max. :8.000 Max. : 0.266729
NA's :9 NA's :14
adj_PlantHeight adj_LeafLoss adj_Glaucousness
Min. :-4.064010 Min. :-4.538660 Min. :-4.027074
1st Qu.:-0.627596 1st Qu.:-1.150594 1st Qu.:-1.485844
Median :-0.026288 Median :-0.113439 Median :-0.373189
Mean :-0.000589 Mean : 0.000217 Mean : 0.001182
3rd Qu.: 0.727739 3rd Qu.: 1.175993 3rd Qu.: 1.251936
Max. : 3.513630 Max. : 4.686780 Max. : 6.144128
NA's :8 NA's :8 NA's :8
adj_Greenness adj_LeafWidth adj_Biomass adj_Yellows
Min. :-4.768577 Min. :-3.942787 Min. :-4.87902 Min. :-1.417275
1st Qu.:-1.097327 1st Qu.:-0.949922 1st Qu.:-0.69445 1st Qu.:-0.605954
Median : 0.084101 Median : 0.018754 Median : 0.04168 Median :-0.402283
Mean : 0.000695 Mean : 0.000468 Mean :-0.00068 Mean : 0.000276
3rd Qu.: 1.049599 3rd Qu.: 0.950542 3rd Qu.: 0.72300 3rd Qu.: 0.415370
Max. : 3.755015 Max. : 3.388017 Max. : 3.33733 Max. : 7.033529
NA's :8 NA's :8 NA's :115 NA's :8
adj_Maturity adj_GrainYield adj_TestWeight
Min. :-22.252293 Min. :-2643.450 Min. :-10.3673
1st Qu.: -4.352765 1st Qu.: -365.178 1st Qu.: -0.9844
Median : 0.584405 Median : 27.237 Median : 0.1853
Mean : -0.001202 Mean : 0.168 Mean : -0.0002
3rd Qu.: 4.641852 3rd Qu.: 389.405 3rd Qu.: 1.1655
Max. : 15.284852 Max. : 2080.314 Max. : 4.9427
NA's :8 NA's :131 NA's :34
adj_GrainSizeTKW adj_GrainProtein
Min. :-14.64684 Min. :-2.85376
1st Qu.: -2.92215 1st Qu.:-0.51878
Median : -0.13660 Median :-0.02669
Mean : 0.00064 Mean : 0.00060
3rd Qu.: 2.79050 3rd Qu.: 0.49063
Max. : 20.14239 Max. : 3.73942
NA's :35 NA's :80 Pheno_dup <- adj_pheno|>
group_by(ID) |>
summarise(count = n()) |>
filter((count >1)) #adj_phenotypes w/ dupllicates
Pheno_dup# A tibble: 8 × 2
ID count
<chr> <int>
1 AYT-O-1994 150
2 AYT-O-2008 150
3 AYT-O-2021 150
4 AYT-O-2031 150
5 AYT-O-2033 150
6 AYT-O-2048 150
7 AYT-O-2052 7
8 AYT-O-2062 150#Check duplicates without NAs
#Outputs implies NA counts
check <- list()
for(i in 1:nrow(Pheno_dup)){
ch <- adj_pheno[adj_pheno$ID == Pheno_dup$ID[i], 8]
check[[i]] <- sum(is.na(ch))
}
check [[1]]
[1] 150
[[2]]
[1] 150
[[3]]
[1] 150
[[4]]
[1] 150
[[5]]
[1] 150
[[6]]
[1] 150
[[7]]
[1] 7
[[8]]
[1] 150#Phenotype without IDs in Pheno_dup(ID==NAs)
y_check <- adj_pheno[!(adj_pheno$ID%in%Pheno_dup$ID),]
dim(y_check)[1] 10367 20summary(y_check) X ID Range Row
Min. : 1 Length:10367 Min. : 1.00 Min. : 1.0
1st Qu.: 2854 Class :character 1st Qu.: 6.00 1st Qu.:120.0
Median : 5707 Mode :character Median :12.00 Median :238.0
Mean : 5709 Mean :12.49 Mean :238.5
3rd Qu.: 8564 3rd Qu.:18.00 3rd Qu.:357.0
Max. :11423 Max. :24.00 Max. :476.0
Location Year GrowthHabit adj_NDVI
Length:10367 Min. :2014 Min. :1.000 Min. :-0.495391
Class :character 1st Qu.:2014 1st Qu.:2.000 1st Qu.:-0.048276
Mode :character Median :2014 Median :2.000 Median : 0.004227
Mean :2014 Mean :2.365 Mean :-0.000125
