Part_5.Rmd

# **Habitat Suitability and Distribution Models**
### with Applications in R
\
**by A. Guisan (1), W. Thuiller (2), N.E. Zimmermann (3) **,\
\
with contribution by V. Di Cola, D. Georges and A. Psomas\
\
_(1) University of Lausanne, Switzerland_\
_(2) CNRS, Université Grenoble Alpes, France_\
_(3) Swiss Federal Research Institute WSL, Switzerland_\


#### Cambridge University Press

http://www.cambridge.org/gb/academic/subjects/life-sciences/quantitative-biology-biostatistics-and-mathematical-modellin/habitat-suitability-and-distribution-models-applications-r

*Citation:* 
@book{
  title={Habitat Suitability and Distribution Models: With Applications in R},
  author={Guisan, A. and Thuiller, W. and Zimmermann, N.E.},
  isbn={9780521758369},
  series={Ecology, Biodiversity and Conservation},
  year={2017},
  publisher={Cambridge University Press}
}

*If you use any of these figures and code examples in a presentation or lecture, somewhere in your set of slides we would really appreciate if you please add the paragraph: "Some of the figures in this presentation are taken from "Habitat Suitability and Distribution Models: with applications in R"  (CUP, 2017) with permission from the authors: A. Guisan, W. Thuiller and N.E. Zimmerman " 
If you wish to use any of these figures in a publication, you must get permission from CUP, and each figure must be accompanied by a similar acknowledgement.*


# Part V "Predictions in Space and Time"
## Chapter 17 Projecting Models in Space and Time
### Additional considerations and assumptions when projecting models: analog environment, niche completeness, and niche stability 

Required packages

```{r load packages, message=FALSE,warning=FALSE}
library(ecospat)
```

Set Working Directory
```{r setwd}
setwd("~/data")
```


#### Preparation of datasets 
Load climate variable for all site of the Eurasian study area (column names should be x,y,X1,X2,...,Xn)
```{r clim1}
clim1<-read.table("tabular/bioclim/current/clim.vulpesNA_100.txt",h=TRUE)
```
Load climate variable for all site of the North American study area (column names should be x,y,X1,X2,...,Xn)
```{r clim2}
clim2<-read.table("tabular/bioclim/current/clim.vulpesEU_100.txt",h=TRUE)
```

Global climate for both ranges
```{r clim12}
clim12<-rbind(clim1,clim2)
```

Loading occurrence sites for the species (column names should be x,y)
```{r occurrences}
occ.sp1<-na.exclude(read.table("tabular/species/vulpes_na.txt",h=TRUE)[c(1,2)])
occ.sp2<-na.exclude(read.table("tabular/species/vulpes_eu.txt",h=TRUE)[c(1,2)])
```

Create sp occurrence dataset by adding climate variables from the global climate datasets
```{r sample_occur}
occ.sp1<-na.exclude(ecospat.sample.envar(dfsp=occ.sp1,colspxy=1:2,colspkept=NULL,dfvar=clim1,colvarxy=1:2,colvar="all",resolution=1))
occ.sp2<-na.exclude(ecospat.sample.envar(dfsp=occ.sp2,colspxy=1:2,colspkept=NULL,dfvar=clim2,colvarxy=1:2,colvar="all",resolution=1))
```


#### ANALYSIS 
Selection of variables to include in the analyses
```{r sel_var}
names(clim12)
Xvar<-c(3:21)
nvar<-length(Xvar)
```

Number of interation for the tests of equivalency and similarity
```{r interations}
iterations<-100
```

Resolution of the gridding of the climate space
```{r resolution}
R=100
```

Row weigthing and grouping factors for ade4 functions  
```{r row_weight}
row.w.1.occ<-1-(nrow(occ.sp1)/nrow(rbind(occ.sp1,occ.sp2))) # prevalence of occ1
row.w.2.occ<-1-(nrow(occ.sp2)/nrow(rbind(occ.sp1,occ.sp2))) # prevalence of occ2
row.w.occ<-c(rep(0, nrow(clim1)),rep(0, nrow(clim2)),rep(row.w.1.occ, nrow(occ.sp1)),rep(row.w.2.occ, nrow(occ.sp2)))
```


```{r rows}
row.w.1.env<-1-(nrow(clim1)/nrow(clim12))  # prevalence of clim1
row.w.2.env<-1-(nrow(clim2)/nrow(clim12))  # prevalence of clim2
row.w.env<-c(rep(row.w.1.env, nrow(clim1)),rep(row.w.2.env, nrow(clim2)),rep(0, nrow(occ.sp1)),rep(0, nrow(occ.sp2)))
```

```{r fact}
fac<-as.factor(c(rep(1, nrow(clim1)),rep(2, nrow(clim2)),rep(1, nrow(occ.sp1)),rep(2, nrow(occ.sp2))))
```

