library(data.table)
library(lattice)
set.seed(314)

Comparison of productivity – 1-m scale

Read in data:

m1dat<-fread("1m_AWGW_Productivity_Comparison.txt",header=T)
head(m1dat)
##    FID AW_fsp_1m GW_fsp_1m
## 1:   0   1.38427   2.48694
## 2:   1   1.38890   2.49483
## 3:   2   1.39355   2.50167
## 4:   3   1.39820   2.50623
## 5:   4   1.40286   2.50886
## 6:   5   1.40753   2.51078

Randomly select 500 rows for calculating and displaying confidence intervals in plots:

length(m1dat$AW_fsp_1m)
## [1] 4531848
m1sub<-m1dat[sample(nrow(m1dat), 500, replace=F),]
head(m1sub)
##        FID AW_fsp_1m GW_fsp_1m
## 1:  447891  1.006530   2.94999
## 2: 1230295  1.562240   1.40491
## 3: 3473787  0.743726   2.68212
## 4: 1018044  2.026610   1.53739
## 5:  917442  0.815759   3.21753
## 6: 1374319  1.570810   1.17833
length(m1sub$AW_fsp_1m)
## [1] 500

Look for zeroes and replace with NA. Productivity models were constrained to estimate values between 0 and 4 and therefore can predict very small numbers, but not zero. These zero values are cells that are outside the nesting areas of woodcock and warblers that were incorrectly assigned a value of zero instead of NA during GIS processing.

head(m1dat)
##    FID AW_fsp_1m GW_fsp_1m
## 1:   0   1.38427   2.48694
## 2:   1   1.38890   2.49483
## 3:   2   1.39355   2.50167
## 4:   3   1.39820   2.50623
## 5:   4   1.40286   2.50886
## 6:   5   1.40753   2.51078
summary(m1dat$AW_fsp_1m)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.0000  0.9302  1.5210  1.5770  2.1740  3.4755
summary(m1dat$GW_fsp_1m)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.000   1.178   1.679   1.697   2.137   3.954
sum(m1dat$AW_fsp_1m==0)
## [1] 5367
sum(m1dat$GW_fsp_1m==0)
## [1] 3466
m1dat[m1dat==0]<-NA

Create a linear model: warbler productivity as a function of woodcock productivity (1-m scale):

lm1m<-lm(GW_fsp_1m~AW_fsp_1m, dat=m1dat)
summary(lm1m)
## 
## Call:
## lm(formula = GW_fsp_1m ~ AW_fsp_1m, data = m1dat)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.95125 -0.51765 -0.03815  0.39789  2.61588 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.2018327  0.0007308  3012.8   <2e-16 ***
## AW_fsp_1m   -0.3190672  0.0004155  -767.9   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.685 on 4523387 degrees of freedom
##   (8459 observations deleted due to missingness)
## Multiple R-squared:  0.1153, Adjusted R-squared:  0.1153 
## F-statistic: 5.897e+05 on 1 and 4523387 DF,  p-value: < 2.2e-16

Plot relationship between woodcock and warbler productivity: NOTE: To visualize the relationship between predicted productivity of woodcock and warblers at the 1-m scale we use a random subset of 500 points. However, the model outputs and statistical relationships are reported from the results of models using the full data set (n=4,531,848).

plot(GW_fsp_1m~AW_fsp_1m, dat=m1sub,xlim=c(0,4), ylim=c(0,4),col="gray80", pch=16, ylab="Predicted warbler productivity", xlab="Predicted woodcock productivity")
abline(lm(GW_fsp_1m~AW_fsp_1m, data=m1sub), col = "dodgerblue4")

newx<-seq(0,4, by=0.1)
conf_interval <- predict(lm(GW_fsp_1m~AW_fsp_1m, data=m1sub), newdata=data.frame(AW_fsp_1m=newx), interval="confidence",level = 0.95)
lines(newx, conf_interval[,2], col="deepskyblue", lty=2)
lines(newx, conf_interval[,3], col="deepskyblue", lty=2)