3rd Qu.:2014 3rd Qu.:3.000 3rd Qu.: 0.050554
Max. :2014 Max. :8.000 Max. : 0.266729
NA's :9 NA's :6
adj_PlantHeight adj_LeafLoss adj_Glaucousness
Min. :-4.064010 Min. :-4.538660 Min. :-4.027074
1st Qu.:-0.627596 1st Qu.:-1.150594 1st Qu.:-1.485844
Median :-0.026288 Median :-0.113439 Median :-0.373189
Mean :-0.000589 Mean : 0.000217 Mean : 0.001182
3rd Qu.: 0.727739 3rd Qu.: 1.175993 3rd Qu.: 1.251936
Max. : 3.513630 Max. : 4.686780 Max. : 6.144128
adj_Greenness adj_LeafWidth adj_Biomass adj_Yellows
Min. :-4.768577 Min. :-3.942787 Min. :-4.87902 Min. :-1.417275
1st Qu.:-1.097327 1st Qu.:-0.949922 1st Qu.:-0.69445 1st Qu.:-0.605954
Median : 0.084101 Median : 0.018754 Median : 0.04168 Median :-0.402283
Mean : 0.000695 Mean : 0.000468 Mean :-0.00068 Mean : 0.000276
3rd Qu.: 1.049599 3rd Qu.: 0.950542 3rd Qu.: 0.72300 3rd Qu.: 0.415370
Max. : 3.755015 Max. : 3.388017 Max. : 3.33733 Max. : 7.033529
NA's :107
adj_Maturity adj_GrainYield adj_TestWeight
Min. :-22.252293 Min. :-2643.450 Min. :-10.367262
1st Qu.: -4.352765 1st Qu.: -365.178 1st Qu.: -0.984365
Median : 0.584405 Median : 27.237 Median : 0.185297
Mean : -0.001202 Mean : 0.168 Mean : -0.000197
3rd Qu.: 4.641852 3rd Qu.: 389.405 3rd Qu.: 1.165534
Max. : 15.284852 Max. : 2080.314 Max. : 4.942738
NA's :123 NA's :26
adj_GrainSizeTKW adj_GrainProtein
Min. :-14.646842 Min. :-2.85376
1st Qu.: -2.922147 1st Qu.:-0.51878
Median : -0.136602 Median :-0.02669
Mean : 0.000636 Mean : 0.00060
3rd Qu.: 2.790503 3rd Qu.: 0.49063
Max. : 20.142392 Max. : 3.73942
NA's :27 NA's :72 R_file <- readRDS("Genotypes.rds")
R_file[1:5, 1:5] #non-standardized markers AXAFFSNP-00001 AXAFFSNP-00002 AXAFFSNP-00003 AXAFFSNP-00004
AYT-O-1848 1 -1 -1 1
AYT-O-0974 -1 -1 -1 1
AYT-S-0579 1 -1 -1 1
AYT-S-0299 1 -1 -1 1
AYT-S-0664 1 -1 -1 1
AXAFFSNP-00005
AYT-O-1848 1
AYT-O-0974 1
AYT-S-0579 1
AYT-S-0299 1
AYT-S-0664 1length(unique(adj_pheno$ID))[1] 10375all(rownames(R_file)%in%adj_pheno$ID)[1] TRUEall(unique(adj_pheno$ID)%in%rownames(R_file))[1] TRUEtable(table(adj_pheno$ID))
1 7 150
10367 1 7 table(table(rownames(R_file)))
1
10375 #Genotype with phenotypes that contain some variables
Geno_n_pheo <- R_file[(rownames(R_file)%in%y_check$ID),]
dim(Geno_n_pheo)[1] 10367 17181load("PC.RData")
dim(PC) [1] 10375 10head(PC) [,1] [,2] [,3] [,4] [,5]
AYT-O-1848 0.0142843657 0.0008520041 0.004599534 0.006290104 0.0040835958
AYT-O-0974 -0.0020205548 0.0039306500 -0.019053867 0.005907936 -0.0052171607
AYT-S-0579 -0.0123209799 -0.0113984018 0.006133443 -0.001420917 0.0095267938
AYT-S-0299 -0.0009560686 0.0020915326 -0.007918294 -0.005763531 -0.0084143525
AYT-S-0664 0.0166148917 -0.0072749232 0.004678868 0.004706790 -0.0006557087
AYT-S-0304 0.0105904204 -0.0009692425 -0.002309381 -0.026689162 -0.0093229600
[,6] [,7] [,8] [,9] [,10]
AYT-O-1848 0.0025967631 -0.003812178 0.0009275762 -0.0003712614 -0.002473555