Global dataset for the analysis and rows for each sub dataset

```{r global_data}
data.env.occ<-rbind(clim1,clim2,occ.sp1,occ.sp2)[Xvar]
row.clim1<-1:nrow(clim1)
row.clim2<-(nrow(clim1)+1):(nrow(clim1)+nrow(clim2))
row.clim12<-1:(nrow(clim1)+nrow(clim2))
row.sp1<-(nrow(clim1)+nrow(clim2)+1):(nrow(clim1)+nrow(clim2)+nrow(occ.sp1))
row.sp2<-(nrow(clim1)+nrow(clim2)+nrow(occ.sp1)+1):(nrow(clim1)+nrow(clim2)+nrow(occ.sp1)+nrow(occ.sp2))
```

#### PCA-ENV 
Measures niche overlap along the two first axes of a PCA calibrated on all the pixels of the study areas
```{r pca}
pca.cal <-dudi.pca(data.env.occ,row.w = row.w.env, center = T, scale = T, scannf = F, nf = 2)
```

Predict the scores on the axes
```{r scores}
scores.clim12<- pca.cal$li[row.clim12,]
scores.clim1<- pca.cal$li[row.clim1,]
scores.clim2<- pca.cal$li[row.clim2,]
scores.sp1<- pca.cal$li[row.sp1,]
scores.sp2<- pca.cal$li[row.sp2,]
```

Calculation of environmental density
```{r env_density_z1}
z1<- ecospat.grid.clim.dyn(scores.clim12,scores.clim1,th.sp= 0,scores.sp1,R)
z1$z.uncor<-z1$Z
```

```{r env_density_z2}
z2<- ecospat.grid.clim.dyn(scores.clim12,scores.clim2,th.sp= 0,scores.sp2,R)
z2$z.uncor<-z2$Z
```

Plot realized environment
```{r plot.realized_niche 17.2}
par(cex=1.5)
ecospat.plot.niche(z1,title="Realized environment in North America",name.axis1="PC1",name.axis2="PC2")
ecospat.plot.niche(z2,title="Realized environment in Eurasia",name.axis1="PC1",name.axis2="PC2")
ecospat.plot.niche.dyn (z1, z2, quant=0.8, title="Realized environment overlap",name.axis1="PC1",name.axis2="PC2", interest = 1, colz1 = "#00FF0050", colz2 = "#FF000050", colinter = "#0000FF50", colZ1 = "green3", colZ2 = "red3") 
```

Calculation of occurence density
```{r occ-density}
z1<- ecospat.grid.clim.dyn(scores.clim12,scores.clim1,th.sp= 0,scores.sp1,R)
z2<- ecospat.grid.clim.dyn(scores.clim12,scores.clim2,th.sp= 0,scores.sp2,R)
```

Plot niche overlap
```{r plot.Niche_overlap1 17.5}
par(cex=1.5)
ecospat.plot.niche(z1,title="North American niche",name.axis1="PC1",name.axis2="PC2")
ecospat.plot.niche(z2,title="Eurasian niche",name.axis1="PC1",name.axis2="PC2")

ecospat.plot.niche.dyn (z1=z1, z2=z2, quant=0.8, title="Niche overlap",name.axis1="PC1",name.axis2="PC2", interest = 1, colz1 = "#00FF0050", colz2 = "#FF000050", colinter = "#0000FF50", colZ1 = "green3", colZ2 = "red3") 
```

## Projecting species distributions in space


Required packages
```{r load packages2, message=FALSE,warning=FALSE}
library(mgcv)
library(ade4)
library(raster)
library(fields)
library(dismo)
library(biomod2)
```

