setwd("") #Home directory 

################################   SET LIBRARIES   #################################
library(raster)
library(rgdal)
library(sp)
library(readxl)
library(car)
library(gstat)
library(GSIF)
library(ranger)
library(ModelMap)
library(caret)
library(corrplot)
library(devtools)
library(randomForest)
library(dplyr)
library(ggplot2)
library(GGally)
library(rattle)
library(rpart.plot)
library(base)
library(Cubist)
library(automap)
library(rJava)
library(extraTrees)
library(rworldmap)
library(ggmap)
library(mapproj)
library(VSURF)

################################   INPUT DATASET   #################################
###Subset Data S1 file to keep only dietary variables 
s_comp1.1 <- readxl::read_excel("Data_S1.xls",col_names=TRUE, na="NA", sheet="Data4.1")
write.csv(s_comp1,file="R_script\\Output\\Tables\\(RF2.1)C13_Initial.csv")
s_avg1 <- s_comp1.1

s_comp1.2 <- readxl::read_excel("Data_S1.xls",col_names=TRUE, na="NA", sheet="Data4.2")
write.csv(s_comp2,file="R_script\\Output\\Tables\\(RF2.2)C13_Initial.csv")
s_avg2 <- s_comp1.2

s_comp1.3 <- readxl::read_excel("Data_S1.xls",col_names=TRUE, na="NA", sheet="Data4.3")
write.csv(s_comp3,file="R_script\\Output\\Tables\\(RF2.3)C13_Initial.csv")
s_proj3 <- project(as.matrix(s_comp3[,c("Lon","Lat")]), "+proj=eck4 +lon_0=0 +x_0=0 +y_0=0 +ellps=WGS84 +units=m +no_defs")
plot(s_proj3)

###Project s-_comp1.3 using the location of residence of volunteers
s_proj1.3 <- project(as.matrix(s_comp1.3[,c("Lon","Lat")]), "+proj=eck4 +lon_0=0 +x_0=0 +y_0=0 +ellps=WGS84 +units=m +no_defs")
plot(s_proj1.3)

################################   INPUT ENVIRONMENTAL COVARIATE RASTERS   #################################
###The projected covariates are available at: https://drive.google.com/drive/folders/1g9rCGo3Kd3hz2o5JKkSbgNsGJclvsuQm?usp=sharing
###Use this link and download the Projected_rasters folder as a .zip file into your working directory (35GO)
###Unzip the file using the 7zip program https://www.7-zip.org/ which can handle large .zip file. 
###Verify that the unzip folder has a name of "Projected_rasters" as below and if necessary rename the folder to the correct name
###Once this is done the following raster should load in your script

### Import Raster Files(see Material and Methods and Table S15 in Supplementary for downloading those raster)
r.sugar     = raster("sugar_reproj.tif")
r.corn      = raster("corn_reproj.tif")
r.pet       = raster("pet_reproj.tif")
r.elevation = raster("elevation_reproj.tif")
r.clay      = raster("rclay_reproj.tif")
r.ph        = raster("rph_reproj.tif")
r.WCmap     = raster("map_reproj.tif")
r.BCA       = raster("BCA_reproj.tif")
r.BCB       = raster("BCB_reproj.tif")
r.SSA       = raster("SSA_reproj.tif")
r.SUL       = raster("SUL_reproj.tif")
r.AOD       = raster("AODpm25_reproj.tif")
r.dust      = raster("dust_reproj.tif")
r.salt      = raster("salt_reproj.tif")
r.mat       = raster("mat_reproj.tif")
r.nman      =raster("nman_reproj.tif")
r.nfert     =raster("nfert_reproj.tif")
r.distance<-raster("D:\\clement_back-up_2017-11-14\\European_Isoscape\\Projected_rasters\\Projected_rasters\\distance.tif")