AYT-O-0974 -0.0119637740 -0.012642017 -0.0222248123 -0.0118447073 0.018452294
AYT-S-0579 -0.0009197395 -0.006211754 0.0099594666 0.0046946866 0.006762153
AYT-S-0299 -0.0147098250 0.001235230 0.0036071933 0.0063621112 -0.002532126
AYT-S-0664 0.0075995266 -0.001902767 -0.0029518912 0.0021473800 0.001026518
AYT-S-0304 0.0110086302 0.003983154 -0.0049505648 -0.0035896452 -0.003298428set.seed(234)
clust <- kmeans(PC[,1:5], nstart = 10, centers = 8)
plot(PC[, 1:2], cex = 0.5, col = clust$cluster)
plot(PC[, c(1,3)], cex = 0.5, col = clust$cluster)
table(clust$cluster)
1 2 3 4 5 6 7 8
1140 1156 949 1298 2437 1250 1049 1096 length(clust$cluster)[1] 10375R_file <- Geno_n_pheo
cst <- clust$cluster[(names(clust$cluster)%in%rownames(R_file))]
length(cst)[1] 10367#Check that names in cluster are equal to rownames in Genotype file
sum(names(cst) == rownames(R_file))[1] 10367clust_data <- tibble(ID = names(cst), cluster = cst)
head(clust_data)# A tibble: 6 × 2
ID cluster
<chr> <int>
1 AYT-O-1848 5
2 AYT-O-0974 2
3 AYT-S-0579 6
4 AYT-S-0299 2
5 AYT-S-0664 5
6 AYT-S-0304 7new_pheno <- left_join(y_check, clust_data, by = join_by(ID)) |>
group_by(cluster)#Create the mean
combn_m <- new_pheno|>
summarise_at(vars(adj_NDVI:adj_GrainProtein), ~ mean(., na.rm = TRUE))
combn_m <- combn_m |>
pivot_longer(cols = adj_NDVI:adj_GrainProtein, names_to = "Trait", values_to = "Mean")
#Create the standard deviation
combn_s <- new_pheno|>
summarise_at(vars(adj_NDVI:adj_GrainProtein),~sd(., na.rm = TRUE))
combn_s <- combn_s |>
pivot_longer(cols = adj_NDVI:adj_GrainProtein, names_to = "Trait", values_to = "SD")
plot_df <- cbind(combn_m, SD = combn_s$SD)
plot_df$cluster <- as.factor(plot_df$cluster)
ggplot(plot_df, aes(y = Mean)) +
geom_col(aes(x = cluster)) + facet_wrap(~Trait, scales = "free") +
geom_errorbar(aes(x = cluster, ymin = Mean - SD, ymax = Mean + SD), width = 0.2)
#Genotype by cluster
c_geno <- list()
for(i in 1:8){
c_geno[[i]] <- R_file[clust_data$cluster == i, ]
}
c_geno[[1]][1:5, 1:5] #cluster one AXAFFSNP-00001 AXAFFSNP-00002 AXAFFSNP-00003 AXAFFSNP-00004
AYT-O-1092 -1 -1 -1 1
AYT-O-1524 0 -1 -1 1
AYT-O-0789 -1 -1 -1 1
AYT-O-1055 1 -1 -1 1
AYT-O-1352 -1 -1 -1 0
AXAFFSNP-00005
AYT-O-1092 1
AYT-O-1524 1
AYT-O-0789 1
AYT-O-1055 1
AYT-O-1352 1#Allele frequnecies by cluster
pclust <- lapply(c_geno, function(x) colMeans(x+1)/2)
sapply(pclust, FUN = summary) [,1] [,2] [,3] [,4] [,5] [,6]
Min. 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.0000000
1st Qu. 0.1357379 0.1739537 0.09335443 0.1177092 0.08081121 0.1081439
Median 0.4943008 0.4986987 0.48076294 0.5057453 0.49978777 0.4982958
Mean 0.5002393 0.4993927 0.49966665 0.5000844 0.50005717 0.5001681
3rd Qu. 0.8673331 0.8236526 0.90596242 0.8786958 0.91888703 0.8895860
Max. 1.0000000 1.0000000 1.00000000 1.0000000 1.00000000 1.0000000