Read mammals and bioclim data
```{r read_data2}
mammals_data <- read.csv("tabular/species/mammals_and_bioclim_table.csv", row.names=1)
```

Fit GAM similar as in Chapter 10.3
```{r gam}
gam1 = gam(VulpesVulpes ~ s(bio3) + s(bio7) + s(bio11) + s(bio12), data=mammals_data, family="binomial")
```

Load current climate data
```{r load_data}
bio3r.cu<-raster("raster/bioclim/current/grd/bio3.grd")
bio7r.cu<-raster("raster/bioclim/current/grd/bio7.grd")
bio11r.cu<-raster("raster/bioclim/current/grd/bio11.grd")
bio12r.cu<-raster("raster/bioclim/current/grd/bio12.grd")
biostack.curr<-stack(bio3r.cu,bio7r.cu,bio11r.cu,bio12r.cu)
names(biostack.curr)
```

Predict to raster stack and visualize
```{r vulpes_curr_gam 17.7}
vulpes.curr <- predict(biostack.curr, gam1, type="response")
plot(vulpes.curr, col=two.colors(start="grey90",end="firebrick4", middle= "orange2"))
```

Predict also standard error to data.frame and visualize
```{r SE_GAM 17.8}
vulpes.se<-predict(gam1, mammals_data, type="response", se.fit=TRUE)
plot(mammals_data[,1:2],pch=15,cex=.25,col="grey70",xlab="Longitude",ylab="Latitude")
points(mammals_data[which(vulpes.se[[2]]>.05),1:2],pch=15,cex=.25,col="#FDD017")
points(mammals_data[which(vulpes.se[[2]]>.10),1:2],pch=15,cex=.25,col="#E56717")
points(mammals_data[which(vulpes.se[[2]]>.15),1:2],pch=15,cex=.25,col="#E42217")
points(mammals_data[which(vulpes.se[[2]]>.20),1:2],pch=15,cex=.25,col="#9F000F")
legend("bottomleft",legend=c("0.00 - 0.05","0.05 - 0.10", "0.10 - 0.15", "0.15 - 0.20","0.20 - 0.25"),
  pch=c(15,15,15,15,15),col=c("grey70","#FDD017","#E56717","#E42217","#9F000F"),cex=.6,bg="white",
  title="GAM Standard error")

```


```{r raster_se 17.9}
vulpes.se_raster <- rasterize(cbind(mammals_data[,c(1:2)]),y=bio3r.cu,field=vulpes.se[[2]])

plot(vulpes.se_raster, col=two.colors(start="grey90",end="firebrick4", middle= "orange2"))
```
```{r}
vulpes_oldnew<-mammals_data[mammals_data$Y_WGS84>30.0,
    c(1:2,8:13)]
tmp1<-dudi.pca(vulpes_oldnew[,c(4,6:8)], nf=2, scannf=F)
tmp2<-data.frame(cbind(vulpes_oldnew,tmp1$li))
cols<-rep("#3090C733",nrow(vulpes_oldnew))
cols[vulpes_oldnew$X_WGS84>-13]<-"#9F000F4D" 
```


```{r diff_old_new 17.10}
par(mfrow=c(1,2))
plot(bio3r.cu, legend=F,col="grey")
points(vulpes_oldnew [,c(1:2)], col=cols, pch=16, cex=0.6)
plot(jitter(tmp2$Axis1,amount=.3),jitter(tmp2$Axis2, amount=.3),col=cols, pch=16,cex=.5,xlab="PCA-Axis 1", ylab="PCA-Axis 2")
par(mfrow=c(1,1))
```

MESS
```{r mess1 17.11 }
vulpes_east<-mammals_data[mammals_data$X_WGS84>-13.0, c(1:2,8:13)]
vulpes_ne<-vulpes_east[vulpes_east$Y_WGS84>30,]
vulpes_europe<-vulpes_ne[vulpes_ne$X_WGS84<60,]

Mess.Vulpes <- mess(biostack.curr, vulpes_oldnew[,c(4,6:8)])
plot(Mess.Vulpes)
points(vulpes_europe[,1:2], col="red", pch=16, cex=0.3)

```

MESS with ECOSPAT
```{r mess_ecospat 17.11b}

library(ecospat)
mess.mammals <- ecospat.mess(mammals_data[,c(1:2,8:13)], vulpes_europe)
ecospat.plot.mess(mammals_data[,c(1:2)], mess.mammals)
```



