Part_3.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 III "Modeling Approaches and Model Calibration"
## Chapter 9: Envelopes and distance-based approaches
### 9.2	Envelope approaches 

```{r Envelope_approaches_b1 9.1, opts.label = 'fig_half_page', fig.cap = "Figure 9.1: Observed and potential distribution of the red fox using a rectilinear envelope model (sre function in the biomod2 package). The potential distributions differ by the use of different percentiles to delineate the envelope. In both maps, black=presence, light gray= absence."}
library(biomod2) # install.packages("biomod2", repos="http://R-Forge.R-project.org")
## Load the species and environmental datasets
mammals_data <- read.csv("tabular/species/mammals_and_bioclim_table.csv", row.names=1)
head(mammals_data)

pred_BIOCLIM = sre(Response = mammals_data$VulpesVulpes, 
                   Explanatory = mammals_data[,c("bio3", "bio7", "bio11", "bio12")], 
                   NewData = mammals_data[,c("bio3", "bio7", "bio11", "bio12")], 
                   Quant = 0)

pred_BIOCLIM_025 = sre(Response = mammals_data$VulpesVulpes, 
                   Explanatory = mammals_data[,c("bio3", "bio7", "bio11", "bio12")], 
                   NewData = mammals_data[,c("bio3",  "bio7", "bio11", "bio12")], 
                   Quant = 0.025)

pred_BIOCLIM_05 = sre(Response = mammals_data$VulpesVulpes, 
                   Explanatory = mammals_data[,c("bio3",  "bio7", "bio11", "bio12")], 
                   NewData = mammals_data[,c("bio3",  "bio7", "bio11", "bio12")], 
                   Quant = 0.05)

par(mfrow=c(2,2))
level.plot(mammals_data$VulpesVulpes, 
           XY=mammals_data[,c("X_WGS84", "Y_WGS84")], 
           color.gradient = "grey", 
           cex=0.3,show.scale=F, 
           title="Original data")

level.plot(pred_BIOCLIM, 
           XY=mammals_data[,c("X_WGS84", "Y_WGS84")], 
           color.gradient = "grey", 
           cex=0.3,show.scale=F, 
           title="BIOCLIM 100%")

level.plot(pred_BIOCLIM_025, 
           XY=mammals_data[,c("X_WGS84", "Y_WGS84")], 
           color.gradient = "grey", 
           cex=0.3,show.scale=F, 
           title="BIOCLIM 97.5%")

level.plot(pred_BIOCLIM_05, 
           XY=mammals_data[,c("X_WGS84", "Y_WGS84")], 
           color.gradient = "grey", 
           cex=0.3,show.scale=F, 
           title="BIOCLIM 95%")
par(mfrow=c(1,1))
```
 
### 9.3	Distance-based methods

```{r code_9.3_Distance-based_methods_b1}
library(adehabitatHS)
library(pROC)
```

```{r code_9.3_Distance-based_methods_b2}
pc <- dudi.pca(mammals_data[,c("bio3", "bio7", "bio11", "bio12")], scannf=FALSE, nf = 2)
```


```{r code_9.3_Distance-based_methods_b3}
en <- enfa(pc, mammals_data$VulpesVulpes, scan=FALSE)
```



```{r Distance-based_methods 9.2, opts.label = 'fig_half_page', fig.cap = 'Figure 9. 2: Ecological niche description of the red fox (function enfa() in the package adehabitatHS)'}
par(mfrow=c(2,2))
barplot(en$s) # the specialization diagram
scatterniche(en$li,mammals_data$VulpesVulpes, pts=T)  # plot the niche
s.arrow(cor(pc$tab,en$li)) # meaning of the axes
```

```{r Distance-based_methods 9.3, opts.label = 'fig_half_page', fig.cap = 'Figure 9. 3: Observed and potential distribution of the red fox modeled using ENFA. The potential distribution is either expressed along a scale of habitat suitability values (light= low suitability to dark = high suitability), or in a binary form picturing presence-absence (black=presence, light gray= absence). '}
par(mfrow=c(2,2))
level.plot(mammals_data$VulpesVulpes, XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3,show.scale=F, title="Original data")
