Last updated: 2021-03-31

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Let’s run a GWAS via GAPIT using the NLR genes as input, and the PCs calculated using SNPs

library(GAPIT3)
library(SNPRelate)
library(tidyverse)
library(ggsignif)
library(cowplot)
library(ggsci)
library(patchwork)

First, we have to make the principal components - making them based on NLR genes alone is probably garbage. Let’s make them based on all publicly available SNPs from here.

I ran the following on a bigger server which is why it’s marked as not to run when I rerun workflowr.

if (!file.exists('data/SNPs_lee.id.biallic_maf_0.05_geno_0.1.vcf.gz')) {
  download.file('https://research-repository.uwa.edu.au/files/89232545/SNPs_lee.id.biallic_maf_0.05_geno_0.1.vcf.gz', 'data/SNPs_lee.id.biallic_maf_0.05_geno_0.1.vcf.gz')
}

#We have to convert the big vcf file

if (!file.exists("data/snp.gds")) {
  vcf.fn <- 'data/SNPs_lee.id.biallic_maf_0.05_geno_0.1.vcf.gz'
  snpgdsVCF2GDS(vcf.fn, "data/snp.gds", method="biallelic.only")
}

genofile <- snpgdsOpen('data/snp.gds')

# Let's prune the SNPs based on 0.2 LD

snpset <- snpgdsLDpruning(genofile, ld.threshold=0.2, autosome.only=F)
snpset.id <- unlist(unname(snpset))

# And now let's run the PCA
pca <- snpgdsPCA(genofile, snp.id=snpset.id, num.thread=2, autosome.only=F)

saveRDS(pca, 'data/pca.rds')

OK let’s load the results I made on the remote server and saved in a file:

# load PCA
pca <- readRDS('data/pca.rds')

A quick diagnostic plot

tab <- data.frame(sample.id = pca$sample.id,
    EV1 = pca$eigenvect[,1],    # the first eigenvector
    EV2 = pca$eigenvect[,2],    # the second eigenvector
    stringsAsFactors = FALSE)
plot(tab$EV2, tab$EV1, xlab="eigenvector 2", ylab="eigenvector 1")

head(tab)
  sample.id         EV1          EV2
1     AB-01 -0.03587935  0.008552839
2     AB-02 -0.03681818  0.010897831
3     BR-01 -0.01975551 -0.016854610
4     BR-02 -0.01651350 -0.015271782
5     BR-03 -0.01702049 -0.018778840
6     BR-04 -0.01639033 -0.021407320

Alright, now we have SNP-based principal components. We’ll use the first two as our own covariates in GAPIT.

I wrote a Python script which takes the NLR-only PAV table and turns that into HapMap format with fake SNPs, see code/transformToGAPIT.py.

myY <- read.table('data/yield.txt', head = TRUE)
myGD <- read.table('data/NLR_PAV_GD.txt', head = TRUE)
myGM <- read.table('data/NLR_PAV_GM.txt', head = TRUE)

GAPIT prints a LOT of stuff so I turn that off here, what’s important are all the output files.

myGAPIT <- GAPIT(
  Y=myY[,c(1,2)],
  CV = tab,
  GD = myGD,
  GM = myGM,
  PCA.total = 0, # turn off PCA calculation as I use my own based on SNPs
  model = c('GLM', 'MLM', 'MLMM', 'FarmCPU')
)
if (! dir.exists('output/GAPIT')){
  dir.create('output/GAPIT')
}

R doesn’t have an in-built function to move files, so I copy and delete the output files here. There’s a package which adds file-moving but I’m not adding a whole dependency just for one convenience function, I’m not a Node.js person ;)

for(file in list.files('.', pattern='GAPIT*')) {
  file.copy(file, 'output/GAPIT')
  file.remove(file)
}

Let’s make a table of the statistically significantly associated SNPs.

results_files <- list.files('output/GAPIT/', pattern='*GWAS.Results.csv', full.names = T)

Let’s use FDR < 0.05 as cutoff

results_df <- NULL
for(i in seq_along(results_files)) {
  this_df <- read_csv(results_files[i])
  filt_df <- this_df %>% filter(`FDR_Adjusted_P-values` < 0.05)
  