## Projecting species in time

```{r future_var}
bio3r.fu<-raster("raster/bioclim/future/grd/bio3.grd")
bio7r.fu<-raster("raster/bioclim/future/grd/bio7.grd")
bio11r.fu<-raster("raster/bioclim/future/grd/bio11.grd")
bio12r.fu<-raster("raster/bioclim/future/grd/bio12.grd")
biostack.fut<-stack(bio3r.fu,bio7r.fu,bio11r.fu,bio12r.fu)
names(biostack.fut)

```

```{r gam_curr_fut 17.13}
vulpes.fut <- predict(biostack.fut, gam1, type="response")
vulpes.na.cur<-crop(vulpes.curr, extent(-170,-50,10,90))
vulpes.na.fut<-crop(vulpes.fut, extent(-170,-50,10,90))
par(mfrow=c(1,2))
  plot(vulpes.na.cur, col=two.colors(start="grey90", 
    end="firebrick4", middle= "orange2"),main="Current climate")
  plot(vulpes.na.fut, col=two.colors(start="grey90",
    end="firebrick4",middle= "orange2"),main="Future climate")
par(mfrow=c(1,1))
```

Future HS and Uncertainty
```{r uncertainty 17.14}
biostack.fut_df <- as.data.frame(rasterToPoints(biostack.fut))
vulpes.fut_se <- predict(gam1, biostack.fut_df, 
    type="response", se.fit=T)
vulpes.fut_se <- rasterFromXYZ(cbind(biostack.fut_df[,1:2],
    vulpes.fut_se), biostack.fut)
vulpes.fut_se<-crop(vulpes.fut_se, extent(-170,-50,10,90))
names(vulpes.fut_se) <- c("Habitat suitability future 
    climate", "Habitat suitability Uncertainty")
plot(vulpes.fut_se, col=two.colors(start="grey90",
    end="firebrick4", middle= "orange2"))
```


## Ensemble projections

```{r load packages3}
library(MASS)
library(earth)
library(randomForest)
library(mda)
library(biomod2)
```

Extract the future layers for the presence and absence points. 
```{r Future_env}
FutureEnv <- as.data.frame(cbind(mammals_data [,c(1:8)], extract(biostack.fut, mammals_data [,c(1,2)])))
FutureEnv <- na.omit(FutureEnv)
```

Create a dataframe to store the evaluation result for each model for each split-sampling
```{r test-results}
nRow <- nrow(mammals_data)
nCV <- 20 # the number of repeated split-sampling. 
Test_results <- as.data.frame(matrix(0,ncol=nCV,nrow=5, 
    dimnames=list(c("GLM","GAM","MARS","FDA","RF"), NULL)))
```

Create an array to store the predicted habitat suitability for current conditions for each single model x single split-sampling
```{r pred-reuslts}
Pred_results <- array(0,c(nRow, 5,nCV), 
    dimnames=list(seq(1:nRow), c("GLM","GAM","MARS","FDA","RF"), 
    seq(1:nCV)))
```

Create an array to store the predicted habitat suitability for future conditions for each single model x cross-validation combination

```{r Proj_future}
ProjFuture_results <- array(0,c(nrow(FutureEnv), 5,nCV), 
    dimnames=list(seq(1:nrow(FutureEnv)), 
    c("GLM","GAM","MARS","FDA","RF"), seq(1:nCV)))
ProjFuture_results_bin <- array(0,c(nrow(FutureEnv), 5,nCV), 
    dimnames=list(seq(1:nrow(FutureEnv)), 
    c("GLM","GAM","MARS","FDA","RF"), seq(1:nCV)))
```

Function to create the calibration and evaluation dataset
```{r SampMat}
SampMat <- function (ref, ratio, as.logi = FALSE) {
    ntot <- length(ref)
    npres <- sum(ref)
    ncal <- ceiling(ntot * ratio)
    pres <- sample(which(ref == 1), ceiling(npres * ratio))
    absc <- sample(which(ref == 0), ncal - length(pres))
    if (as.logi){
        calib <- rep(FALSE, ntot)
        calib[c(pres, absc)] <- TRUE
        eval <- !calib
    }
    else {
        calib <- c(pres, absc)
        eval <- (1:ntot)[-c(pres, absc)]
    }
    return(list(calibration = calib, evaluation = eval))
}
```