Comparison of productivity – 10-m scale

Read in data:

m10dat<-fread("10m_AWGW_Productivity_Comparison.txt",header=T)
head(m10dat)
##      FID AW_fsp_10m GW_fsp_10m
## 1: 31890   1.403950   0.000026
## 2: 31891   1.413510   0.000295
## 3: 31590   1.425820   0.001229
## 4: 36855   0.790661   0.003036
## 5: 37155   0.787652   0.003214
## 6: 37156   0.757358   0.008777

Randomly select 500 rows for calculating and displaying confidence intervals in plots:

length(m10dat$AW_fsp_10m)
## [1] 48462
m10sub<-m10dat[sample(nrow(m10dat), 500, replace=F),]
head(m10sub)
##      FID AW_fsp_10m GW_fsp_10m
## 1: 32553   1.574850    1.28506
## 2:  7398   0.658935    2.76299
## 3: 32558   1.650390    1.04486
## 4: 38902   1.015460    1.27343
## 5: 28725   0.862085    2.32546
## 6: 34244   2.484060    1.68034
length(m10sub$AW_fsp_10m)
## [1] 500

Look for zeroes and replace with NA

summary(m10dat$AW_fsp_10m)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.0000  0.9204  1.5163  1.5704  2.1715  3.4737
summary(m10dat$GW_fsp_10m)
##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
## 0.000026 1.197037 1.703970 1.715658 2.142030 3.947770
sum(m10dat$AW_fsp_10m==0)
## [1] 53
sum(m10dat$GW_fsp_10m==0)
## [1] 0
m10dat[m10dat==0]<-NA

Create a linear model: warbler productivity ~ woodcock productivity (10-m scale):

lm10m<-lm(GW_fsp_10m~AW_fsp_10m, dat=m10dat)
summary(lm10m)
## 
## Call:
## lm(formula = GW_fsp_10m ~ AW_fsp_10m, data = m10dat)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.9673 -0.5120 -0.0335  0.3924  2.5903 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.215533   0.007000  316.48   <2e-16 ***
## AW_fsp_10m  -0.317925   0.003993  -79.62   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6818 on 48407 degrees of freedom
##   (53 observations deleted due to missingness)
## Multiple R-squared:  0.1158, Adjusted R-squared:  0.1158 
## F-statistic:  6340 on 1 and 48407 DF,  p-value: < 2.2e-16

Plot relationship between woodcock and warbler productivity: NOTE: To visualize the relationship between predicted productivity of woodcock and warblers at the 1-m scale we use a random subset of 500 points. However, the model outputs and statistical relationships are reported from the results of models using the full data set (n=48,462).

plot(GW_fsp_10m~AW_fsp_10m, dat=m10sub,xlim=c(0,4), ylim=c(0,4),col="gray80", pch=16, ylab="Predicted warbler productivity", xlab="Predicted woodcock productivity")
abline(lm(GW_fsp_10m~AW_fsp_10m, data=m10sub), col = "dodgerblue4")

newx<-seq(0,4, by=0.1)
conf_interval <- predict(lm(GW_fsp_10m~AW_fsp_10m, data=m10sub), newdata=data.frame(AW_fsp_10m=newx), interval="confidence",level = 0.95)
lines(newx, conf_interval[,2], col="deepskyblue", lty=2)
lines(newx, conf_interval[,3], col="deepskyblue", lty=2)

Comparison of productivity – 100-m scale

Read in data:

m100dat<-fread("100m_AWGW_Productivity_Comparison.txt",header=T)
head(m100dat)
##    FID AW_fsp_100m GW_fsp_100m
## 1: 385    0.652698    0.086628
## 2: 755    2.864630    0.276092
## 3: 692    2.921150    0.353741
## 4: 816    3.417580    0.387830
## 5: 691    2.937080    0.413255
## 6: 787    3.087190    0.425296