[,7] [,8]
Min. 0.00000000 0.0000000
1st Qu. 0.09677943 0.2054046
Median 0.50136861 0.5025376
Mean 0.49944482 0.5006256
3rd Qu. 0.90113898 0.7919156
Max. 1.00000000 1.0000000qclust <- lapply(pclust, function(x) 1-x)
sapply(qclust, FUN = summary) [,1] [,2] [,3] [,4] [,5] [,6]
Min. 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.0000000
1st Qu. 0.1326669 0.1763474 0.09403758 0.1213042 0.08111297 0.1104140
Median 0.5056992 0.5013013 0.51923706 0.4942547 0.50021223 0.5017042
Mean 0.4997607 0.5006073 0.50033335 0.4999156 0.49994283 0.4998319
3rd Qu. 0.8642621 0.8260463 0.90664557 0.8822908 0.91918879 0.8918561
Max. 1.0000000 1.0000000 1.00000000 1.0000000 1.00000000 1.0000000
[,7] [,8]
Min. 0.00000000 0.0000000
1st Qu. 0.09886102 0.2080844
Median 0.49863139 0.4974624
Mean 0.50055518 0.4993744
3rd Qu. 0.90322057 0.7945954
Max. 1.00000000 1.0000000#Compute minor allele frequencies
maf <- lapply(pclust, function(x) pmin(x, 1-x))
maf_1 <- lapply(maf, function(x) x>0.05)
#Obtain new genotype object with MAF >0.05
new_geno <- list()
for(i in seq_along(c_geno)){
new_geno[[i]] <- c_geno[[i]][, maf_1[[i]]]
}
#Obtain new allele frequencies
pw <- lapply(new_geno, function(x) colMeans(x+1)/2)
sapply(pw, FUN = summary) [,1] [,2] [,3] [,4] [,5] [,6]
Min. 0.05000483 0.05004018 0.05000427 0.05000896 0.05006137 0.05000463
1st Qu. 0.23009933 0.26063250 0.16051355 0.21993617 0.14770626 0.19264260
Median 0.49687102 0.50139067 0.51161663 0.50873067 0.50845270 0.49837105
Mean 0.50174849 0.50066385 0.50118703 0.50170389 0.50182858 0.50034948
3rd Qu. 0.77683962 0.74367034 0.84382579 0.78253646 0.85285452 0.81142281
Max. 0.94987878 0.94984258 0.94997281 0.94999920 0.94998864 0.94996741
[,7] [,8]
Min. 0.05004766 0.05011191
1st Qu. 0.20776171 0.27214164
Median 0.50591085 0.50357837
Mean 0.50323207 0.50172105
3rd Qu. 0.79919621 0.72878893
Max. 0.94995234 0.94983241qw <- lapply(pw, function(x) 1-x)
sapply(qw, FUN = summary) [,1] [,2] [,3] [,4] [,5] [,6]
Min. 0.05012122 0.05015742 0.05002719 0.0500008 0.05001136 0.05003259
1st Qu. 0.22316038 0.25632966 0.15617421 0.2174635 0.14714548 0.18857719
Median 0.50312898 0.49860933 0.48838337 0.4912693 0.49154730 0.50162895
Mean 0.49825151 0.49933615 0.49881297 0.4982961 0.49817142 0.49965052
3rd Qu. 0.76990067 0.73936750 0.83948645 0.7800638 0.85229374 0.80735740
Max. 0.94999517 0.94995982 0.94999573 0.9499910 0.94993863 0.94999537
[,7] [,8]
Min. 0.05004766 0.05016759
1st Qu. 0.20080379 0.27121107
Median 0.49408915 0.49642163
Mean 0.49676793 0.49827895
3rd Qu. 0.79223829 0.72785836
Max. 0.94995234 0.94988809Genotype by cluster (1 - 8): 1137x11868 1156x12773 948x11166 1297x11438 2436x10544 1250x11330 1049x10452 1094x13488 Phenotype: 10367 20 \(P = 2(p_i - 0.5)\) as pclust_all. Check Efficient methods to compute genomic predictions for more details.