#### Loop across the 20-fold repeated split sampling
```{r loop.20fold, warning=FALSE}
for(i in 1:nCV) {
    # separate the original data into one subset for calibration 
    # and the other for evaluation. 
    a <- SampMat(ref=mammals_data$VulpesVulpes, ratio=0.7) 
        # function from the biomod2 package
    calib <- mammals_data[a$calibration,]
    eval <- mammals_data[a$evaluation,]
  
    ### GLM ###
    glmStart <- glm(VulpesVulpes~1, data=calib, family=binomial)
    glm.formula <- 
    makeFormula("VulpesVulpes",mammals_data[,c("bio3",  "bio7", 
    "bio11", "bio12")],"quadratic",interaction.level=1)
    glmModAIC <- stepAIC( glmStart, glm.formula, data = calib, 
        direction = "both", trace = FALSE, k = 2, 
        control=glm.control(maxit=100))
    # prediction to the evaluation data and evaluation using the 
    # TSS approach
    Pred_test <-  predict(glmModAIC, eval, type="response")
    # The Find.Optim.Stat from biomod2 computes the TSS and will 
    # provide the cutoff that optimizes it. Within biomod2, 
    # probabilities of presence are transformed into integers after 
    # being multiplied by 1,000 (to save memory space). We will 
    # therefore multiply here the probability of occurrence by 1,000. 
    Test <- Find.Optim.Stat(Stat='TSS', Fit=Pred_test*1000, 
        Obs=eval$VulpesVulpes)
    Test_results["GLM",i] <- Test[1,1]
    # prediction on the total dataset for current and future.
    Pred_results[,"GLM",i] <- predict(glmModAIC, mammals_data, 
        type="response")
    ProjFuture_results[,"GLM",i] <- predict(glmModAIC, FutureEnv, 
        type="response")
    # transform the probability of occurrence into binary 
    # predictions. Use the cutoff that optimizes the TSS 
    # statistics divided by 1,000.  
    ProjFuture_results_bin[ProjFuture_results[,
        "GLM",i]>=(Test[1,2]/1000),"GLM",i] <- 1
  
    ### GAM ###  
    gam_mgcv <- gam(VulpesVulpes~
        s(bio3)+s(bio7)+s(bio11)+s(bio12),data=calib, 
        family="binomial")
    # prediction on the evaluation data and evaluation using the 
    # TSS approach
    Pred_test <-  predict(gam_mgcv, eval, type="response")
    Test <- Find.Optim.Stat(Stat='TSS', Fit=Pred_test*1000, 
        Obs=eval$VulpesVulpes)
    Test_results["GAM",i] <- Test[1,1]
    # prediction on the total dataset
    Pred_results [Pred_results[,"GAM",i] >= 
        (Test[1,2]/1000),"GAM",i] <- 1
    ProjFuture_results[,"GAM",i] <- predict(gam_mgcv, FutureEnv, 
        type="response")
    ProjFuture_results_bin[ProjFuture_results[,"GAM",i] >= 
        (Test[1,2]/1000),"GAM",i] <- 1
  
    ### MARS ###
    Mars_int2 = earth(VulpesVulpes ~ 1+bio3+bio7+bio11+bio12, 
        data=calib, degree = 2, glm=list(family=binomial))
    # prediction on the evaluation data and evaluation using the 
    # TSS approach
    Pred_test <-  predict(Mars_int2, eval, type="response")
    Test <- Find.Optim.Stat(Stat='TSS', Fit=Pred_test*1000, 
        Obs=eval$VulpesVulpes)
    Test_results["MARS",i] <- Test[1,1]
    # prediction on the total dataset
    Pred_results[,"MARS",i] <- predict(Mars_int2, mammals_data, 
        type="response")
    ProjFuture_results[,"MARS",i] <- predict(Mars_int2, 
        FutureEnv, type="response")
    ProjFuture_results_bin[ProjFuture_results[,"MARS",i] >= 
        (Test[1,2]/1000),"MARS",i] <- 1
  
    ### FDA ###
    fda_mod = fda(VulpesVulpes ~ 1+bio3+bio7+bio11+bio12, 
        data=calib,method=mars)
    # prediction on the evaluation data and evaluation using the 
    # TSS approach
    Pred_test <-  predict(fda_mod, eval, type = "posterior")[,2]
    Test <- Find.Optim.Stat(Stat='TSS', Fit=Pred_test*1000, 
        Obs=eval$VulpesVulpes)
    Test_results["FDA",i] <- Test[1,1]
    # prediction on the total dataset
    Pred_results[,"FDA",i] = predict(fda_mod, 
        mammals_data[,c("bio3",  "bio7", "bio11", "bio12")], 
        type="posterior")[,2]
    ProjFuture_results[,"FDA",i] = predict(fda_mod, 
        FutureEnv[,c("bio3",  "bio7", "bio11", "bio12")], 
        type="posterior")[,2]
    ProjFuture_results_bin[ProjFuture_results[,"FDA",i] >= 
        (Test[1,2]/1000),"FDA",i] <- 1
  
    ### Random Forest ###  
    RF_mod = randomForest(x = calib[,c("bio3",  "bio7", "bio11", 
        "bio12")],y = as.factor(calib$VulpesVulpes), ntree = 
        1000, importance = TRUE)
    # prediction on the evaluation data and evaluation using the 
    # TSS approach
    Pred_test <-  predict(RF_mod, eval, type="prob")[,2]
    Test <- Find.Optim.Stat(Stat='TSS', Fit=Pred_test*1000, 
        Obs=eval$VulpesVulpes)
    Test_results["RF",i] <- Test[1,1]  
    # prediction on the total dataset
    Pred_results[,"RF",i] = predict(RF_mod, mammals_data, 
        type="prob")[,2]
    ProjFuture_results[,"RF",i] = predict(RF_mod, FutureEnv, 
        type="prob")[,2]
    ProjFuture_results_bin[ProjFuture_results[,"RF",i] >= 
        (Test[1,2]/1000),"RF",i] <- 1
}
```

