Introduction

The goal of this script is to analyze the genotypes of the individuals in the

# Load library

library(ggplot2)

Warning: package 'ggplot2' was built under R version 3.4.4

library(cowplot)

Warning: package 'cowplot' was built under R version 3.4.4

Attaching package: 'cowplot'

The following object is masked from 'package:ggplot2':

    ggsave

# Load the PC genotype data

usa2.pcawithref.menv <- read.table("../data/usa2.pcawithref.menv.mds_cov", stringsAsFactors = FALSE, header = TRUE)

# Reformat cells

test <- t(unlist(strsplit(as.character(usa2.pcawithref.menv[1,]), " ")))

reformat_array <- array(NA, dim = c(nrow(usa2.pcawithref.menv),28))

for (i in 1:nrow(usa2.pcawithref.menv)){

reformat_array[i,] <- t(unlist(strsplit(as.character(usa2.pcawithref.menv[i,]), " ")))
}

colnames(reformat_array) <- c("FID", "IID", "SOL", "C1", "C2", "C3", "C4", "C5", "C6", "C7", "C8", "C9", "C10", "C11", "C12", "C13", "C14", "C15", "C16", "C17", "C18", "C19", "C20", "st1", "st2", "st3", "st4", "st5")

reformat_array <- as.data.frame(reformat_array, stringsAsFactors = FALSE)

# BAN to genotype ids

Ban_geno <- read.csv("../data/Ban_geno.csv")
Ban_geno <- Ban_geno[,1:3]

link <- merge(reformat_array, Ban_geno, by.x = c("IID"), by.y = c("External_code"))

Genotype PCs

# Initial plot
plot(link$C1, link$C2)

# Reorder by BAN_ID

order_link <- link[order(link$BAN_ID),] 

# Integrate with race/ethnicity

clinical_info <- read.csv("../data/clinical_sample_info_geno.csv")

race_eth <- cbind(clinical_info$BAN_ID, clinical_info$Race, clinical_info$Ethnicity)

dedup <- race_eth[!duplicated(race_eth),]
colnames(dedup) <- c("BAN_ID", "Race", "Ethnicity")

# Combine PCs and Race/Ethnicity

pcs_race <- merge(order_link, dedup, by = c("BAN_ID"))

# Plot Race
summary(pcs_race$Race)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  2.000   2.000   2.000   2.121   2.000   5.000 

pcs_race$C1 <- as.numeric(pcs_race$C1)
pcs_race$C2 <- as.numeric(pcs_race$C2)
pcs_race$Race <- as.factor(pcs_race$Race)

race_plot <- ggplot(pcs_race, aes(C1, C2, color = Race)) + geom_point(aes(color = pcs_race$Race)) + xlab("PC1") + ylab("PC2") + scale_color_discrete(name = c("Race"), labels = c("White", "Black", "Asian")) 

plot_grid(race_plot)

#save_plot("/Users/laurenblake/Dropbox/Lauren Blake/Figures/PCA_genotype_33.png", race_plot,
#          base_aspect_ratio = 1)

# Plot Ethnicity

summary(pcs_race$Ethnicity)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  1.000   2.000   2.000   1.939   2.000   2.000 

race_ethnicity <- ggplot(pcs_race, aes(as.numeric(C1), as.numeric(C2))) + geom_point(color = as.factor(pcs_race$Ethnicity))

plot_grid(race_ethnicity)

Do genotype PCs correlate with gene expression PCs?