level.plot(en$li[,1], XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3,show.scale=F, title="ENFA")

roc_enfa <- roc(mammals_data$VulpesVulpes, en$li[,1])
threshold_enfa <- coords(roc_enfa, "best", ret=c("threshold"))

Pred01=as.numeric(en$li[,1] > threshold_enfa)
level.plot(Pred01, XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3,show.scale=F, title="ENFA binary")
```



## Chapter 10	Regression-based approaches

### 10.2	Generalized Linear Models (GLM)


```{r code_10.2_Generalized_Linear_Models_GLM_b1, opts.label = 'fig_half_page', fig.cap = 'Figure 10. 1: Observed (black=presence, light gray= absence) and potential distribution of species Sp290 modeled by different GLM differing by the complexity of the parameters (linear, quadratic and 2nd order polynomials). The gray scale of predictions (up-right and lower panels) shows habitat suitability values between 0 (light, unsuitable) and 1 (dark, highly suitable)'}
glm1 = glm(VulpesVulpes ~ 1+bio3+bio7+bio11+bio12, data=mammals_data, family="binomial")
glm2 = glm(VulpesVulpes ~ 1+poly(bio3,2)+poly(bio7,2)+poly(bio11,2)+poly(bio12,2), data=mammals_data, family="binomial")
```
```{r GLM1 10.1, fig.height=8,fig.width=8}
library(biomod2)
par(mfrow=c(2,2))
level.plot(mammals_data$VulpesVulpes, XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3,show.scale=F, title="Original data")
level.plot(fitted(glm1), XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3,show.scale=F, title="GLM with linear terms")
level.plot(fitted(glm2), XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3,show.scale=F, title="GLM with quadratic terms")
```


```{r GLM_b2 10.2, message=FALSE,warning=FALSE, opts.label = 'fig_quarter_page', fig.cap = 'Figure 10. 2: Response curves of model glm1 (linear terms) and glm2 (only quadratic terms).'}
library(ggplot2)
## create the response plot 
rp <- response.plot2(models = c('glm1','glm2'),
               Data = mammals_data[,c("bio3", "bio7", "bio11", "bio12")],
               show.variables = c("bio3",  "bio7", "bio11", "bio12"),
               fixed.var.metric = 'mean', plot = FALSE, use.formal.names = TRUE)
## define a custom ggplot2 theme
rp.gg.theme <- theme(legend.title = element_blank(),
                     axis.text.x = element_text(angle = 90, vjust = .5),
                     panel.background = element_rect(fill = NA, colour = "gray70"),
                     strip.background = element_rect(fill = NA, colour = "gray70"),
                     panel.grid.major = element_line(colour = "grey90"),
                     legend.key = element_rect(fill = NA, colour = "gray70"))
## display the reponse plot
gg.rp <- ggplot(rp, aes(x = expl.val, y = pred.val, lty = pred.name)) +
  geom_line() + ylab("prob of occ") + xlab("") + 
  rp.gg.theme + 
  facet_grid(~ expl.name, scales = 'free_x')
print(gg.rp)
```


```{r code_10.2_Generalized_Linear_Models_GLM_b3}
library(MASS)
glmStart <- glm(VulpesVulpes~1, data=mammals_data, family=binomial)
glm.formula <- formula("VulpesVulpes ~ 1 + 1 + poly(bio3,2) + poly(bio7,2) + poly(bio11,2) + poly(bio12,2) + bio3:bio7 + bio3:bio11 + bio3:bio12 + bio7:bio11 + bio7:bio12 + bio11:bio12")
glm.formula
```

```{r GLM_b4 10.3, opts.label = 'fig_quarter_page', fig.cap = 'Figure 10. 3: 2D response curves for the different fitted models'}
glmModAIC <- stepAIC( glmStart, 
                      glm.formula,
                      data = mammals_data,
                      direction = "both", trace = FALSE, 
                      k = 2, 
                      control=glm.control(maxit=100))

glmModBIC <- stepAIC( glmStart, 
                      glm.formula, 
                      direction="both", trace=FALSE,
                      k=log(nrow(mammals_data)),