### Crop Rasters to Canada Extent
canada <- as.vector(c(-12000000,-4000000,5000000,8000000))
r.pet       = crop(r.pet, canada, snap='near')
r.elevation = crop(r.elevation, r.pet, snap='near')
r.clay      = crop(r.clay, r.pet, snap='near')
r.ph        = crop(r.ph, r.pet, snap='near')
r.WCmap     = crop(r.WCmap, r.pet, snap='near')
r.BCA       = crop(r.BCA, r.pet, snap='near')
r.BCB       = crop(r.BCB, r.pet, snap='near')
r.SUL       = crop(r.SUL, r.pet, snap='near')
r.AOD       = crop(r.AOD, r.pet, snap='near')
r.dust      = crop(r.dust, r.pet, snap='near')
r.salt      = crop(r.salt, r.pet, snap='near')
r.mat       = crop(r.mat,r.pet,snap='near')
r.nman      = crop(r.nman,r.pet,snap='near')
r.nfert     = crop(r.nfert,r.pet,snap='near')
r.sugar     = crop(r.sugar,r.pet,snap='near')
r.corn      = crop(r.corn,r.pet,snap='near')
r.distance      = crop(r.distance,r.pet,snap='near')

###Resample all rasters at the same resolution
#r.mat= aggregate(r.mat, fact = 1000)
#r.nfert=aggregate(r.nfert, fact = 1000)
#r.nman=aggregate(r.nman, fact = 1000)
#r.dust = aggregate(r.dust, fact = 1000)
#r.WCmap = aggregate(r.WCmap, fact = 1000)
#r.salt = aggregate(r.salt, fact = 1000)
#r.ai = aggregate(r.ai, fact = 1000)
#r.pet = aggregate(r.pet, fact = 1000)
#r.elevation = aggregate(r.elevation, fact = 1000)
#r.clay = aggregate(r.clay, fact = 1000)
#r.ph = aggregate(r.ph, fact = 1000)
#r.BCA   = aggregate(r.BCA, fact = 1000)
#r.BCB   = aggregate(r.BCB, fact = 1000)
#r.SUL   = aggregate(r.SUL, fact = 1000)
#r.AOD   = aggregate(r.AOD, fact = 1000)
#r.sugar =aggregate(r.sugar, fact = 1000)
#r.corn =aggregate(r.corn, fact = 1000)


#############################   EXTRACT RASTER VALUES   ############################


Mode <- function(x) {
  ux <- unique(x)
  ux[which.max(tabulate(match(x, ux)))]
}

### Extract raster covariate values (with 10km2 buffer)
petxy       <-extract(r.pet, s_proj1.3, buffer=10000, fun=Mode,na.rm=TRUE)
elevationxy <-extract(r.elevation, s_proj1.3, buffer=10000, fun=Mode, na.rm=TRUE)
clayxy      <-extract(r.clay, s_proj1.3, buffer=10000, fun=Mode, na.rm=TRUE)
phxy        <-extract(r.ph, s_proj1.3, buffer=10000, fun=Mode, na.rm=TRUE)
WCmapxy     <-extract(r.WCmap, s_proj1.3, buffer=10000, fun=Mode,na.rm=TRUE)
BCAxy       <-extract(r.BCA, s_proj1.3, buffer=10000, fun=Mode,na.rm=TRUE)
BCBxy       <-extract(r.BCB, s_proj1.3, buffer=10000, fun=Mode,na.rm=TRUE)
SULxy       <-extract(r.SUL, s_proj1.3, buffer=10000, fun=Mode,na.rm=TRUE)
AODxy       <-extract(r.AOD, s_proj1.3, buffer=10000, fun=Mode,na.rm=TRUE)
Dustxy      <-extract(r.dust, s_proj1.3, buffer=10000, fun=Mode,na.rm=TRUE)
Saltxy      <-extract(r.salt, s_proj1.3, buffer=10000, fun=Mode,na.rm=TRUE)
matxy       <-extract(r.mat, s_proj1.3,  buffer=10000, fun=Mode,na.rm=TRUE)
nfertxy     <-extract(r.nfert,s_proj1.3, buffer=20000, fun=Mode,na.rm=TRUE)
nmanxy      <-extract(r.nman,s_proj1.3, buffer=60000, fun=Mode,na.rm=TRUE)
sugarxy     <-extract(r.sugar, s_proj1.3, buffer=10000, fun=Mode,na.rm=TRUE) 
cornxy      <-extract(r.corn, s_proj1.3, buffer=10000, fun=Mode,na.rm=TRUE)
distancexy      <-extract(r.distance, s_proj1.3, buffer=10000, fun=Mode,na.rm=TRUE)