# Load individuals

inds <- read.csv("../data/lm_covar_fixed_random.csv")


# Load gene expression data from all 156 samples

normalized_data <- read.csv("../data/gene_expression_filtered_T1T5.csv")

# Run PCA on the normalized data

pca_genes <- prcomp(t(normalized_data[,2:157]), scale = TRUE, center = TRUE)

matrixpca <- pca_genes$x
PC1 <- matrixpca[,1]
PC2 <- matrixpca[,2]
pc3 <- matrixpca[,3]
pc4 <- matrixpca[,4]
pc5 <- matrixpca[,5]

matrixpca <- as.data.frame(matrixpca)

ggplot(matrixpca, aes(PC1, PC2)) + geom_point(color = as.factor(inds$Race))

# Merge

pcs_gene <- merge(inds, pcs_race, by.x = c("Individual"), by.y = c("BAN_ID"), all.x = TRUE)

#write.csv(pcs_gene, file = "../data/pcs_genes.csv")

# Genotype PCs and gene expression PCs

# Genotype PCs- inds PC1, PC2, pc3, pc4, pc5

geno_pcs <- cbind(pcs_gene$C1, pcs_gene$C2, pcs_gene$C3, pcs_gene$C4, pcs_gene$C5)

# Gene expression PCs PC1, PC2, pc3, pc4, pc5

exp_pcs <- matrixpca

# Look at the correlation between genotype and gene expression PCs 

PC_pvalues <- matrix(data = NA, nrow = 5, ncol = 5)
PC_r2 <- matrix(data = NA, nrow = 5, ncol = 5)

j=1
for (i in 1:5){
  for (j in 1:5){
  
  checkPC1 <- lm(exp_pcs[,j] ~ geno_pcs[,i])

#Get the summary statistics from it
  summary(checkPC1)

#Get the p-value of the F-statistic
  summary(checkPC1)$fstatistic

  fstat <- as.data.frame(summary(checkPC1)$fstatistic)
  p_fstat <- 1-pf(fstat[1,], fstat[2,], fstat[3,])
  
#Fraction of the variance explained by the model
  r2_value <- summary(checkPC1)$r.squared

#Put the summary statistics into the matrix w

  PC_pvalues[j, i] <- p_fstat
  PC_r2[j, i] <- sqrt(r2_value)
  
  }

}

PC_pvalues

          [,1]      [,2]      [,3]      [,4]       [,5]
[1,] 0.7284291 0.8718604 0.9758057 0.6688093 0.44217602
[2,] 0.5334731 0.3182166 0.6805427 0.7026873 0.54787400
[3,] 0.7640570 0.7281449 0.7094446 0.9547397 0.68724443
[4,] 0.6279917 0.3637570 0.1395446 0.3894734 0.12304434
[5,] 0.2668212 0.2760426 0.0537522 0.1497131 0.04555031

PC_r2

          [,1]      [,2]      [,3]      [,4]      [,5]
[1,] 0.3747362 0.3395651 0.3122323 0.4380801 0.5642826
[2,] 0.4101985 0.4481101 0.4107386 0.4317606 0.5477315
[3,] 0.3672563 0.3747938 0.4052225 0.3558263 0.5246404
[4,] 0.3937424 0.4396422 0.5145687 0.4855540 0.6259618
[5,] 0.4583122 0.4564179 0.5492556 0.5352130 0.6569248

# 

summary(lm(exp_pcs$PC1 ~ as.factor(inds$Individual)))

Call:
lm(formula = exp_pcs$PC1 ~ as.factor(inds$Individual))

Residuals:
     Min       1Q   Median       3Q      Max 
-105.572  -25.606    0.263   29.322   82.106 