Randomly select 500 rows for calculating and displaying confidence intervals in plots:

length(m100dat$AW_fsp_100m)
## [1] 651
m100sub<-m100dat[sample(nrow(m100dat), 500, replace=F),]
head(m100sub)
##    FID AW_fsp_100m GW_fsp_100m
## 1:   1    1.436660     3.17184
## 2: 302    2.409880     1.46802
## 3: 529    1.962190     1.94752
## 4:  81    0.401154     3.37097
## 5: 187    2.077020     1.61532
## 6: 889    1.074140     2.60639
length(m100sub$AW_fsp_100m)
## [1] 500

Look for zeroes and replace with NA

summary(m100dat$AW_fsp_100m)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.1507  0.8905  1.4590  1.5402  2.1606  3.4176
summary(m100dat$GW_fsp_100m)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 0.08663 1.39831 1.73658 1.80167 2.11624 3.87699
sum(m100dat$AW_fsp_100m==0)
## [1] 0
sum(m100dat$GW_fsp_100m==0)
## [1] 0
m100dat[m100dat==0]<-NA

Create a linear model: warbler productivity ~ woodcock productivity (100-m scale):

lm100m<-lm(GW_fsp_100m~AW_fsp_100m, dat=m100dat)
summary(lm100m)
## 
## Call:
## lm(formula = GW_fsp_100m ~ AW_fsp_100m, data = m100dat)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.99298 -0.43403 -0.08285  0.32173  2.30616 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.28402    0.05557  41.100   <2e-16 ***
## AW_fsp_100m -0.31318    0.03221  -9.722   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6386 on 649 degrees of freedom
## Multiple R-squared:  0.1271, Adjusted R-squared:  0.1258 
## F-statistic: 94.51 on 1 and 649 DF,  p-value: < 2.2e-16

Plot relationship between woodcock and warbler productivity: NOTE: To visualize the relationship between predicted productivity of woodcock and warblers at the 1-m scale we use a random subset of 500 points. However, the model outputs and statistical relationships are reported from the results of models using the full data set (n=651).

plot(GW_fsp_100m~AW_fsp_100m, dat=m100sub,xlim=c(0,4), ylim=c(0,4),col="gray80", pch=16, ylab="Predicted warbler productivity", xlab="Predicted woodcock productivity")
abline(lm(GW_fsp_100m~AW_fsp_100m, data=m100sub), col = "dodgerblue4")

newx<-seq(0,4, by=0.1)
conf_interval <- predict(lm(GW_fsp_100m~AW_fsp_100m, data=m100sub), newdata=data.frame(AW_fsp_100m=newx), interval="confidence",level = 0.95)
lines(newx, conf_interval[,2], col="deepskyblue", lty=2)
lines(newx, conf_interval[,3], col="deepskyblue", lty=2)

Comparison of productivity – 500-m scale

Read in data:

m500dat<-fread("500m_AWGW_Productivity_Comparison.txt",header=T)
head(m500dat)
##    FID AW_fsp_500m GW_fsp_500m
## 1:   0    0.944799     2.88861
## 2:   1    1.132840     2.41723
## 3:   2    0.941431     1.82450
## 4:   3    1.239690     1.35565
## 5:   4    0.415716     2.97291
## 6:   5    1.355230     3.27760

Length of data is <500 so we won’t randomly sample 500 points:

length(m500dat$AW_fsp_500m)
## [1] 36

Look for zeroes and replace with NA

summary(m500dat$AW_fsp_500m)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.3225  0.9440  1.3899  1.5226  2.0559  2.9460
summary(m500dat$GW_fsp_500m)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.7889  1.5506  1.7603  1.8398  2.0465  3.2776
sum(m500dat$AW_fsp_500m==0)
## [1] 0
sum(m500dat$GW_fsp_500m==0)
## [1] 0

Create a linear model: warbler productivity ~ woodcock productivity (500-m scale):

lm500m<-lm(GW_fsp_500m~AW_fsp_500m, dat=m500dat)
summary(lm500m)
## 
## Call:
## lm(formula = GW_fsp_500m ~ AW_fsp_500m, data = m500dat)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.6867 -0.3960 -0.1449  0.2658  1.3805 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   2.3614     0.2076  11.376 3.89e-13 ***
## AW_fsp_500m  -0.3426     0.1242  -2.759  0.00928 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5138 on 34 degrees of freedom
## Multiple R-squared:  0.1829, Adjusted R-squared:  0.1589 
## F-statistic:  7.61 on 1 and 34 DF,  p-value: 0.009277