                      control=glm.control(maxit=100))


rp <- response.plot2(models = c('glm1','glm2','glmModAIC','glmModBIC'),
                     Data = mammals_data[,c("bio3", "bio7", "bio11", "bio12")],
                     show.variables = c("bio3",  "bio7", "bio11", "bio12"),
                     fixed.var.metric = 'mean', plot = FALSE, use.formal.names = TRUE)

gg.rp <- ggplot(rp, aes(x = expl.val, y = pred.val, lty = pred.name)) +
  geom_line() + ylab("prob of occ") + xlab("") + 
  rp.gg.theme + 
  facet_grid(~ expl.name, scales = 'free_x')
print(gg.rp)
```
 


```{r GLM_b5 10.4, opts.label = 'fig_quarter_page', fig.cap = 'Figure 10. 4: Bivariate response curves from the model glmModAIC for four predictor variables.'}
rp.2D <- response.plot2( models = c('glmModAIC'),
                         Data = mammals_data[,c("bio3", "bio7", "bio11", "bio12")],
                         show.variables = c("bio3",  "bio7", "bio11", "bio12"),
                         fixed.var.metric = 'median', 
                         do.bivariate=T,
                         plot = FALSE, use.formal.names = TRUE )

gg.rp.2D <- ggplot(rp.2D, aes(x = expl1.val, y = expl2.val, fill = pred.val)) +
  geom_raster() + rp.gg.theme  + ylab("") + xlab("") + theme(legend.title = element_text()) +
  scale_fill_gradient(name = "prob of occ.", low = "#f0f0f0", high = "#000000") + 
  facet_grid(expl2.name ~ expl1.name, scales = 'free')
print(gg.rp.2D)
```
 

```{r code_10.2_Generalized_Linear_Models_GLM_b6}
anova(glmModAIC)
```

```{r GLM_b7 10.5, opts.label = 'fig_half_page', fig.cap = 'Figure 10. 5: Observed (black=presence, light gray= absence) and potential distribution of red fox extracted from glmModAIC and glmModBIC models. The gray scale of predictions shows habitat suitability values between 0 (light, unsuitable) and 1 (dark, highly suitable).'}
par(mfrow=c(2,2))
level.plot(mammals_data$VulpesVulpes, XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3,level.range=c(0,1), show.scale=F, title="Original data")
level.plot(fitted(glmModAIC), XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3, level.range=c(0,1), show.scale=F, title="Stepwise GLM with AIC")
level.plot(fitted(glmModBIC), XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3,level.range=c(0,1), show.scale=F, title="Stepwise GLM with BIC")
```
 

### 10.3	Generalized Additive Models


```{r code_10.3_Generalized_Additive_Models_b1}
if(is.element("package:mgcv", search())) detach("package:mgcv") ## make sure the mgcv package is not loaded to avoid conflicts
library(gam)
gam1 = gam(VulpesVulpes ~ s(bio3,2) + s(bio7,2) + s(bio11,2) + s(bio12,2), data=mammals_data, family="binomial")
gam2 = gam(VulpesVulpes ~ s(bio3,4) + s(bio7,4) + s(bio11,4) + s(bio12,4), data=mammals_data, family="binomial")
```


```{r GAMb2 10.6, opts.label = 'fig_half_page', fig.cap = 'Figure 10. 6: Response curves of model gam1 expressed in logit scale (function plot.gam() from the gam package).'}
par(mfrow=c(2,2))
plot(gam1, se=T)
```


```{r GAMb3 10.7, message=FALSE,warning=FALSE, opts.label = 'fig_quarter_page', fig.cap = 'Figure 10. 7: Response curves of the gam1 (degree of smoothing = 2) and gam2 (degree of smoothing = 4) models.'}
rp <- response.plot2(models = c('gam1', 'gam2'),
                     Data = mammals_data[,c("bio3", "bio7", "bio11", "bio12")],
                     show.variables = c("bio3",  "bio7", "bio11", "bio12"),
                     fixed.var.metric = 'mean', plot = FALSE, use.formal.names = TRUE)

gg.rp <- ggplot(rp, aes(x = expl.val, y = pred.val, lty = pred.name)) +
  geom_line() + ylab("prob of occ") + xlab("") + 
  rp.gg.theme + 
  facet_grid(~ expl.name, scales = 'free_x')
print(gg.rp)
```