### Combine data in S34
s_proj1.3_xy <- data.frame(s_proj1.3,s_comp1.3$FID ,s_comp1.3$N15 ,s_comp1.3$C13,s_comp1.3$S34 ,s_comp1.3$Sea,s_comp1.3$Wat, s_comp1.3$Pop,s_comp1.3$Pop,petxy,petxy,elevationxy,clayxy,phxy,WCmapxy,BCAxy,BCBxy,SULxy,AODxy,Dustxy,Saltxy,matxy,nfertxy,nmanxy,sugarxy,cornxy,distancexy)
s_proj1.4_xy <- data.frame(s_proj1.3,s_comp1.3$FID ,s_comp1.3$N15 ,s_comp1.3$C13,s_comp1.3$S34 ,s_comp1.3$Lat,s_comp1.3$Lon ,petxy,elevationxy,clayxy,phxy,WCmapxy,BCAxy,BCBxy,SULxy,AODxy,Dustxy,Saltxy,matxy,nfertxy,nmanxy,sugarxy,cornxy,distancexy)
s_proj1.5_xy <- data.frame(s_proj1.3,s_comp1.3$FID ,s_comp1.3$N15 ,s_comp1.3$C13,s_comp1.3$S34 ,petxy,elevationxy,clayxy,phxy,WCmapxy,BCAxy,BCBxy,SULxy,AODxy,Dustxy,Saltxy,matxy,nfertxy,nmanxy,sugarxy,cornxy,distancexy)
str(s_proj1.3_xy)
str(s_proj1.4_xy)
str(s_proj1.5_xy)

colnames(s_proj1.3_xy)<-c("X","Y","FID","15N","C13","S34","Lat","Lon","Sea","wat","Pop","r.pet","r.elevation","r.clay","r.ph","r.WCmap","r.BCA","r.BCB","r.SUL","r.AOD","r.dust","r.salt","r.mat","r.nfert","r.nman","r.sugar","r.corn","r.distance")
colnames(s_proj1.4_xy)<-c("X","Y","FID","15N","C13","S34","Lat","Lon","r.pet","r.elevation","r.clay","r.ph","r.WCmap","r.BCA","r.BCB","r.SUL","r.AOD","r.dust","r.salt","r.mat","r.nfert","r.nman","r.sugar","r.corn","r.distance")
colnames(s_proj1.5_xy)<-c("X","Y","FID","15N","C13","S34","r.pet","r.elevation","r.clay","r.ph","r.WCmap","r.BCA","r.BCB","r.SUL","r.AOD","r.dust","r.salt","r.mat","r.nfert","r.nman","r.sugar","r.corn","r.distance")

###Dataset including dietary geographic and environmental data
s_avg1.3 <- s_proj1.3_xy

### Dataset including geographic and environmental data only
s_avg1.4 <- s_proj1.4_xy

### Dataset including environmental variables only
s_avg1.5 <- s_proj1.5_xy


###############################CORRELATION fIGURES#################################
library("dplyr")
library("ggcorrplot")
library("Hmisc")

pdf("Correlation_d13C_diet.pdf", width=10, height=10)
cor_5 <- rcorr(as.matrix(s_avg2[,2:20]))
M <- cor_5$r
p_mat <- cor_5$P
par(mfrow=c(1,1))
corrplot(M, method = "color", col = col(200),  
         type = "upper",  
         addCoef.col = "black", # Add coefficient of correlation
         tl.col = "black", tl.srt = 45, #Text label color and rotation
         # Combine with significance level
         p.mat = p_mat, sig.level = 0.01,  
         # hide correlation coefficient on the principal diagonal
         diag = FALSE 
)
dev.off()

pdf("Correlation_d13C_EVS.pdf", width=10, height=10)
cor_5 <- rcorr(as.matrix(s_avg1.5[,4:23]))
M <- cor_5$r
p_mat <- cor_5$P
par(mfrow=c(1,1))
corrplot(M, method = "color", col = col(200),  
         type = "upper",  
         addCoef.col = "black", # Add coefficient of correlation
         tl.col = "black", tl.srt = 45, #Text label color and rotation
         # Combine with significance level
         p.mat = p_mat, sig.level = 0.01,  
         # hide correlation coefficient on the principal diagonal
         diag = FALSE 
)
dev.off()