  # pull the method name out and add to dataframe
  this_method <- str_split(results_files[i], "\\.")[[1]][2]
  filt_df <- filt_df %>% add_column(Method = this_method, .before = 'SNP')
  if (is.null(results_df)) {
    results_df <- filt_df
  } else {
    results_df <- rbind(results_df, filt_df)
  }
}
Parsed with column specification:
cols(
  SNP = col_character(),
  Chromosome = col_double(),
  Position = col_double(),
  P.value = col_double(),
  maf = col_double(),
  nobs = col_double(),
  Rsquare.of.Model.without.SNP = col_logical(),
  Rsquare.of.Model.with.SNP = col_logical(),
  `FDR_Adjusted_P-values` = col_double(),
  effect = col_double()
)
Parsed with column specification:
cols(
  SNP = col_character(),
  Chromosome = col_double(),
  Position = col_double(),
  P.value = col_double(),
  maf = col_double(),
  nobs = col_double(),
  Rsquare.of.Model.without.SNP = col_double(),
  Rsquare.of.Model.with.SNP = col_double(),
  `FDR_Adjusted_P-values` = col_double(),
  effect = col_double()
)
Parsed with column specification:
cols(
  SNP = col_character(),
  Chromosome = col_double(),
  Position = col_double(),
  P.value = col_double(),
  maf = col_double(),
  nobs = col_double(),
  Rsquare.of.Model.without.SNP = col_double(),
  Rsquare.of.Model.with.SNP = col_double(),
  `FDR_Adjusted_P-values` = col_double(),
  effect = col_double()
)
Parsed with column specification:
cols(
  SNP = col_character(),
  Chromosome = col_double(),
  Position = col_double(),
  P.value = col_double(),
  maf = col_double(),
  nobs = col_double(),
  Rsquare.of.Model.without.SNP = col_logical(),
  Rsquare.of.Model.with.SNP = col_logical(),
  `FDR_Adjusted_P-values` = col_double(),
  effect = col_logical()
)
results_df %>% knitr::kable()
Method SNP Chromosome Position P.value maf nobs Rsquare.of.Model.without.SNP Rsquare.of.Model.with.SNP FDR_Adjusted_P-values effect
FarmCPU GlymaLee.02G228600.1.p 2 49198872 0.0000038 0.0013004 769 NA NA 0.0018691 -1.7185122
FarmCPU UWASoyPan04354 22 277 0.0000373 0.1040312 769 NA NA 0.0090673 0.1505357
FarmCPU UWASoyPan00316 22 405 0.0000813 0.1235371 769 NA NA 0.0131697 -0.1361126
FarmCPU GlymaLee.01G030900.1.p 1 3567950 0.0001897 0.4928479 769 NA NA 0.0230510 0.0837741
FarmCPU UWASoyPan00772 22 326 0.0002724 0.1976593 769 NA NA 0.0264748 0.1073770
FarmCPU GlymaLee.14G022000.1.p 14 1789365 0.0004215 0.2236671 769 NA NA 0.0341436 -0.0953602
GLM GlymaLee.02G228600.1.p 2 49198872 0.0000000 0.0013004 769 0.3795503 0.4064602 0.0000058 -1.9354957
GLM UWASoyPan04354 22 277 0.0000150 0.1040312 769 0.3795503 0.3949224 0.0036512 0.1706430
GLM UWASoyPan00772 22 326 0.0000315 0.1976593 769 0.3795503 0.3937506 0.0051105 0.1291152
GLM UWASoyPan00316 22 405 0.0000446 0.1235371 769 0.3795503 0.3932066 0.0054160 -0.1498671
GLM GlymaLee.16G111300.1.p 16 30996392 0.0001209 0.0676203 769 0.3795503 0.3916447 0.0117547 0.1830838
GLM UWASoyPan00022 22 958 0.0003783 0.0364109 769 0.3795503 0.3898773 0.0267416 0.2285028
GLM GlymaLee.01G030900.1.p 1 3567950 0.0003852 0.4928479 769 0.3795503 0.3898498 0.0267416 0.0861666
MLM GlymaLee.02G228600.1.p 2 49198872 0.0000005 0.0013004 769 0.4220320 0.4413330 0.0002584 -1.6924714
MLMM GlymaLee.02G228600.1.p 2 49198872 0.0000003 0.0013004 769 NA NA 0.0001373 NA