```{r code_10.3_Generalized_Additive_Models_b4}
gamStart <- gam(VulpesVulpes~1, data=mammals_data, family=binomial)
gamModAIC <- step.gam(gamStart, biomod2:::.scope(mammals_data[1:3,c("bio3",  "bio7", "bio11", "bio12")], "s", 4), trace=F, direction = "both")        
```

```{r code_10.3_Generalized_Additive_Models_b4b, echo=FALSE, eval = FALSE}
## test of the multiple smoother case
biomod2:::.scope(mammals_data[1:3,c("bio3",  "bio7", "bio11", "bio12")], "s", 2:4)
gamModAIC.test <- step.gam(gamStart, biomod2:::.scope(mammals_data[1:3,c("bio3",  "bio7", "bio11", "bio12")], "s", 2:4), trace=F, direction = "both")
```


```{r GAMb5 10.8, opts.label = 'fig_quarter_page', fig.cap = 'Figure 10. 8. Observed (black=presence, light gray= absence) and potential distribution of Vulpes vulpes extracted from gamModAIC. The gray scale of prediction illustratesshows habitat suitability values between 0 (light, unsuitable) and 1 (dark, highly suitable)'}
par(mfrow=c(1,2))
level.plot(mammals_data$VulpesVulpes, XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3,level.range=c(0,1), show.scale=F, title="Original data")
level.plot(fitted(gamModAIC), XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3, level.range=c(0,1), show.scale=F, title="Stepwise GAM with AIC")
```



```{r code_10.3_Generalized_Additive_Models_b6, fig.keep = FALSE}
if(is.element("package:gam", search())) detach("package:gam") ## make sure the gam package is not loaded to avoid conflicts
library(mgcv)
gam_mgcv <- gam(VulpesVulpes~s(bio3)+s(bio7)+s(bio11)+s(bio12),data = mammals_data, family = "binomial")
## see a range of summary statistics
summary(gam_mgcv)
gam.check(gam_mgcv)
```


```{r GAMb7 10.9, opts.label = 'fig_half_page', fig.cap = 'Figure 10.9. Response curves of model gam_mgcv plotted using the internal function of mgcv().'}
plot(gam_mgcv,pages=1, seWithMean=TRUE)  
```
  

```{r GAMb8 10.10, opts.label = 'fig_quarter_page', fig.cap = 'Figure 10.10. Response curves from the model calibrated with the mgcv package (gam_mgcv).'}
rp <- response.plot2(models = c('gam_mgcv'),
                     Data = mammals_data[,c("bio3", "bio7", "bio11", "bio12")],
                     show.variables = c("bio3",  "bio7", "bio11", "bio12"),
                     fixed.var.metric = 'mean', plot = FALSE, use.formal.names = TRUE)

gg.rp <- ggplot(rp, aes(x = expl.val, y = pred.val, lty = pred.name)) +
  geom_line() + ylab("prob of occ") + xlab("") + 
  rp.gg.theme + 
  facet_grid(~ expl.name, scales = 'free_x')
print(gg.rp)
```

```{r GAMb9 10.11, opts.label = 'fig_quarter_page', fig.cap = 'Figure 10.11. Observed (black=presence, light gray= absence) and potential distribution of Vulpes vulpes extracted from the gam_mgcv object. The gray scale of predictions illustrates shows habitat suitability values between 0 (light, unsuitable) and 1 (dark, highly suitable).'}
par(mfrow=c(1,2))
level.plot(mammals_data$VulpesVulpes, XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3,level.range=c(0,1), show.scale=F, title="Original data")
level.plot(fitted(gam_mgcv), XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3, level.range=c(0,1), show.scale=F, title="GAM with mgcv")
par(mfrow=c(1,1))
```


### 10.4	Multivariate Adaptive Regression Splines

```{r code_10.4_Multivariate_Adaptive_Regression_Splines_b1}
library(earth)
Mars_int1 <- earth(VulpesVulpes ~ 1+bio3+bio7+bio11+bio12, 
                  data = mammals_data,
                  degree = 1,
                  glm = list(family = binomial))

Mars_int2 <- earth(VulpesVulpes ~ 1+bio3+bio7+bio11+bio12, 
                  data = mammals_data,
                  degree = 2,
                  glm = list(family = binomial))

## print the summary of objects
Mars_int1