###############################   DATA SPLITTING   #################################

### Identification of significant predictors using VSURF for RandomForest models 
### Remove colinear covariates

set.seed(123)
s_avg1.1.vsurf<-VSURF(s_avg1[,3:16],s_avg1$S34)
s_avg1.1.vsurf$varselect.pred
plot(s_avg1.1.vsurf)
s_avg1.1.sub<-s_avg1[,3:16]

s_avg1.2.vsurf<-VSURF(s_avg2[,3:18],s_avg2$S34)
s_avg1.2.vsurf$varselect.pred
plot(s_avg1.2.vsurf)
s_avg1.2.sub<-s_avg1.2[,3:18]

s_avg1.3.vsurf<-VSURF(s_avg1.3[,5:24],s_avg1.3$S34)
s_avg1.3.vsurf$varselect.pred
plot(s_avg1.3.vsurf)
s_avg1.3.sub<-s_avg1.3[,5:24]

s_avg1.4.vsurf<-VSURF(s_avg1.4[,5:22],s_avg1.4$S34)
s_avg1.4.vsurf$varselect.pred
plot(s_avg1.4.vsurf)
s_avg1.4.sub<-s_avg1.4[,5:21]

s_avg1.5.vsurf<-VSURF(s_avg1.5[,5:20],s_avg1.5$S34)
s_avg1.5.vsurf$varselect.pred
plot(s_avg1.5.vsurf)
s_avg1.5.sub<-s_avg1.5[,5:15]

### Important Variable Selection Using VSURF Identified Variables
names(s_avg1.1.sub)
names(s_avg1.2.sub)
names(s_avg1.3.sub)
names(s_avg1.4.sub)
names(s_avg1.5.sub)

###Subset each dataset using the significant predictors only
set.seed(123)
###Dietary predictors (Fig. 6A)
s_avg1.1_VSURF<-subset(s_avg1, select=c("S34", "Sea"))
###Dietary + Geographic predictors (Fig. 6B)
s_avg1.2_VSURF<-subset(s_avg2, select=c("S34", "Lon","Lat","Sea"))
###Dietary + Environmental predictors (Fig. 6D)
s_avg1.3_VSURF<-subset(s_avg1.3, select=c("S34", "r.salt", "Sea", "r.ph"))               #(Manual Selection)
###Geographic predictor only
s_avg1.4_VSURF<-subset(s_avg1.4, select=c("S34", "Lon","Lat"))
###Environmental predictors only (Fig 6C)
s_avg1.5_VSURF<-subset(s_avg1.3, select=c("S34", "r.salt","r.WCmap", "r.ph"))

s_avg1.1_VSURF
s_avg1.2_VSURF
s_avg1.3_VSURF
s_avg1.4_VSURF
s_avg1.5_VSURF



### Splitting data for 10-fold cross-validation (Repeated 5 times)
set.seed(123)
training1 <- s_avg1.1_VSURF;
training2 <- s_avg1.2_VSURF;
training3 <- s_avg1.3_VSURF;
training4 <- s_avg1.4_VSURF;
training5 <- s_avg1.5_VSURF;

fitControl <- trainControl(method = "repeatedcv", number = 10, repeats = 5, verboseIter=FALSE, returnResamp="final", savePredictions="all")

##############################   MODEL COMPARISON   ################################

### Random forest model (Different models using caret cross-validation algorithms on the training dataset)
mtry <- 6
tunegrid <- expand.grid(.mtry=mtry)

set.seed(124)
bestmtry <- tuneRF(training1, training1$S34, stepFactor=1, improve=1e-7, ntree=500)
RF1 <- train(S34 ~ ., data = training1, method = "rf", tuneGrid=tunegrid,trControl= fitControl)

set.seed(124)
bestmtry <- tuneRF(training2, training2$S34, stepFactor=1, improve=1e-7, ntree=500)
RF2 <- train(S34 ~ ., data = training2, method = "rf", tuneGrid=tunegrid,trControl= fitControl)

set.seed(124)
bestmtry <- tuneRF(training3, training3$S34, stepFactor=1, improve=1e-7, ntree=500)
RF3 <- train(S34 ~ ., data = training3, method = "rf", tuneGrid=tunegrid,trControl= fitControl)

set.seed(124)
bestmtry <- tuneRF(training4, training4$S34, stepFactor=1, improve=1e-7, ntree=500)
RF4 <- train(S34 ~ ., data = training4, method = "rf", tuneGrid=tunegrid,trControl= fitControl)

set.seed(124)
bestmtry <- tuneRF(training5, training5$S34, stepFactor=1, improve=1e-7, ntree=500)
RF5 <- train(S34 ~ ., data = training5, method = "rf", tuneGrid=tunegrid,trControl= fitControl)