Ah beautiful, one NLR gene found by all methods, and a bunch of extra pangenome genes found by FarmCPU/GLM. However the one gene found by all methods has a horrible MAF so we’ll probably end up ignoring that.

results_df %>% group_by(SNP) %>% count() %>% arrange(n)
# A tibble: 8 x 2
# Groups:   SNP [8]
  SNP                        n
  <chr>                  <int>
1 GlymaLee.14G022000.1.p     1
2 GlymaLee.16G111300.1.p     1
3 UWASoyPan00022             1
4 GlymaLee.01G030900.1.p     2
5 UWASoyPan00316             2
6 UWASoyPan00772             2
7 UWASoyPan04354             2
8 GlymaLee.02G228600.1.p     4
candidates <- results_df %>% 
  group_by(SNP) %>% 
  count() %>% 
  filter(n >= 2)

candidates %>% knitr::kable()
SNP n
GlymaLee.01G030900.1.p 2
GlymaLee.02G228600.1.p 4
UWASoyPan00316 2
UWASoyPan00772 2
UWASoyPan04354 2

Let’s focus on genes found by more than one method.

This particular R-gene GlymaLee.02G228600.1.p seems to have a strong negative impact on yield (effect -1.69 in MLM, -1.94 in GLM, -1.72 in FarmCPU) but it also has a horrible MAF, normally this would get filtered in SNPs but we don’t have SNPs here. Let’s plot the yield for individuals who have vs those who don’t have those genes that appear in more than one method.

pav_table <- read_tsv('./data/soybean_pan_pav.matrix_gene.txt.gz')
Parsed with column specification:
cols(
  .default = col_double(),
  Individual = col_character()
)
See spec(...) for full column specifications.
yield <- read_tsv('./data/yield.txt')
Parsed with column specification:
cols(
  Line = col_character(),
  Yield = col_double()
)
pav_table %>% 
  filter(Individual == 'GlymaLee.02G228600.1.p') %>% 
  pivot_longer(!Individual, names_to = 'Line', values_to = 'Presence') %>% 
  inner_join(yield) %>% arrange(Presence) %>% head()
Joining, by = "Line"
# A tibble: 6 x 4
  Individual             Line    Presence Yield
  <chr>                  <chr>      <dbl> <dbl>
1 GlymaLee.02G228600.1.p USB-762        0  2.88
2 GlymaLee.02G228600.1.p AB-01          1  1.54
3 GlymaLee.02G228600.1.p AB-02          1  1.3 
4 GlymaLee.02G228600.1.p For            1  3.34
5 GlymaLee.02G228600.1.p HN001          1  3.54
6 GlymaLee.02G228600.1.p HN005          1  2.15

OK this gene is ‘boring’ - it’s lost only in a single line, and we can’t trust that. We’ll remove it.

pav_table %>% 
  filter(Individual == 'GlymaLee.02G228600.1.p') %>% 
  pivot_longer(!Individual, names_to = 'Line', values_to = 'Presence') %>% 
  inner_join(yield) %>% 
  summarise(median_y= median(Yield))
Joining, by = "Line"
# A tibble: 1 x 1
  median_y
     <dbl>
1     2.18

At least this particular line with the lost gene has slightly higher yield than the median? but soooo many different reasons… Let’s remove this gene as MAF < 5%.