\(Z = M - P\), where \(M\) is the marker allele individual inherited \(\{-1/0/1\}\)
\(G = \frac{ZZ'}{2pq}\) or
\(G = \frac{ZZ'}{4pq}\) accounting for inbreeding
pclust_all <- lapply(pw, function(x) 2*(x-0.5))
Z_cl <- list()
for (i in seq_along(new_geno)) {
Z_cl[[i]] <- sweep(new_geno[[i]], 2, pclust_all[[i]], FUN = "-")
}
Z_tc <- lapply(Z_cl, FUN = tcrossprod)
sum_2pq <- list()
for(i in seq_along(pw)){
sum_2pq[[i]] <- sum(2*pw[[i]]*qw[[i]])
}
G_cl <- lapply(seq_along(Z_tc), function(i) Z_tc[[i]] / sum_2pq[[i]])sum_4pq <- list()
for(i in seq_along(pw)){
sum_4pq[[i]] <- sum(4*pw[[i]]*qw[[i]])
}
G_cl4 <- lapply(seq_along(Z_tc), function(i) Z_tc[[i]] / sum_4pq[[i]])# Adjusted Allele frequencies
sapply(pclust_all, function(x) summary(x)) [,1] [,2] [,3] [,4] [,5]
Min. -0.899990349 -0.899919635 -0.899991462 -0.899982086 -0.899877256
1st Qu. -0.539801350 -0.478735007 -0.678972895 -0.560127659 -0.704587490
Median -0.006257964 0.002781343 0.023233251 0.017461340 0.016905394
Mean 0.003496989 0.001327695 0.002374063 0.003407778 0.003657153
3rd Qu. 0.553679247 0.487340689 0.687651580 0.565072928 0.705709040
Max. 0.899757557 0.899685162 0.899945619 0.899998396 0.899977273
[,6] [,7] [,8]
Min. -0.8999907395 -0.899904671 -0.899776170
1st Qu. -0.6147148024 -0.584476586 -0.455716729
Median -0.0032579027 0.011821706 0.007156736
Mean 0.0006989691 0.006464136 0.003442105
3rd Qu. 0.6228456164 0.598392412 0.457577854
Max. 0.8999348120 0.899904671 0.899664824#Z matrices
sapply(Z_cl, function(x) summary(colMeans(x))) [,1] [,2] [,3] [,4] [,5]
Min. -1.295748e-16 -1.125589e-16 -1.551736e-16 -1.118355e-16 -1.685160e-16
1st Qu. -4.071794e-17 -3.966454e-17 -4.005235e-17 -3.967528e-17 -4.034015e-17
Median -5.004303e-19 4.802003e-19 8.197849e-19 3.637971e-19 4.557566e-20
Mean -2.781852e-19 3.784483e-19 1.929573e-19 1.597456e-19 -1.738176e-19
3rd Qu. 3.988796e-17 4.072098e-17 4.005235e-17 4.056872e-17 4.058085e-17
Max. 1.890406e-16 1.235555e-16 1.190445e-16 1.129911e-16 1.126175e-16
[,6] [,7] [,8]
Min. -1.111333e-16 -1.111281e-16 -1.308115e-16
1st Qu. -3.955725e-17 -4.085944e-17 -4.089761e-17
Median 4.884981e-19 -2.116726e-19 -2.029658e-19
Mean 2.079781e-19 -5.457801e-19 -1.634410e-19
3rd Qu. 4.026779e-17 3.894777e-17 3.998427e-17
Max. 1.170841e-16 1.314884e-16 1.116185e-16#Z tcrossprod
sapply(Z_tc, function(x) summary(diag(x))) [,1] [,2] [,3] [,4] [,5] [,6] [,7]
Min. 3128.078 4542.555 1572.900 3596.515 1630.612 2829.882 2979.005