Coefficients:
                               Estimate Std. Error t value Pr(>|t|)  
(Intercept)                    -19.3616    28.7645  -0.673   0.5024  
as.factor(inds$Individual)2202  13.3167    36.3846   0.366   0.7151  
as.factor(inds$Individual)2203  89.9787    45.4807   1.978   0.0506 .
as.factor(inds$Individual)2204  22.3070    40.6792   0.548   0.5847  
as.factor(inds$Individual)2205  92.5553    45.4807   2.035   0.0445 *
as.factor(inds$Individual)2206 101.6186    40.6792   2.498   0.0141 *
as.factor(inds$Individual)2207  64.4914    40.6792   1.585   0.1160  
as.factor(inds$Individual)2208  19.5135    40.6792   0.480   0.6325  
as.factor(inds$Individual)2209   1.0985    36.3846   0.030   0.9760  
as.factor(inds$Individual)2210  39.7511    40.6792   0.977   0.3308  
as.factor(inds$Individual)2212  67.0229    45.4807   1.474   0.1437  
as.factor(inds$Individual)2215   0.0947    40.6792   0.002   0.9981  
as.factor(inds$Individual)2216  49.5588    40.6792   1.218   0.2260  
as.factor(inds$Individual)2218   8.7791    36.3846   0.241   0.8098  
as.factor(inds$Individual)2219  30.9841    40.6792   0.762   0.4480  
as.factor(inds$Individual)2220 -13.4357    36.3846  -0.369   0.7127  
as.factor(inds$Individual)2221   1.7413    40.6792   0.043   0.9659  
as.factor(inds$Individual)2222  46.4545    45.4807   1.021   0.3095  
as.factor(inds$Individual)2224  28.9250    40.6792   0.711   0.4787  
as.factor(inds$Individual)2226  -8.7533    36.3846  -0.241   0.8104  
as.factor(inds$Individual)2228   2.4691    36.3846   0.068   0.9460  
as.factor(inds$Individual)2229 -20.3303    45.4807  -0.447   0.6558  
as.factor(inds$Individual)2232 -29.3737    40.6792  -0.722   0.4719  
as.factor(inds$Individual)2233  31.1382    40.6792   0.765   0.4458  
as.factor(inds$Individual)2234  34.1855    40.6792   0.840   0.4027  
as.factor(inds$Individual)2235  64.7807    40.6792   1.592   0.1144  
as.factor(inds$Individual)2236  33.9494    45.4807   0.746   0.4571  
as.factor(inds$Individual)2239  42.2090    40.6792   1.038   0.3019  
as.factor(inds$Individual)2240  21.1739    45.4807   0.466   0.6425  
as.factor(inds$Individual)2242  -8.9251    40.6792  -0.219   0.8268  
as.factor(inds$Individual)2243 -39.8009    40.6792  -0.978   0.3302  
as.factor(inds$Individual)2245  22.4821    45.4807   0.494   0.6222  
as.factor(inds$Individual)2247   5.2058    45.4807   0.114   0.9091  
as.factor(inds$Individual)2248  31.6231    40.6792   0.777   0.4388  
as.factor(inds$Individual)2249 -23.7633    45.4807  -0.522   0.6025  
as.factor(inds$Individual)2250 -18.4777    45.4807  -0.406   0.6854  
as.factor(inds$Individual)2251   4.4844    45.4807   0.099   0.9217  
as.factor(inds$Individual)2252 -48.3774    45.4807  -1.064   0.2900  
as.factor(inds$Individual)2253  46.4340    45.4807   1.021   0.3097  
as.factor(inds$Individual)2254  58.5507    40.6792   1.439   0.1531  
as.factor(inds$Individual)2255  62.8194    45.4807   1.381   0.1703  
as.factor(inds$Individual)2256  -3.9874    40.6792  -0.098   0.9221  
as.factor(inds$Individual)2257 -34.4837    45.4807  -0.758   0.4501  
as.factor(inds$Individual)2258  24.9128    40.6792   0.612   0.5416  
as.factor(inds$Individual)2260  18.8908    40.6792   0.464   0.6434  
as.factor(inds$Individual)2261  46.9656    45.4807   1.033   0.3042  
as.factor(inds$Individual)2262   4.7721    45.4807   0.105   0.9166  
as.factor(inds$Individual)2266  23.1074    40.6792   0.568   0.5713  
as.factor(inds$Individual)2267  13.4927    45.4807   0.297   0.7673  
as.factor(inds$Individual)2268  38.2483    40.6792   0.940   0.3493  
as.factor(inds$Individual)2269  -7.0156    45.4807  -0.154   0.8777  
as.factor(inds$Individual)2270 -38.0309    45.4807  -0.836   0.4050  
as.factor(inds$Individual)2271  16.0481    40.6792   0.395   0.6940  
as.factor(inds$Individual)2272   4.4790    40.6792   0.110   0.9125  
as.factor(inds$Individual)2274  91.0681    40.6792   2.239   0.0274 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 49.82 on 101 degrees of freedom
Multiple R-squared:  0.4016,    Adjusted R-squared:  0.08168 
F-statistic: 1.255 on 54 and 101 DF,  p-value: 0.1624

summary(lm(exp_pcs$PC1 ~ as.factor(inds$Race)))