######################   MODEL COMPARISON (OBSERVATIONS)   #########################

results <- resamples(list(RF1.1=RF1, RF1.2=RF2, RF1.3=RF3, RF1.4=RF4, RF1.5=RF5))
summary(results)
theme1<-trellis.par.get()
theme1$plot.symbol$col = rgb(.2, .2, .2, .4)
theme1$plot.symbol$pch = 16
theme1$plot.line$col = rgb(1, 0, 0, .7)
theme1$plot.line$lwd <- 2
trellis.par.set(theme1)
trellis.par.set(theme1)
bwplot(results, layout = c(1, 3), scales =list(x =list(relation = "free", limits = rep(list(c(0, 1), c(0, 1), c(0, 1))))))
splom(results)

############################   Visualize Best Model   ##############################

### Final Variable Importance Plot
par(mfrow=c(2,3))
varImpPlot(RF1$finalModel,main='RF1')
varImpPlot(RF2$finalModel,main='RF2')
varImpPlot(RF3$finalModel,main='RF3')
varImpPlot(RF4$finalModel,main='RF4')
varImpPlot(RF5$finalModel,main='RF5')

### Partial Dependance Plots

par(mfrow = c(2,2))
partialPlot(RF1$finalModel, training1, x.var = "Sea")


par(mfrow = c(2,2))
partialPlot(RF2$finalModel, training2, x.var = "Lon")
partialPlot(RF2$finalModel, training2, x.var = "Sea")
partialPlot(RF2$finalModel, training2, x.var = "Lat")


par(mfrow = c(2,2))
partialPlot(RF3$finalModel, training3, x.var = "r.salt")
partialPlot(RF3$finalModel, training3, x.var = "r.WCmap")
partialPlot(RF3$finalModel, training3, x.var = "r.ph")
partialPlot(RF3$finalModel, training3, x.var = "Sea")

par(mfrow = c(2,2))
partialPlot(RF4$finalModel, training4, x.var = "Long")
partialPlot(RF4$finalModel, training4, x.var = "Lat")


par(mfrow = c(2,2))
partialPlot(RF5$finalModel, training5, x.var = "r.WCmap")
partialPlot(RF5$finalModel, training5, x.var = "r.salt")
partialPlot(RF5$finalModel, training5, x.var = "r.ph")

### Training Data Plot
par(mfrow = c(2,2))
pred1<-as.data.frame(predict(RF1,training1))
plot(pred1$`predict(RF1, training1)`,training1$S34,pch=19,col="black",xlim=c(0,3),ylim=c(0,3.5),xlab="Modelled d34S",ylab="Observed d34S",cex.lab=1.5, cex.axis=1.5)
lmA.1<-lm(training1$S34~pred1$`predict(RF1, training1)`)
abline(lmA.1)

pred2<-as.data.frame(predict(RF2,training2))
plot(pred2$`predict(RF2, training2)`,training2$S34,pch=19,col="black",xlim=c(0,3),ylim=c(0,3.5),xlab="Modelled d34S",ylab="Observed d34S",cex.lab=1.5, cex.axis=1.5)
lmA.2<-lm(training2$S34~pred2$`predict(RF2, training2)`)
abline(lmA.2)

pred3<-as.data.frame(predict(RF3,training3))
plot(pred3$`predict(RF3, training3)`,training3$S34,pch=19,col="black",xlim=c(0,3),ylim=c(0,3.5),xlab="Modelled d34S",ylab="Observed d34S",cex.lab=1.5, cex.axis=1.5)
lmA.3<-lm(training3$S34~pred3$`predict(RF3, training3)`)
abline(lmA.3)

pred4<-as.data.frame(predict(RF4,training4))
plot(pred4$`predict(RF4, training4)`,training4$S34,pch=19,col="black",xlim=c(0,3),ylim=c(0,3.5),xlab="Modelled d34S",ylab="Observed d34S",cex.lab=1.5, cex.axis=1.5)
lmA.4<-lm(training4$S34~pred4$`predict(RF4, training4)`)
abline(lmA.4)

pred5<-as.data.frame(predict(RF5,training5))
plot(pred5$`predict(RF5, training5)`,training5$S34,pch=19,col="black",xlim=c(0,3),ylim=c(0,3.5),xlab="Modelled d34S",ylab="Observed d34S",cex.lab=1.5, cex.axis=1.5)
lmA.5<-lm(training5$S34~pred5$`predict(RF5, training5)`)
abline(lmA.5)