Plot relationship between woodcock and warbler productivity:

plot(GW_fsp_500m~AW_fsp_500m, dat=m500dat,xlim=c(0,4), ylim=c(0,4),col="gray80", pch=16, ylab="Predicted warbler productivity", xlab="Predicted woodcock productivity")
abline(lm(GW_fsp_500m~AW_fsp_500m, data=m500dat), col = "dodgerblue4")

newx<-seq(0,4, by=0.1)
conf_interval <- predict(lm(GW_fsp_500m~AW_fsp_500m, data=m500dat), newdata=data.frame(AW_fsp_500m=newx), interval="confidence",level = 0.95)
lines(newx, conf_interval[,2], col="deepskyblue", lty=2)
lines(newx, conf_interval[,3], col="deepskyblue", lty=2)

Comparison of productivity – 1,000-m scale

Read in data:

m1000dat<-fread("1000m_AWGW_Productivity_Comparison.txt",header=T)
head(m1000dat)
##    FID AW_fsp_1000m GW_fsp_1000m
## 1:   0     1.479250      1.81228
## 2:   1     1.178510      1.54574
## 3:   2     0.881557      2.68942
## 4:   3     1.940510      1.73216
## 5:   4     2.078460      1.62952
## 6:   5     0.692374      1.73047

Length of data is <500 so we won’t randomly sample 500 points:

length(m1000dat$AW_fsp_1000m)
## [1] 9

Look for zeroes and replace with NA

summary(m1000dat$AW_fsp_1000m)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.6924  1.1785  1.4792  1.5502  2.0785  2.2934
summary(m1000dat$GW_fsp_1000m)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.097   1.630   1.730   1.742   1.772   2.689
sum(m1000dat$AW_fsp_1000m==0)
## [1] 0
sum(m1000dat$GW_fsp_1000m==0)
## [1] 0

Create a linear model: warbler productivity ~ woodcock productivity (1,000-m scale):

lm1000m<-lm(GW_fsp_1000m~AW_fsp_1000m, dat=m1000dat)
summary(lm1000m)
## 
## Call:
## lm(formula = GW_fsp_1000m ~ AW_fsp_1000m, data = m1000dat)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.36981 -0.32865  0.04413  0.13457  0.70025 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    2.3151     0.3667   6.314 0.000399 ***
## AW_fsp_1000m  -0.3698     0.2224  -1.663 0.140258    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3753 on 7 degrees of freedom
## Multiple R-squared:  0.2832, Adjusted R-squared:  0.1808 
## F-statistic: 2.766 on 1 and 7 DF,  p-value: 0.1403

Plot relationship between woodcock and warbler productivity:

plot(GW_fsp_1000m~AW_fsp_1000m, dat=m1000dat,xlim=c(0,4), ylim=c(0,4),col="gray80", pch=16, ylab="Predicted warbler productivity", xlab="Predicted woodcock productivity")
abline(lm(GW_fsp_1000m~AW_fsp_1000m, data=m1000dat), col = "dodgerblue4")

newx<-seq(0,4, by=0.1)
conf_interval <- predict(lm(GW_fsp_1000m~AW_fsp_1000m, data=m1000dat), newdata=data.frame(AW_fsp_1000m=newx), interval="confidence",level = 0.95)
lines(newx, conf_interval[,2], col="deepskyblue", lty=2)
lines(newx, conf_interval[,3], col="deepskyblue", lty=2)

Now look at the relationship between predicted productivity of both woodcock and warblers at observed nesting sites. Start with observed woodcock nests. Read in data:

amwo.nest<-read.csv("AMWO_nests_P.csv", header=T)
head(amwo.nest)
##   woodcockNest latitude longitude  AW_prod GW_prod
## 1            0 47.01400 -95.55981 0.530463 1.97729
## 2            1 47.01559 -95.56278 0.640692 2.54529
## 3            3 47.01454 -95.58684 1.290080 2.50420
## 4            4 47.01691 -95.58857 2.082880 1.27677
## 5            5 47.00407 -95.58846 2.187890 2.06897
## 6            6 46.99916 -95.60613 0.998835 2.47945