1st Qu. 6310.200 7358.895 4389.980 5477.433 3949.128 5422.668 5206.944
Median 7251.185 8135.607 5423.748 6564.930 4860.234 6350.592 6082.779
Mean 7391.636 8253.989 5490.644 6678.949 4940.544 6286.974 6160.460
3rd Qu. 8274.891 8958.878 6495.350 7784.395 5970.492 7177.905 6923.493
Max. 12008.138 11435.085 9543.387 10744.136 9106.588 9472.882 10000.699
[,8]
Min. 5021.360
1st Qu. 8501.080
Median 9043.462
Mean 8881.487
3rd Qu. 9449.546
Max. 10665.394#sum 2pq
sum_2pq[[1]]
[1] 3933.18
[[2]]
[1] 4474.099
[[3]]
[1] 3044.081
[[4]]
[1] 3737.895
[[5]]
[1] 2832.316
[[6]]
[1] 3479.487
[[7]]
[1] 3350.206
[[8]]
[1] 4869.144#sum 4pq
sum_4pq[[1]]
[1] 7866.361
[[2]]
[1] 8948.197
[[3]]
[1] 6088.161
[[4]]
[1] 7475.791
[[5]]
[1] 5664.633
[[6]]
[1] 6958.973
[[7]]
[1] 6700.413
[[8]]
[1] 9738.288# GRM with 2pq
sapply(G_cl, dim) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 1137 1156 948 1297 2436 1250 1049 1094
[2,] 1137 1156 948 1297 2436 1250 1049 1094sapply(G_cl, function(x) summary(diag(x))) [,1] [,2] [,3] [,4] [,5] [,6] [,7]
Min. 0.7953049 1.015301 0.5167077 0.9621764 0.5757169 0.8133046 0.8892006
1st Qu. 1.6043505 1.644777 1.4421367 1.4653789 1.3943103 1.5584680 1.5542158
Median 1.8435933 1.818379 1.7817359 1.7563173 1.7159927 1.8251520 1.8156432
Mean 1.8793026 1.844838 1.8037116 1.7868207 1.7443475 1.8068682 1.8388300
3rd Qu. 2.1038677 2.002387 2.1337642 2.0825610 2.1079889 2.0629207 2.0665870
Max. 3.0530351 2.555841 3.1350638 2.8743812 3.2152438 2.7224941 2.9850993
[,8]
Min. 1.031261
1st Qu. 1.745908
Median 1.857300
Mean 1.824035
3rd Qu. 1.940700
Max. 2.190404# GRM with 4pq
sapply(G_cl4, dim) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 1137 1156 948 1297 2436 1250 1049 1094
[2,] 1137 1156 948 1297 2436 1250 1049 1094sapply(G_cl4, function(x) summary(diag(x))) [,1] [,2] [,3] [,4] [,5] [,6] [,7]
Min. 0.3976525 0.5076503 0.2583538 0.4810882 0.2878584 0.4066523 0.4446003
1st Qu. 0.8021752 0.8223885 0.7210684 0.7326895 0.6971551 0.7792340 0.7771079
Median 0.9217966 0.9091895 0.8908679 0.8781586 0.8579963 0.9125760 0.9078216
Mean 0.9396513 0.9224192 0.9018558 0.8934104 0.8721737 0.9034341 0.9194150
3rd Qu. 1.0519339 1.0011936 1.0668821 1.0412805 1.0539944 1.0314603 1.0332935
Max. 1.5265176 1.2779205 1.5675319 1.4371906 1.6076219 1.3612470 1.4925496
[,8]
Min. 0.5156307
1st Qu. 0.8729542
Median 0.9286501
Mean 0.9120173
3rd Qu. 0.9703498
Max. 1.0952021\(Z^* = scale(Z)\)
\(G^* = \frac{Z^*{Z^*}'}{p}\), p is the number of columns in \(Z^*\)