### Testing Data Plot (10-fold testing datasets)
par(mfrow = c(2,2))
plot(RF1$pred$pred,RF1$pred$obs,pch=19, col="black", xlim=c(-1,5),ylim=c(-1,5),xlab="Modelled d34S",ylab="Observed d34S",cex.lab=1.5, cex.axis=1.5)
lmB.1<-lm(RF1$pred$obs~RF1$pred$pred)
abline(lmB.1)

plot(RF2$pred$pred,RF2$pred$obs,pch=19, col="black", xlim=c(-1,5),ylim=c(-1,5),xlab="Modelled d34S",ylab="Observed d34S",cex.lab=1.5, cex.axis=1.5)
lmB.2<-lm(RF2$pred$obs~RF2$pred$pred)
abline(lmB.2)

plot(RF4$pred$pred,RF4$pred$obs,pch=19, col="black", xlim=c(-1,5),ylim=c(-1,5),xlab="Modelled d34S",ylab="Observed d34S",cex.lab=1.5, cex.axis=1.5)
lmB.4<-lm(RF4$pred$obs~RF4$pred$pred)
abline(lmB.4)

plot(RF3$pred$pred,RF3$pred$obs,pch=19, col="black", xlim=c(-1,5),ylim=c(-1,5),xlab="Modelled d34S",ylab="Observed d34S",cex.lab=1.5, cex.axis=1.5)
lmB.3<-lm(RF3$pred$obs~RF3$pred$pred)
abline(lmB.3)


plot(RF5$pred$pred,RF5$pred$obs,pch=19, col="black", xlim=c(-1,5),ylim=c(-1,5),xlab="Modelled d34S",ylab="Observed d34S",cex.lab=1.5, cex.axis=1.5)
lmB.5<-lm(RF5$pred$obs~RF5$pred$pred)
abline(lmB.5)



##############################   RESIDUALS ANALYSIS   ##############################

### Extract residuals and add to original dataset
par(mfrow = c(2,3))
pred_RF1_final<-predict(RF1,s_avg1.1)
residuals<-s_avg1.1$S34-pred_RF1_final
train1<-s_avg1.1
train1$resid<-residuals
plot(train1$S34,train1$resid,pch=19, col="black", xlim=c(-2,4),ylim=c(-2,2),xlab="training1 d34S",ylab="Residuals",cex.lab=1.5, cex.axis=1.5)

pred_RF2_final<-predict(RF2,s_avg1.2)
residuals<-s_avg1.2$S34-pred_RF2_final
train2<-s_avg1.2
train2$resid<-residuals
plot(train2$S34,train2$resid,pch=19, col="black", xlim=c(-2,4),ylim=c(-2,2),xlab="training2 d34S",ylab="Residuals",cex.lab=1.5, cex.axis=1.5)

pred_RF3_final<-predict(RF3,s_avg1.3)
residuals<-s_avg1.3$S34-pred_RF3_final
train3<-s_avg1.3
train3$resid<-residuals
plot(train3$S34,train3$resid,pch=19, col="black", xlim=c(-2,4),ylim=c(-2,2),xlab="training3 d34S",ylab="Residuals",cex.lab=1.5, cex.axis=1.5)

pred_RF4_final<-predict(RF4,s_avg1.4)
residuals<-s_avg1.4$S34-pred_RF4_final
train4<-s_avg1.4
train4$resid<-residuals
plot(train4$S34,train4$resid,pch=19, col="black", xlim=c(-2,4),ylim=c(-2,2),xlab="training4 d34S",ylab="Residuals",cex.lab=1.5, cex.axis=1.5)

pred_RF5_final<-predict(RF5,s_avg1.5)
residuals<-s_avg1.5$S34-pred_RF5_final
train5<-s_avg1.5
train5$resid<-residuals
plot(train5$S34,train5$resid,pch=19, col="black", xlim=c(-2,4),ylim=c(-2,2),xlab="training5 d34S",ylab="Residuals",cex.lab=1.5, cex.axis=1.5)

write.csv(train1,file="R_script//Output//Tables//(RF1.1)Residuals.csv")
write.csv(train2,file="R_script//Output//Tables//(RF1.2)Residuals.csv")
write.csv(train3,file="R_script//Output//Tables//(RF1.3)Residuals.csv")
write.csv(train4,file="R_script//Output//Tables//(RF1.4)Residuals.csv")
write.csv(train5,file="R_script//Output//Tables//(RF1.5)Residuals.csv")