Mars_int2
```


```{r code_10.4_Multivariate_Adaptive_Regression_Splines_b2}
summary(fitted.values(Mars_int1))
```


```{r code_10.4_Multivariate_Adaptive_Regression_Splines_b3}
pred_Mars_int1 <- predict(Mars_int1, type="response")
summary(pred_Mars_int1)

pred_Mars_int2 <- predict(Mars_int2, type="response")
summary(pred_Mars_int2)
```


```{r MARS_b4 10.12, opts.label = 'fig_half_page', fig.cap = 'Figure 10. 12. The distribution of the predicted values from MARS for both the presence and absence of Vulpes vulpes.'}
plotd(Mars_int1, hist = T)
```


```{r MARS_b5 10.13, opts.label = 'fig_quarter_page', fig.cap = 'Figure 10. 13: Differences between probability of occurrence between a MARS model with a maximum of 1 degree of interaction and a MARS model with a maximum of 2 degrees of interaction.'}
plot(pred_Mars_int1, pred_Mars_int2, xlab="MARS with max inter degree 1", ylab="MARS with max inter degree 2")
```


```{r MARS_b6 10.14, opts.label = 'fig_half_page', fig.cap = 'Figure 10. 14: Observed (black=presence, light gray= absence) and potential distribution of Vulpes vulpes extracted from the MARS 1 and MARS 2 objects. The gray scale of predictions (upper-right and lower-left panels) illustratesshows habitat suitability values between 0 (light, unsuitable) and 1 (dark, highly suitable)'}
par(mfrow=c(2,2))
level.plot(mammals_data$VulpesVulpes, XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3,level.range=c(0,1),show.scale=F, title="Original data")
level.plot(pred_Mars_int1, XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3,level.range=c(0,1),show.scale=F, title="MARS with interaction degree 1")
level.plot(pred_Mars_int2, XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3,level.range=c(0,1),show.scale=F, title="MARS with interaction degree 2")
par(mfrow=c(1,1))
```


## Chapter 11: Classification approaches and machine learning systems
### 11.2	Recursive partitioning


```{r code_11.2_Recursive_partitioning_b1}
library(rpart)
RP = rpart(VulpesVulpes ~ 1+bio3+bio7+bio11+bio12, data=mammals_data, control=rpart.control(xval=10), method="class")
```


```{r RP_b2 11.1, opts.label = 'fig_half_page', fig.cap = 'Figure 11. 1: Classification tree for Vulpes vulpes using the rpart() function'}
plot(RP, uniform=F, margin = 0.1, branch = 0.5, compress=T)
text(RP, cex=0.8)
```
  

```{r RP_b3 11.2, opts.label = 'fig_quarter_page', fig.cap = 'Figure 11. 2: Observed (left; black=presence, light gray= absence) and potential distribution (right) of Vulpes vulpes predicted by recursive partitioning. The gray scale of predictions illustrates shows habitat suitability values between 0 (light, unsuitable) and 1 (dark, highly suitable)'}
RP.pred = predict(RP, type="prob")[,2]
par(mfrow=c(1,2))
level.plot(mammals_data$VulpesVulpes, XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3,show.scale=F, title="Original data")
level.plot(RP.pred, XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3,level.range=c(0,1),show.scale=F, title="Recursive partitioning")
```


```{r RP_b4 11.3, opts.label = 'fig_quarter_page', fig.cap = 'Figure 11.3: Response curves of a recursive partitioning (RP) model.'}
rp <- response.plot2(models = c('RP'),
                     Data = mammals_data[,c("bio3", "bio7", "bio11", "bio12")],
                     show.variables = c("bio3",  "bio7", "bio11", "bio12"),
                     fixed.var.metric = 'mean', plot = FALSE, use.formal.names = TRUE)

gg.rp <- ggplot(rp, aes(x = expl.val, y = pred.val, lty = pred.name)) +
  geom_line() + ylab("prob of occ") + xlab("") + 
  rp.gg.theme + 
  facet_grid(~ expl.name, scales = 'free_x')
print(gg.rp)
```
 

## 11.3	Linear Discriminant Analysis and extensions


```{r code_11.3_Linear_Discriminant_Analysis_and_extensions_b1}