Call:
lm(formula = exp_pcs$PC1 ~ as.factor(inds$Race))

Residuals:
     Min       1Q   Median       3Q      Max 
-122.346  -35.217    0.932   34.715  124.450 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)   
(Intercept)             -2.289      4.183  -0.547  0.58503   
as.factor(inds$Race)3   84.546     29.676   2.849  0.00499 **
as.factor(inds$Race)5   20.687     23.139   0.894  0.37269   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 50.89 on 153 degrees of freedom
Multiple R-squared:  0.05434,   Adjusted R-squared:  0.04198 
F-statistic: 4.396 on 2 and 153 DF,  p-value: 0.01392

summary(lm(exp_pcs$PC2 ~ as.factor(inds$Race)))

Call:
lm(formula = exp_pcs$PC2 ~ as.factor(inds$Race))

Residuals:
     Min       1Q   Median       3Q      Max 
-100.011  -26.679   -4.111   29.069  112.690 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)
(Intercept)            -0.3734     3.2498  -0.115    0.909
as.factor(inds$Race)3  -2.4307    23.0562  -0.105    0.916
as.factor(inds$Race)5  13.1076    17.9771   0.729    0.467

Residual standard error: 39.54 on 153 degrees of freedom
Multiple R-squared:  0.003563,  Adjusted R-squared:  -0.009463 
F-statistic: 0.2735 on 2 and 153 DF,  p-value: 0.7611

summary(lm(exp_pcs$PC1 ~ geno_pcs[,1]))

Call:
lm(formula = exp_pcs$PC1 ~ geno_pcs[, 1])

Residuals:
     Min       1Q   Median       3Q      Max 
-132.705  -35.717    5.717   38.461  100.425 

Coefficients:
                     Estimate Std. Error t value Pr(>|t|)
(Intercept)             4.626     38.640   0.120    0.905
geno_pcs[, 1]-0.0071   -4.667     54.646  -0.085    0.932
geno_pcs[, 1]-0.0081  -24.651     54.646  -0.451    0.653
geno_pcs[, 1]-0.0082   45.110     54.646   0.825    0.412
geno_pcs[, 1]-0.0083  -62.019     54.646  -1.135    0.260
geno_pcs[, 1]-0.0084  -15.831     44.618  -0.355    0.724
geno_pcs[, 1]-0.0085  -23.988     49.884  -0.481    0.632
geno_pcs[, 1]-0.0087  -18.743     47.324  -0.396    0.693
geno_pcs[, 1]-0.0088   -3.293     44.618  -0.074    0.941
geno_pcs[, 1]-0.0089  -14.351     43.201  -0.332    0.741
geno_pcs[, 1]-0.009     3.443     40.623   0.085    0.933
geno_pcs[, 1]-0.0091   20.686     43.201   0.479    0.633
geno_pcs[, 1]-0.0092  -12.740     43.201  -0.295    0.769
geno_pcs[, 1]-0.0093   -5.280     43.201  -0.122    0.903
geno_pcs[, 1]-0.0094   22.865     45.720   0.500    0.618
geno_pcs[, 1]0.0078     6.759     49.884   0.135    0.893
geno_pcs[, 1]0.0277    54.431     49.884   1.091    0.279

Residual standard error: 54.65 on 74 degrees of freedom
  (65 observations deleted due to missingness)
Multiple R-squared:  0.1404,    Adjusted R-squared:  -0.04543 
F-statistic: 0.7556 on 16 and 74 DF,  p-value: 0.7284

summary(lm(exp_pcs$PC2 ~ geno_pcs[,1]))

Call:
lm(formula = exp_pcs$PC2 ~ geno_pcs[, 1])