Z_alt <- lapply(Z_cl, function(x) scale(x))
sapply(Z_alt, function(x) summary(colMeans(x))) [,1] [,2] [,3] [,4] [,5]
Min. -1.183335e-16 -1.507769e-16 -1.167535e-16 -1.188894e-16 -1.358610e-16
1st Qu. -2.255598e-17 -2.373390e-17 -2.019635e-17 -2.246982e-17 -1.958169e-17
Median 6.102809e-20 -1.440601e-19 2.653322e-19 -4.065967e-19 -1.595148e-19
Mean 4.499391e-19 1.349149e-19 2.714749e-19 2.345482e-19 3.208878e-21
3rd Qu. 2.334935e-17 2.360184e-17 2.098503e-17 2.241766e-17 1.993561e-17
Max. 1.465773e-16 1.379953e-16 1.205743e-16 1.394159e-16 1.116547e-16
[,6] [,7] [,8]
Min. -1.270359e-16 -1.262892e-16 -1.339828e-16
1st Qu. -2.170486e-17 -2.194863e-17 -2.405145e-17
Median 2.692291e-19 -2.579760e-19 -9.640876e-19
Mean -1.378772e-19 1.391687e-19 -4.290848e-19
3rd Qu. 2.171319e-17 2.253321e-17 2.317933e-17
Max. 1.165845e-16 1.311610e-16 1.409661e-16Z_trans <- lapply(Z_alt, FUN = tcrossprod)
sapply(Z_trans, function(x) summary(diag(x))) [,1] [,2] [,3] [,4] [,5] [,6] [,7]
Min. 5031.637 6464.258 2635.339 4879.816 2827.216 4016.239 3986.458
1st Qu. 9503.992 10579.287 8807.958 9256.664 7935.705 9420.770 8322.558
Median 11531.552 12563.944 11007.572 11227.615 10230.546 11400.253 10229.281
Mean 11857.562 12761.951 11154.222 11429.181 10539.672 11320.936 10442.036
3rd Qu. 13864.848 14450.498 13401.581 13646.197 13183.871 13176.901 12220.785
Max. 22802.686 20600.626 20554.402 19808.034 20747.528 17916.448 19204.892
[,8]
Min. 7456.676
1st Qu. 12521.257
Median 13577.480
Mean 13475.671
3rd Qu. 14499.559
Max. 17907.692#Number of columns per cluster
colm <- lapply(Z_alt, function(x) ncol(x))
#GRM by cluster
G_alt <- lapply(seq_along(Z_trans), function(i) Z_trans[[i]] / colm[[i]])
sapply(G_alt, dim) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 1137 1156 948 1297 2436 1250 1049 1094
[2,] 1137 1156 948 1297 2436 1250 1049 1094sapply(G_alt, function(x) summary(diag(x))) [,1] [,2] [,3] [,4] [,5] [,6] [,7]
Min. 0.4239667 0.5060877 0.2360146 0.4266319 0.2681351 0.3544783 0.3814063
1st Qu. 0.8008082 0.8282539 0.7888195 0.8092904 0.7526275 0.8314889 0.7962646
Median 0.9716509 0.9836330 0.9858116 0.9816065 0.9702718 1.0062006 0.9786912
Mean 0.9991205 0.9991349 0.9989451 0.9992290 0.9995895 0.9992000 0.9990467
3rd Qu. 1.1682548 1.1313315 1.2002132 1.1930580 1.2503671 1.1630098 1.1692293
Max. 1.9213588 1.6128260 1.8408026 1.7317743 1.9677094 1.5813281 1.8374371
[,8]
Min. 0.5528378
1st Qu. 0.9283257
Median 1.0066341
Mean 0.9990859
3rd Qu. 1.0749970
Max. 1.3276758