library(mda)
fda_mod = fda(VulpesVulpes ~ 1+bio3+bio7+bio11+bio12, data=mammals_data,method=mars)
```


```{r code_11.3_Linear_Discriminant_Analysis_and_extensions_b2}
fda_mod$confusion
```


```{r FDA_b3 11.4, opts.label = 'fig_quarter_page', fig.cap = 'Figure 11.4: Observed and potential distribution of Vulpes vulpes predicted by flexible discriminant analysis based on MARS algorithm.'}
FDA.pred = predict(fda_mod, mammals_data[,c("bio3",  "bio7", "bio11", "bio12")], type = "posterior")[,2]
par(mfrow=c(1,2))
level.plot(mammals_data$VulpesVulpes, XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3,show.scale=F, title="Original data")
level.plot(FDA.pred, XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3,show.scale=F, title="FDA")
```

```{r FDA_b4 11.5, opts.label = 'fig_quarter_page', fig.cap = 'Figure 11. 5: Response curve of Vulpes vulpes modeled using flexible discriminant analysis.'}
rp <- response.plot2(models = c('fda_mod'),
                     Data = mammals_data[,c("bio3", "bio7", "bio11", "bio12")],
                     show.variables = c("bio3",  "bio7", "bio11", "bio12"),
                     fixed.var.metric = 'mean', plot = FALSE, use.formal.names = TRUE)

gg.rp <- ggplot(rp, aes(x = expl.val, y = pred.val, lty = pred.name)) +
  geom_line() + ylab("prob of occ") + xlab("") + 
  rp.gg.theme + 
  facet_grid(~ expl.name, scales = 'free_x')
print(gg.rp)
```


```{r FDA_b5 11.6, opts.label = 'fig_half_page', fig.cap = 'Figure 11. 6: Bivariate.response curve of Vulpes vulpes modeled using flexible discriminant analysis along four predictor variables.'}
rp.2D <- response.plot2( models = c('fda_mod'),
                         Data = mammals_data[,c("bio3", "bio7", "bio11", "bio12")],
                         show.variables = c("bio3",  "bio7", "bio11", "bio12"),
                         fixed.var.metric = 'median', 
                         do.bivariate=T,
                         plot = FALSE, use.formal.names = TRUE )

gg.rp.2D <- ggplot(rp.2D, aes(x = expl1.val, y = expl2.val, fill = pred.val)) +
  geom_raster() + rp.gg.theme  + ylab("") + xlab("") + theme(legend.title = element_text()) +
  scale_fill_gradient(name = "prob of occ.", low = "#f0f0f0", high = "#000000") + 
  facet_grid(expl2.name ~ expl1.name, scales = 'free')
print(gg.rp.2D)
```


## 11.4	Artificial Neural Networks


```{r code_11.4_Artificial_Neural_Networks_b1}
library(nnet)
set.seed(555)
nnet.Init = nnet(mammals_data[,c("bio3",  "bio7", "bio11", "bio12")], mammals_data$VulpesVulpes, size = 2, rang = 0.1, decay = 5e-4, maxit = 200)
```

Interested readers are advised to take a look at the source code for this function by typing: *biomod2:::.CV.nnet* in R
 

```{r code_11.4_Artificial_Neural_Networks_b2}
set.seed(555)
CV_nnet = biomod2:::.CV.nnet(Input= mammals_data[,c("bio3",  "bio7", "bio11", "bio12")], Target=mammals_data$VulpesVulpes)
nnet.Final = nnet(mammals_data[,c("bio3",  "bio7", "bio11", "bio12")], mammals_data$VulpesVulpes, size = CV_nnet[1,1], rang = 0.1, decay = CV_nnet[1,2], maxit = 200, trace=F)
```

```{r code_11.4_Artificial_Neural_Networks_b3}
CV_nnet
```

```{r NNET_b4 11.7, opts.label = 'fig_half_page', fig.cap = 'Figure 11. 7: Observed (black=presence, light gray= absence) and potential distribution of Vulpes vulpes modeled using a neural network algorithm with two different sets of SIZE and DECAY. The gray scale of predictions (upper-right and lower-left panels) illustrates shows habitat suitability values between 0 (light, unsuitable) and 1 (dark, highly suitable)'}
nnet.Init.pred = predict(nnet.Init, mammals_data[,c("bio3",  "bio7", "bio11", "bio12")])