Variation in TSS between models and cross-validation runs
```{r TSS}
library(ggplot2)
TSS <- unlist(Test_results)
TSS <- as.data.frame(TSS)
Test_results_ggplot <- cbind(TSS, model=rep(rownames(Test_results), times=20))
```



Variability in predictive accuracy between cross-validation runs and models. 
```{r tss_plot 17.5} 
p <- ggplot(Test_results_ggplot, aes(model, TSS))
p + geom_boxplot()
```



```{r pred_proj}
## Average prediction (mean and median) and standard deviation
Pred_total_mean <- apply(Pred_results,1,mean)
Pred_total_median <- apply(Pred_results,1,median)
Pred_total_sd <- apply(Pred_results,1,sd)

## Average projection into the future (mean and median) and variance
ProjFuture_total_mean <- apply(ProjFuture_results,1,mean)
ProjFuture_total_median <- apply(ProjFuture_results,1,median)
ProjFuture_total_sd <- apply(ProjFuture_results,1,sd)
```


Transformation in raster objects to facilitate the representation.

```{r uncertainty 17.16}
Obs <- rasterFromXYZ(mammals_data[,c("X_WGS84", "Y_WGS84", 
    "VulpesVulpes")])
Pred_total_mean_r <- 
    rasterFromXYZ(cbind(mammals_data[,c("X_WGS84", 
    "Y_WGS84")],Pred_total_mean))
Pred_total_median_r <- 
    rasterFromXYZ(cbind(mammals_data[,c("X_WGS84", 
    "Y_WGS84")],Pred_total_median))
Pred_total_sd_r <- 
    rasterFromXYZ(cbind(mammals_data[,c("X_WGS84", 
    "Y_WGS84")],Pred_total_sd))
Out <- stack(Obs,Pred_total_mean_r, 
    Pred_total_median_r,Pred_total_sd_r)
names(Out) <- c("Observed Vulpes vulpes","Ensemble modeling_mean","Ensemble modeling_median", "Ensemble modeling_sd")
```

Habitat suitability maps for Vulpes vulpes predicted by the different model averaging methods and the associated uncertainty map. 

```{r plot_uncert 17.16}
plot(Out)
```