Let’s check the other genes.

candidates <- candidates %>% 
  filter(SNP != 'GlymaLee.02G228600.1.p')
candidates %>% knitr::kable()
SNP n
GlymaLee.01G030900.1.p 2
UWASoyPan00316 2
UWASoyPan00772 2
UWASoyPan04354 2 
plots <- list()
for(i in 1:nrow(candidates)) {
  this_cand = candidates[i,]
  p <- pav_table %>% 
    filter(Individual == this_cand$SNP) %>% 
    pivot_longer(!Individual, names_to = 'Line', values_to = 'Presence') %>% 
    inner_join(yield) %>% 
    mutate(Presence = case_when(
      Presence == 0.0 ~ 'Lost',
      Presence == 1.0 ~ 'Present'
    )) %>% 
    ggplot(aes(x=Presence, y = Yield, group=Presence)) + 
    geom_boxplot() + 
    geom_jitter(alpha=0.9, size=0.4) + 
    geom_signif(comparisons = list(c('Lost', 'Present')), 
              map_signif_level = T) +
    theme_minimal_hgrid()
    #xlab(paste('Presence', str_replace(this_cand$SNP, '.1.p',''))) # make the gene name a bit nicer
  plots[[i]] <- p
}
Joining, by = "Line"
Joining, by = "Line"
Joining, by = "Line"
Joining, by = "Line"
wrap_plots(plots) + 
  plot_annotation(tag_levels = 'A')

Four nice plots we have now, we’ll use those as supplementary. It’s interesting how the reference gene has a positive impact on yield, the pangenome extra gene has a negative impact, and the other two don’t do much. Then again there are many reasons why we see this outcome.

For myself, the four labels: GlymaLee.01G030900.1.p, UWASoyPan00316, UWASoyPan00772, UWASoyPan04354

Let’s also make those plots, grouped by breeding group

groups <- read_csv('./data/Table_of_cultivar_groups.csv')
Parsed with column specification:
cols(
  `Data-storage-ID` = col_character(),
  `PI-ID` = col_character(),
  `Group in violin table` = col_character()
)
groups <- groups %>% dplyr::rename(Group = `Group in violin table`)
groups <- groups %>% 
  mutate(Group = str_replace_all(Group, 'landrace', 'Landrace')) %>%
  mutate(Group = str_replace_all(Group, 'Old_cultivar', 'Old cultivar')) %>%
  mutate(Group = str_replace_all(Group, 'Modern_cultivar', 'Modern cultivar')) %>%
  mutate(Group = str_replace_all(Group, 'Wild-type', 'Wild'))

groups$Group <-
  factor(
    groups$Group,
    levels = c('Wild',
               'Landrace',
               'Old cultivar',
               'Modern cultivar')
  )
npg_col = pal_npg("nrc")(9)

col_list <- c(`Wild`=npg_col[8],
   Landrace = npg_col[3],
  `Old cultivar`=npg_col[2],
  `Modern cultivar`=npg_col[4])


plots <- list()
for(i in 1:nrow(candidates)) {
  this_cand = candidates[i,]
  p <- pav_table %>% 
    filter(Individual == this_cand$SNP) %>% 
    pivot_longer(!Individual, names_to = 'Line', values_to = 'Presence') %>% 
    inner_join(yield) %>% 
    inner_join(groups, by = c('Line'='Data-storage-ID')) %>% 
    mutate(Presence = case_when(
      Presence == 0.0 ~ 'Lost',
      Presence == 1.0 ~ 'Present'
    )) %>% 
    ggplot(aes(x=Presence, y = Yield, group=Presence, color=Group)) + 
    geom_boxplot() + 
    geom_jitter(alpha=0.9, size=0.4) + 
    facet_wrap(~Group) +
    geom_signif(comparisons = list(c('Lost', 'Present')), 
              map_signif_level = T) +
    theme_minimal_hgrid() +
    ylab(expression(paste('Yield [Mg ', ha ^ -1, ']'))) +
    scale_color_manual(values = col_list)