Fit a linear model to the relationship between predicted warbler productivity and predicted woodcock productivity at observed woodcock nest sites:

aw.mod<-lm(GW_prod~AW_prod, data=amwo.nest)
summary(aw.mod)
## 
## Call:
## lm(formula = GW_prod ~ AW_prod, data = amwo.nest)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.1573 -0.4919 -0.1235  0.3481  2.0985 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   2.0007     0.1884  10.617 1.82e-13 ***
## AW_prod      -0.2357     0.1200  -1.964   0.0561 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6503 on 42 degrees of freedom
## Multiple R-squared:  0.08413,    Adjusted R-squared:  0.06233 
## F-statistic: 3.858 on 1 and 42 DF,  p-value: 0.05614

Plot results:

newx<-seq(0,4, by=0.1)
conf_interval <- predict(aw.mod, newdata=data.frame(AW_prod=newx), interval="confidence", level = 0.95)

plot(GW_prod~AW_prod, data=amwo.nest, xlim=c(0,4), ylim=c(0,4), pch=17,col="gray80", ylab="Predicted American Woodcock Productivity", xlab="Predicted Golden-winged Warbler Productivity")
abline(aw.mod, col = "orangered4", lwd=2.5)
lines(newx, conf_interval[,2], col="orangered", lty=2, lwd=2.5)
lines(newx, conf_interval[,3], col="orangered", lty=2, lwd=2.5)

Now look at the relationship between predicted warbler and predicted woodcock productivity at observed warbler nest sites. Read in the data:

gwwa.nest<-read.csv("GWWA_nest_P.csv", header=T)
head(gwwa.nest)
##   warblerNest latitude longitude  AW_prod GW_prod
## 1           1 47.01785 -95.58181 2.002660 1.04543
## 2           2 47.01241 -95.61644 0.833307 2.00133
## 3           3 47.01468 -95.56257 0.619742 2.42882
## 4           4 47.01204 -95.61756 0.842108 1.58087
## 5           5 47.01221 -95.61774 0.834223 1.55911
## 6           6 47.01248 -95.61583 0.829187 2.30904

Fit linear model between predicted warbler productivity and predicted woodcock productivity at observed warbler nest sites:

gw.mod<-lm(GW_prod~AW_prod, data=gwwa.nest)
summary(gw.mod)
## 
## Call:
## lm(formula = GW_prod ~ AW_prod, data = gwwa.nest)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.38321 -0.39079  0.02935  0.36409  1.18654 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.09115    0.08641   24.20  < 2e-16 ***
## AW_prod     -0.33032    0.06292   -5.25 5.44e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.507 on 142 degrees of freedom
## Multiple R-squared:  0.1625, Adjusted R-squared:  0.1566 
## F-statistic: 27.56 on 1 and 142 DF,  p-value: 5.442e-07

Visualize the results:

newx<-seq(0,4, by=0.1)
conf_interval <- predict(gw.mod, newdata=data.frame(AW_prod=newx), interval="confidence", level = 0.95)

plot(GW_prod~AW_prod, data=gwwa.nest, xlim=c(0,4), ylim=c(0,4), pch=17,col="gray80", xlab="Predicted American Woodcock Productivity", ylab="Predicted Golden-winged Warbler Productivity")
abline(gw.mod, col = "orangered4", lwd=2.5)
lines(newx, conf_interval[,2], col="orangered", lty=2, lwd=2.5)
lines(newx, conf_interval[,3], col="orangered", lty=2, lwd=2.5)