Residuals:
     Min       1Q   Median       3Q      Max 
-107.090  -21.031    1.545   25.131   60.190 

Coefficients:
                     Estimate Std. Error t value Pr(>|t|)  
(Intercept)          -18.7717    25.5348  -0.735   0.4646  
geno_pcs[, 1]-0.0071  60.2004    36.1117   1.667   0.0997 .
geno_pcs[, 1]-0.0081  25.6306    36.1117   0.710   0.4801  
geno_pcs[, 1]-0.0082  32.8006    36.1117   0.908   0.3667  
geno_pcs[, 1]-0.0083 -17.9777    36.1117  -0.498   0.6201  
geno_pcs[, 1]-0.0084  10.7153    29.4850   0.363   0.7173  
geno_pcs[, 1]-0.0085   4.5755    32.9653   0.139   0.8900  
geno_pcs[, 1]-0.0087  36.0867    31.2736   1.154   0.2523  
geno_pcs[, 1]-0.0088  26.2883    29.4850   0.892   0.3755  
geno_pcs[, 1]-0.0089  26.4590    28.5488   0.927   0.3570  
geno_pcs[, 1]-0.009   17.6991    26.8451   0.659   0.5117  
geno_pcs[, 1]-0.0091  14.9706    28.5488   0.524   0.6016  
geno_pcs[, 1]-0.0092  25.4771    28.5488   0.892   0.3751  
geno_pcs[, 1]-0.0093  -0.3447    28.5488  -0.012   0.9904  
geno_pcs[, 1]-0.0094  19.9330    30.2132   0.660   0.5115  
geno_pcs[, 1]0.0078   30.0521    32.9653   0.912   0.3649  
geno_pcs[, 1]0.0277  -24.4411    32.9653  -0.741   0.4608  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 36.11 on 74 degrees of freedom
  (65 observations deleted due to missingness)
Multiple R-squared:  0.1683,    Adjusted R-squared:  -0.01157 
F-statistic: 0.9357 on 16 and 74 DF,  p-value: 0.5335

summary(lm(geno_pcs[,1] ~ as.factor(inds$Race)))

Call:
lm(formula = geno_pcs[, 1] ~ as.factor(inds$Race))

Residuals:
      Min        1Q    Median        3Q       Max 
-0.012367 -0.001801 -0.001701 -0.001101  0.034999 

Coefficients:
                        Estimate Std. Error t value Pr(>|t|)    
(Intercept)           -0.0072988  0.0007568  -9.644 1.94e-15 ***
as.factor(inds$Race)3  0.0102655  0.0040990   2.504   0.0141 *  
as.factor(inds$Race)5 -0.0014678  0.0040990  -0.358   0.7211    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.006978 on 88 degrees of freedom
  (65 observations deleted due to missingness)
Multiple R-squared:  0.06848,   Adjusted R-squared:  0.04731 
F-statistic: 3.234 on 2 and 88 DF,  p-value: 0.04411

summary(lm(geno_pcs[,2] ~ as.factor(inds$Race)))

Call:
lm(formula = geno_pcs[, 2] ~ as.factor(inds$Race))

Residuals:
      Min        1Q    Median        3Q       Max 
-0.040096  0.001004  0.001204  0.001654  0.007704 

Coefficients:
                       Estimate Std. Error t value Pr(>|t|)    
(Intercept)           0.0043965  0.0008272   5.315 7.98e-07 ***
as.factor(inds$Race)3 0.0036369  0.0044801   0.812    0.419    
as.factor(inds$Race)5 0.0015702  0.0044801   0.350    0.727    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.007626 on 88 degrees of freedom
  (65 observations deleted due to missingness)
Multiple R-squared:  0.0086,    Adjusted R-squared:  -0.01393 
F-statistic: 0.3817 on 2 and 88 DF,  p-value: 0.6839

summary(lm(geno_pcs[,3] ~ as.factor(inds$Race)))

Call:
lm(formula = geno_pcs[, 3] ~ as.factor(inds$Race))