###SPATIAL MODEL (Fig. 7)####
###Create a raster stack with the environmental predictors
canada_stack<-stack(r.salt, r.WCmap,r.ph)
names(canada_stack)<-c("r.salt","r.WCmap", "r.ph")

####Create a grid to apply model extent
canada.grid<-r.ph/r.ph

###Apply model spatially and create raster for mean d34S (Fig. 7)
rf2 <- predict(canada_stack, RF5, ext=canada.grid, na.rm=TRUE, overwrite=TRUE, progress='text')
writeRaster(rf2, filename="rf_enviro", format="GTiff", overwrite=TRUE)


pred_RF5_final<-predict(RF5,s_avg1.5)
residuals<-s_avg1.5$S34-pred_RF5_final
train5<-s_avg1.5
train5$resid<-residuals
plot(train5$S34,train5$resid,pch=19, col="black", xlim=c(-2,4),ylim=c(-2,2),xlab="training5 d34S",ylab="Residuals",cex.lab=1.5, cex.axis=1.5)


###Test factors influencing the residuals of the model (seafood consumption and travel history)
train5<-train5[complete.cases(train5), ]
train5$sea<-as.numeric(train5$sea)

par(mfrow = c(1,3))
plot(train$resid~train5$S34)
lm5<-lm(train5$resid~train5$S34)
abline(lm5)
plot(train5$sea,train5$resid,pch=1)
plot(train5$travel,train5$resid)





residuals_p <- SpatialPointsDataFrame(coords      = train5[,c("X","Y")], 
                                      data        = train5,
                                      proj4string = crs(r.salt))



sp_canada_stack2<-as(canada_stack, "SpatialPixelsDataFrame")

omm1 <- fit.gstatModel(residuals_p, S34~r.salt+r.ph+r.WCmap, sp_canada_stack2,method = "ranger")
rk1 <- predict(omm1, sp_canada_stack2)

omm2 <- fit.gstatModel(residuals_p, S34~r.salt+r.ph+r.WCmap, sp_canada_stack2,method = "randomForest")
rf_2 <- predict(omm2, sp_canada_stack2)

summary(rk1)$RMSE
summary(rf_2)$RMSE

res1 <- rk1@validation$residual
res2 <- rf_2@validation$residual
t_test <- t.test(res1, res2, alternative = "greater", paired = TRUE)
v_test <- var.test(res1, res2, alternative = "greater")


breakpoints<-c(-2,-1.5,-1,-0.5,0,0.5,1,1.5,2,2.5,3,3.5,4,4.5,5)
d34S_agg$Col <- matlab.like2(15)[as.numeric(cut(d34S_agg$d34S,breaks = breakpoints))]

pdf("d34S_isoscape_rk.pdf",width=7, height=5)
par(mfrow=c(1,1))
plot(rk1, col= matlab.like2(11), breaks=breakpoints, axes = FALSE)
plot(wrld_simpl_p,add=TRUE)
points(d34S_agg$X.1,d34S_agg$Y.1,pch=21,col="black",bg=d34S_agg$Col,cex=1)
#scaleBar(crs(na.dH_Hobson2012$mean), "topright",cex=1, seg.len=2,box.color = NULL)
dev.off()

pdf("d34S_isoscape_rf2.pdf",width=7, height=5)
par(mfrow=c(1,1))
plot(rf_2, col= matlab.like2(11), breaks=breakpoints, axes = FALSE)
plot(wrld_simpl_p,add=TRUE)
points(d34S_agg$X.1,d34S_agg$Y.1,pch=21,col="black",bg=d34S_agg$Col,cex=1)
#scaleBar(crs(na.dH_Hobson2012$mean), "topright",cex=1, seg.len=2,box.color = NULL)
dev.off()