Lastly, we can look at the density plots of productivity (1-m scale) over the study area for both species:

d.woodcock<-density(m1dat$AW_fsp_1m, bw = 0.07381, na.rm=TRUE)
plot(d.woodcock, main= "American woodcock", xlab="Predicted productivity", ylab="Density")
polygon(d.woodcock, col="lightblue")

d.warbler<-density(m1dat$GW_fsp_1m, bw=0.07395, na.rm=TRUE)
plot(d.warbler, main= "Golden-winged warbler", xlab="Predicted productivity", ylab="Density")
polygon(d.warbler, col="lightgreen")

devtools::session_info()
## - Session info ----------------------------------------------------------
##  setting  value                       
##  version  R version 3.5.1 (2018-07-02)
##  os       Windows 7 x64 SP 1          
##  system   x86_64, mingw32             
##  ui       RTerm                       
##  language (EN)                        
##  collate  English_United States.1252  
##  ctype    English_United States.1252  
##  tz       America/New_York            
##  date     2019-02-05                  
## 
## - Packages --------------------------------------------------------------
##  package     * version date       lib source        
##  assertthat    0.2.0   2017-04-11 [1] CRAN (R 3.5.1)
##  backports     1.1.2   2017-12-13 [1] CRAN (R 3.5.0)
##  callr         3.1.0   2018-12-10 [1] CRAN (R 3.5.1)
##  cli           1.0.1   2018-09-25 [1] CRAN (R 3.5.1)
##  crayon        1.3.4   2017-09-16 [1] CRAN (R 3.5.1)
##  data.table  * 1.11.4  2018-05-27 [1] CRAN (R 3.5.1)
##  desc          1.2.0   2018-05-01 [1] CRAN (R 3.5.1)
##  devtools    * 2.0.1   2018-10-26 [1] CRAN (R 3.5.1)
##  digest        0.6.18  2018-10-10 [1] CRAN (R 3.5.1)
##  evaluate      0.11    2018-07-17 [1] CRAN (R 3.5.1)
##  fs            1.2.6   2018-08-23 [1] CRAN (R 3.5.1)
##  glue          1.3.0   2018-07-17 [1] CRAN (R 3.5.1)
##  htmltools     0.3.6   2017-04-28 [1] CRAN (R 3.5.1)
##  knitr         1.20    2018-02-20 [1] CRAN (R 3.5.1)
##  lattice     * 0.20-35 2017-03-25 [1] CRAN (R 3.5.1)
##  magrittr      1.5     2014-11-22 [1] CRAN (R 3.5.1)
##  memoise       1.1.0   2017-04-21 [1] CRAN (R 3.5.1)
##  pkgbuild      1.0.2   2018-10-16 [1] CRAN (R 3.5.1)
##  pkgload       1.0.2   2018-10-29 [1] CRAN (R 3.5.1)
##  prettyunits   1.0.2   2015-07-13 [1] CRAN (R 3.5.1)
##  processx      3.2.1   2018-12-05 [1] CRAN (R 3.5.1)
##  ps            1.2.1   2018-11-06 [1] CRAN (R 3.5.1)
##  R6            2.3.0   2018-10-04 [1] CRAN (R 3.5.1)
##  Rcpp          1.0.0   2018-11-07 [1] CRAN (R 3.5.1)
##  remotes       2.0.2   2018-10-30 [1] CRAN (R 3.5.1)
##  rlang         0.3.0.1 2018-10-25 [1] CRAN (R 3.5.1)
##  rmarkdown     1.10    2018-06-11 [1] CRAN (R 3.5.1)
##  rprojroot     1.3-2   2018-01-03 [1] CRAN (R 3.5.1)
##  sessioninfo   1.1.1   2018-11-05 [1] CRAN (R 3.5.1)
##  stringi       1.2.4   2018-07-20 [1] CRAN (R 3.5.1)
##  stringr       1.3.1   2018-05-10 [1] CRAN (R 3.5.1)
##  usethis     * 1.4.0   2018-08-14 [1] CRAN (R 3.5.1)
##  withr         2.1.2   2018-03-15 [1] CRAN (R 3.5.1)
##  yaml          2.2.0   2018-07-25 [1] CRAN (R 3.5.1)
## 
## [1] C:/Program Files/R/R-3.5.1/library

```