Transformation in raster objects to facilitate the representation. 
```{r future}
ObsF <- rasterFromXYZ(FutureEnv[,c("X_WGS84", "Y_WGS84", "VulpesVulpes")])
ProjFuture_total_mean_r <- rasterFromXYZ(cbind(FutureEnv[,c("X_WGS84", "Y_WGS84")],ProjFuture_total_mean))
ProjFuture_total_median_r <- rasterFromXYZ(cbind(FutureEnv[,c("X_WGS84", "Y_WGS84")],ProjFuture_total_median))
ProjFuture_total_sd_r <- rasterFromXYZ(cbind(FutureEnv[,c("X_WGS84", "Y_WGS84")],ProjFuture_total_sd))
OutFut <- stack(ObsF, ProjFuture_total_mean_r, ProjFuture_total_median_r,ProjFuture_total_sd_r)
names(OutFut) <- c("Observed Vulpes vulpes","Ensemble_modeling_mean","Ensemble_modeling_median", "Ensemble_modeling_sd")
```

Future Habitat suitability maps for Vulpes vulpes predicted by the different model averaging methods and uncertainty map. 
```{r plot_future 17.17}
plot(OutFut)
```

#### Committee averaging: Sum the binary all binary projections from the 5 models and 20 repetitions. 
```{r Committee_averaging }
ProjFuture_CA<-as.data.frame(apply(ProjFuture_results_bin,1:2, 
                                     sum))
ProjFuture_CA$CA <- rowSums(ProjFuture_CA)
```


Link between committee averaging and mean probabilities across the models and repetitions. 
```{r plot_comm_aver 17.18}
plot(ProjFuture_CA$CA,ProjFuture_total_mean, xlab="Committee averaging", ylab="Mean probability")
```

Committee averaging all

```{r CA_all_ plot 17.19}
ProjFuture_CAglm<-rasterFromXYZ(cbind(FutureEnv[,c("X_WGS84", 
                                                     "Y_WGS84")],ProjFuture_CA$GLM))
ProjFuture_CAgam<-rasterFromXYZ(cbind(FutureEnv[,c("X_WGS84", 
                                                     "Y_WGS84")],ProjFuture_CA$GAM))
ProjFuture_CAmars<-rasterFromXYZ(cbind(FutureEnv[,c("X_WGS84", 
                                                      "Y_WGS84")],ProjFuture_CA$MARS))
ProjFuture_CAfda<-rasterFromXYZ(cbind(FutureEnv[,c("X_WGS84", 
                                                     "Y_WGS84")],ProjFuture_CA$FDA))
ProjFuture_CArf<-rasterFromXYZ(cbind(FutureEnv[,c("X_WGS84", 
                                                    "Y_WGS84")],ProjFuture_CA$RF))
ProjFuture_CAall<-rasterFromXYZ(cbind(FutureEnv[,c("X_WGS84", 
                                                     "Y_WGS84")],ProjFuture_CA$CA))
OutFut_CA <- stack(ProjFuture_CAglm, 
                     ProjFuture_CAgam,ProjFuture_CAmars, ProjFuture_CAfda, 
                     ProjFuture_CArf,ProjFuture_CAall)
names(OutFut_CA) <- c("CA_GLM","CA_GAM","CA_MARS","CA_FDA", 
                        "CA_RF", "CA_ALL")
plot(OutFut_CA, nc=2)
```




#### Species range change
```{r sp_range_change 17.20}
SRG <- 100*(colSums(ProjFuture_results_bin)-sum(FutureEnv$VulpesVulpes))/sum(FutureEnv$VulpesVulpes)
SRG_ToPlot <- as.data.frame(as.numeric(SRG))
SRG_ToPlot$Model <- rep(c("GLM","GAM","MARS","FDA","RF"), 20)
colnames(SRG_ToPlot)[1] <- "SRG"
library(ggplot2)
ggplot(SRG_ToPlot, aes(SRG)) + geom_histogram(aes(y = ..density.., fill = ..count..), binwidth=1) + geom_density() + scale_fill_gradient("Count", low = "lightgrey", high = "black") + xlab("Species Range Change (%)")# Density 
```

```{r variation _sp_range 17.21}
p <- ggplot(SRG_ToPlot, aes(SRG, colour=Model))
p + geom_density()+ xlab("Species Range Change (%)")
```