  plots[[i]] <- p
}
Joining, by = "Line"
Joining, by = "Line"
Joining, by = "Line"
Joining, by = "Line"
wrap_plots(plots) + 
  plot_annotation(tag_levels = 'A') +
  plot_layout(guides='collect') & theme(legend.position = 'none')
Warning in wilcox.test.default(c(2.19, 2.6, 2.74, 1.63, 1.61, 2.45, 1.21, :
cannot compute exact p-value with ties
Warning in wilcox.test.default(c(4, 2.66, 1.52, 2.47, 4.34, 2.21, 3.23, : cannot
compute exact p-value with ties
Warning in wilcox.test.default(c(2.66, 1.54, 2.21, 0.77, 2.84, 2.51, 0.89:
cannot compute exact p-value with ties
Warning in wilcox.test.default(c(4.38, 4.16, 4, 4.48, 4.12, 3.24, 2.59, : cannot
compute exact p-value with ties
Warning in wilcox.test.default(c(2.19, 2.6, 2.74, 1.63, 2.88, 2.29, 2.17, :
cannot compute exact p-value with ties
Warning in wilcox.test.default(c(3.54, 4.38, 4.16, 4.05, 4.06, 2.75, 4.27, :
cannot compute exact p-value with ties
Warning in wilcox.test.default(c(2.19, 2.66, 2.6, 2.74, 1.63, 1.61, 1.21, :
cannot compute exact p-value with ties

I also need a presence/absence percentage for all candidates

big_t <- NULL
for(i in 1:nrow(candidates)) {
  this_cand = candidates[i,]
  t <- pav_table %>% 
    filter(Individual == this_cand$SNP) %>% 
    pivot_longer(!Individual, names_to = 'Line', values_to = 'Presence') %>%
    inner_join(groups, by = c('Line'='Data-storage-ID')) %>% group_by(Group) %>% 
    dplyr::select(Presence, Group) %>% 
    table() %>% as_tibble()
  #t <- t %>% add_column(Presence=c(0,1), .before = '.')
  t<- t %>% add_column(Gene=this_cand$SNP, .before='Presence')
  if(is.null(big_t)) {
    big_t <- t
  } else {
    big_t <- rbind(big_t, t)
  }
}

big_t %>% group_by(Group, Gene) %>% mutate(group_sum = sum(n)) %>% 
  mutate(`Percentage` = n/group_sum*100) %>% 
  dplyr::select(-group_sum) %>% 
  rename(Count=n) %>% 
  mutate(Presence = case_when(
      Presence == 0.0 ~ 'Lost',
      Presence == 1.0 ~ 'Present'
    ))  %>%
  knitr::kable(digits=2)
Gene Presence Group Count Percentage
GlymaLee.01G030900.1.p Lost Wild 29 18.47
GlymaLee.01G030900.1.p Present Wild 128 81.53
GlymaLee.01G030900.1.p Lost Landrace 359 49.65
GlymaLee.01G030900.1.p Present Landrace 364 50.35
GlymaLee.01G030900.1.p Lost Old cultivar 30 65.22
GlymaLee.01G030900.1.p Present Old cultivar 16 34.78
GlymaLee.01G030900.1.p Lost Modern cultivar 41 28.67
GlymaLee.01G030900.1.p Present Modern cultivar 102 71.33
UWASoyPan00316 Lost Wild 14 8.92
UWASoyPan00316 Present Wild 143 91.08
UWASoyPan00316 Lost Landrace 68 9.41
UWASoyPan00316 Present Landrace 655 90.59
UWASoyPan00316 Lost Old cultivar 9 19.57
UWASoyPan00316 Present Old cultivar 37 80.43
UWASoyPan00316 Lost Modern cultivar 71 49.65
UWASoyPan00316 Present Modern cultivar 72 50.35
UWASoyPan00772 Lost Wild 71 45.22
UWASoyPan00772 Present Wild 86 54.78
UWASoyPan00772 Lost Landrace 586 81.05
UWASoyPan00772 Present Landrace 137 18.95
UWASoyPan00772 Lost Old cultivar 32 69.57
UWASoyPan00772 Present Old cultivar 14 30.43
UWASoyPan00772 Lost Modern cultivar 126 88.11
UWASoyPan00772 Present Modern cultivar 17 11.89
UWASoyPan04354 Lost Wild 87 55.41
UWASoyPan04354 Present Wild 70 44.59
UWASoyPan04354 Lost Landrace 636 87.97
UWASoyPan04354 Present Landrace 87 12.03
UWASoyPan04354 Lost Old cultivar 44 95.65
UWASoyPan04354 Present Old cultivar 2 4.35
UWASoyPan04354 Lost Modern cultivar 141 98.60
UWASoyPan04354 Present Modern cultivar 2 1.40 
big_t %>% group_by(Group, Gene) %>% mutate(group_sum = sum(n)) %>%
  mutate(Gene = str_replace_all(Gene, '.1.p','')) %>% 
  mutate(`Percentage` = n/group_sum*100) %>% 
  dplyr::select(-group_sum) %>% 
  filter(Presence == '1') %>% 
  mutate(Group = factor(Group, levels=c('Wild', 'Landrace', 'Old cultivar', 'Modern cultivar'))) %>% 
  ggplot(aes(x = Group, y = Percentage, group=Gene, color=Gene)) + 
  geom_line(size=1.5) +
  theme_minimal_hgrid() +
  ylab('Percentage present') +
  scale_color_brewer(palette = 'Dark2')