Residuals:
       Min         1Q     Median         3Q        Max 
-0.0099165 -0.0003249  0.0000000  0.0006835  0.0055835 

Coefficients:
                        Estimate Std. Error t value Pr(>|t|)    
(Intercept)           -0.0041835  0.0002342 -17.861   <2e-16 ***
as.factor(inds$Race)3  0.0002169  0.0012686   0.171    0.865    
as.factor(inds$Race)5  0.0003835  0.0012686   0.302    0.763    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.002159 on 88 degrees of freedom
  (65 observations deleted due to missingness)
Multiple R-squared:  0.001331,  Adjusted R-squared:  -0.02137 
F-statistic: 0.05862 on 2 and 88 DF,  p-value: 0.9431

summary(lm(geno_pcs[,4] ~ as.factor(inds$Race)))

Call:
lm(formula = geno_pcs[, 4] ~ as.factor(inds$Race))

Residuals:
       Min         1Q     Median         3Q        Max 
-0.0054424 -0.0003545  0.0001576  0.0006576  0.0025576 

Coefficients:
                        Estimate Std. Error t value Pr(>|t|)    
(Intercept)           -0.0031576  0.0001347 -23.440   <2e-16 ***
as.factor(inds$Race)3  0.0016243  0.0007296   2.226   0.0285 *  
as.factor(inds$Race)5 -0.0009757  0.0007296  -1.337   0.1846    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.001242 on 88 degrees of freedom
  (65 observations deleted due to missingness)
Multiple R-squared:  0.07325,   Adjusted R-squared:  0.05219 
F-statistic: 3.478 on 2 and 88 DF,  p-value: 0.03518

summary(lm(geno_pcs[,5] ~ as.factor(inds$Race)))

Call:
lm(formula = geno_pcs[, 5] ~ as.factor(inds$Race))

Residuals:
       Min         1Q     Median         3Q        Max 
-0.0091176 -0.0047176 -0.0016176  0.0007245  0.0278824 

Coefficients:
                        Estimate Std. Error t value Pr(>|t|)    
(Intercept)           -0.0044824  0.0008647  -5.184 1.37e-06 ***
as.factor(inds$Race)3 -0.0001843  0.0046831  -0.039    0.969    
as.factor(inds$Race)5 -0.0039843  0.0046831  -0.851    0.397    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.007972 on 88 degrees of freedom
  (65 observations deleted due to missingness)
Multiple R-squared:  0.008159,  Adjusted R-squared:  -0.01438 
F-statistic: 0.362 on 2 and 88 DF,  p-value: 0.6973

sessionInfo()

R version 3.4.3 (2017-11-30)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: OS X El Capitan 10.11.6

Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

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

other attached packages:
[1] cowplot_0.9.3 ggplot2_3.0.0

loaded via a namespace (and not attached):
 [1] Rcpp_0.12.18      compiler_3.4.3    pillar_1.3.0     
 [4] git2r_0.23.0      plyr_1.8.4        workflowr_1.1.1  
 [7] bindr_0.1.1       R.methodsS3_1.7.1 R.utils_2.6.0    
[10] tools_3.4.3       digest_0.6.16     evaluate_0.11    
[13] tibble_1.4.2      gtable_0.2.0      pkgconfig_2.0.2  
[16] rlang_0.2.2       yaml_2.2.0        bindrcpp_0.2.2   
[19] withr_2.1.2       stringr_1.3.1     dplyr_0.7.6      
[22] knitr_1.20        rprojroot_1.3-2   grid_3.4.3       
[25] tidyselect_0.2.4  glue_1.3.0        R6_2.2.2         
[28] rmarkdown_1.10    purrr_0.2.5       magrittr_1.5     
[31] whisker_0.3-2     backports_1.1.2   scales_1.0.0     
[34] htmltools_0.3.6   assertthat_0.2.0  colorspace_1.3-2 
[37] labeling_0.3      stringi_1.2.4     lazyeval_0.2.1   
[40] munsell_0.5.0     crayon_1.3.4      R.oo_1.22.0