and let’s also get the per-gene mean and median yield

yields <- NULL
for(i in 1:nrow(candidates)) {
  this_cand = candidates[i,]
  this_t <- pav_table %>% 
    filter(Individual == this_cand$SNP) %>% 
    pivot_longer(!Individual, names_to = 'Line', values_to = 'Presence') %>% 
    inner_join(yield) %>%
    inner_join(groups, by = c('Line'='Data-storage-ID')) %>% 
    group_by(Presence, Group) %>% 
    summarise(`Mean yield` = mean(Yield)) %>% 
    add_column(Gene=this_cand$SNP, .before='Presence') %>% 
    arrange(Group)
  if (is.null(yields)) {
    yields <- this_t
  } else {
    yields <- rbind(yields, this_t)
  }
}
Joining, by = "Line"
`summarise()` regrouping output by 'Presence' (override with `.groups` argument)
Joining, by = "Line"
`summarise()` regrouping output by 'Presence' (override with `.groups` argument)
Joining, by = "Line"
`summarise()` regrouping output by 'Presence' (override with `.groups` argument)
Joining, by = "Line"
`summarise()` regrouping output by 'Presence' (override with `.groups` argument)
yields %>% knitr::kable(digits=2)
Gene Presence Group Mean yield
GlymaLee.01G030900.1.p 0 Landrace 2.00
GlymaLee.01G030900.1.p 1 Landrace 2.22
GlymaLee.01G030900.1.p 0 Old cultivar 1.73
GlymaLee.01G030900.1.p 1 Old cultivar 2.27
GlymaLee.01G030900.1.p 0 Modern cultivar 3.06
GlymaLee.01G030900.1.p 1 Modern cultivar 3.28
UWASoyPan00316 0 Landrace 2.29
UWASoyPan00316 1 Landrace 2.09
UWASoyPan00316 0 Old cultivar 1.92
UWASoyPan00316 1 Old cultivar 1.90
UWASoyPan00316 0 Modern cultivar 3.42
UWASoyPan00316 1 Modern cultivar 3.06
UWASoyPan00772 0 Landrace 2.06
UWASoyPan00772 1 Landrace 2.30
UWASoyPan00772 0 Old cultivar 1.97
UWASoyPan00772 1 Old cultivar 1.74
UWASoyPan00772 0 Modern cultivar 3.27
UWASoyPan00772 1 Modern cultivar 2.89
UWASoyPan04354 0 Landrace 2.09
UWASoyPan04354 1 Landrace 2.24
UWASoyPan04354 0 Old cultivar 1.88
UWASoyPan04354 1 Old cultivar 2.31
UWASoyPan04354 0 Modern cultivar 3.20
UWASoyPan04354 1 Modern cultivar 4.34 
yields %>% 
  group_by(Gene, Group) %>% 
  summarise('Yield difference when gene present' = diff(`Mean yield`)) %>% 
  knitr::kable(digits=2)
`summarise()` regrouping output by 'Gene' (override with `.groups` argument)
Gene Group Yield difference when gene present
GlymaLee.01G030900.1.p Landrace 0.21
GlymaLee.01G030900.1.p Old cultivar 0.54
GlymaLee.01G030900.1.p Modern cultivar 0.22
UWASoyPan00316 Landrace -0.20
UWASoyPan00316 Old cultivar -0.01
UWASoyPan00316 Modern cultivar -0.36
UWASoyPan00772 Landrace 0.24
UWASoyPan00772 Old cultivar -0.23
UWASoyPan00772 Modern cultivar -0.39
UWASoyPan04354 Landrace 0.15
UWASoyPan04354 Old cultivar 0.43
UWASoyPan04354 Modern cultivar 1.14 

sessionInfo()
R version 3.6.3 (2020-02-29)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 17134)

Matrix products: default

locale:
[1] LC_COLLATE=English_Australia.1252  LC_CTYPE=English_Australia.1252   
[3] LC_MONETARY=English_Australia.1252 LC_NUMERIC=C                      
[5] LC_TIME=English_Australia.1252    

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

other attached packages:
 [1] biganalytics_1.1.21  biglm_0.9-2          DBI_1.1.0           
 [4] foreach_1.4.8        bigmemory_4.5.36     scatterplot3d_0.3-41
 [7] EMMREML_3.1          Matrix_1.2-18        ape_5.3             
[10] genetics_1.3.8.1.2   mvtnorm_1.1-1        MASS_7.3-51.6       
[13] gtools_3.8.1         gdata_2.18.0         combinat_0.0-8      
[16] LDheatmap_0.99-8     gplots_3.0.3         multtest_2.42.0     
[19] Biobase_2.46.0       BiocGenerics_0.32.0  patchwork_1.0.0     
[22] ggsci_2.9            cowplot_1.0.0        ggsignif_0.6.0      
[25] forcats_0.5.0        stringr_1.4.0        dplyr_1.0.0         
[28] purrr_0.3.4          readr_1.3.1          tidyr_1.1.0         
[31] tibble_3.0.2         ggplot2_3.3.2        tidyverse_1.3.0     
[34] SNPRelate_1.20.1     gdsfmt_1.22.0        GAPIT3_3.1.0        
[37] workflowr_1.6.2.9000

loaded via a namespace (and not attached):
 [1] bigmemory.sri_0.1.3 colorspace_1.4-1    ellipsis_0.3.1     
 [4] rprojroot_1.3-2     fs_1.5.0.9000       rstudioapi_0.11    
 [7] farver_2.0.3        fansi_0.4.1         lubridate_1.7.9    
[10] xml2_1.3.2          codetools_0.2-16    splines_3.6.3      
[13] knitr_1.29          jsonlite_1.7.1      broom_0.5.6        
[16] dbplyr_1.4.4        httr_1.4.2          backports_1.1.10   
[19] assertthat_0.2.1    cli_2.0.2           later_1.1.0.1      
[22] htmltools_0.5.0     tools_3.6.3         gtable_0.3.0       
[25] glue_1.4.2          Rcpp_1.0.5          cellranger_1.1.0   
[28] vctrs_0.3.1         nlme_3.1-148        iterators_1.0.12   
[31] xfun_0.17           ps_1.3.4            rvest_0.3.5        
[34] lifecycle_0.2.0     getPass_0.2-2       scales_1.1.1       
[37] hms_0.5.3           promises_1.1.1      RColorBrewer_1.1-2 
[40] yaml_2.2.1          stringi_1.5.3       highr_0.8          
[43] caTools_1.18.0      rlang_0.4.7         pkgconfig_2.0.3    
[46] bitops_1.0-6        evaluate_0.14       lattice_0.20-41    
[49] labeling_0.3        processx_3.4.4      tidyselect_1.1.0   
[52] magrittr_1.5        R6_2.4.1            generics_0.0.2     
[55] pillar_1.4.4        haven_2.3.1         whisker_0.4        
[58] withr_2.2.0         survival_3.2-3      modelr_0.1.8       
[61] crayon_1.3.4        KernSmooth_2.23-17  utf8_1.1.4         
[64] rmarkdown_2.3       grid_3.6.3          readxl_1.3.1       
[67] blob_1.2.1          callr_3.4.4         git2r_0.27.1       
[70] reprex_0.3.0        digest_0.6.25       httpuv_1.5.4       
[73] stats4_3.6.3        munsell_0.5.0