nnet.Final.pred = predict(nnet.Final, mammals_data[,c("bio3",  "bio7", "bio11", "bio12")])

par(mfrow=c(2,2))
level.plot(mammals_data$VulpesVulpes, XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3,show.scale=F, title="Original data")
level.plot(nnet.Init.pred, XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3,show.scale=F, title="nnet.Init")
level.plot(nnet.Final.pred, XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3,show.scale=F, title="nnet.Final")
par(mfrow=c(1,1))
```


```{r NNET_b5 11.8, opts.label = 'fig_quarter_page', fig.cap = 'Figure 11. 8: Response curve of Vulpes vulpes modeled by neural networks. The red lines represent a first model with reasonable but not optimized parameters set for SIZE and DECAY, while the blue line represents the final model with optimized parameters.'}
rp <- response.plot2(models = c('nnet.Init','nnet.Final'),
                     Data = mammals_data[,c("bio3", "bio7", "bio11", "bio12")],
                     show.variables = c("bio3",  "bio7", "bio11", "bio12"),
                     fixed.var.metric = 'mean', plot = FALSE, use.formal.names = TRUE)

gg.rp <- ggplot(rp, aes(x = expl.val, y = pred.val, lty = pred.name)) +
  geom_line() + ylab("prob of occ") + xlab("") + 
  rp.gg.theme + 
  facet_grid(~ expl.name, scales = 'free_x')
print(gg.rp)

```

## Chapter 12: Boosting and bagging approaches
### 12.2	Random Forests


```{r code_12.2_ Random_Forests_b1}
set.seed(555)
RP.PantheraOnca = rpart(mammals_data$PantheraOnca ~ bio3+bio7+bio11+bio12, data=mammals_data, control = rpart.control(xval = 10), method="class")
```
 

```{r RF_b2 12.1, opts.label = 'fig_half_page', fig.cap = 'Figure 12.1. Classification tree for Panthera onca using the rpart() function.'}
plot(RP.PantheraOnca, uniform=F, margin = 0.1, branch = 0.5, compress=T)
text(RP.PantheraOnca, cex=0.8)
```

```{r code_12.2_ Random_Forests_b3}
trees = vector(mode = "list", length = 50)
n <- nrow(mammals_data)
boot = rmultinom(length(trees), n, rep(1, n)/n)
```

```{r code_12.2_ Random_Forests_b4}
Full_tree = rpart(mammals_data$PantheraOnca~ bio3+bio7+bio11+bio12, data=mammals_data, control = rpart.control(xval = 0), method="class" )

for(i in 1:length(trees)) {
  trees[[i]] <- update(Full_tree, weights = boot[,i])	
}
```

```{r code_12.2_ Random_Forests_b5}
table(sapply(trees, function(x) as.character(x$frame$var[1])))
table(sapply(trees, function(x) as.character(x$frame$var[3])))
table(sapply(trees, function(x) as.character(x$frame$var[5])))
table(sapply(trees, function(x) as.character(x$frame$var[10])))
```



```{r code_12.2_ Random_Forests_b6}
Pred <- matrix(0, nrow = n, ncol = length(trees))

for (i in 1:length(trees)) {
  # extract the prediction for each of the trees
	Pred[,i] <- predict(trees[[i]], newdata = mammals_data[,c("bio3", "bio7", "bio11", "bio12")], type='prob')[,2]
  # remove potential predictions with a negative weight in the bootstrap procedure
	Pred[boot[,i] < 0,i] <- NA	
}
## calculate the average probability of occurrence (e.g. habitat suitability)
Pred.AVG <- rowMeans(Pred, na.rm = TRUE) 
```


```{r code_12.2_ Random_Forests_b7}
require(pROC,quietly=T)
roc_AVG <- roc(mammals_data$PantheraOnca, Pred.AVG, percent=T)
AUC_AVG <- as.numeric(auc(roc_AVG))
AUC_AVG

roc_RP <- roc(mammals_data$PantheraOnca, predict(RP.PantheraOnca, type='prob')[,2], percent=T)
AUC_RP <- as.numeric(auc(roc_RP))
AUC_RP
```

```{r code_12.2_ Random_Forests_b8}
library(randomForest)
RF = randomForest(x = mammals_data[,c("bio3",  "bio7", "bio11", "bio12")],y = as.factor(mammals_data$VulpesVulpes), ntree = 1000, importance = TRUE)
```


```{r code_12.2_ Random_Forests_b9}
importance(RF)
```


```{r RF_b10 12.2, opts.label = 'fig_quarter_page', fig.cap = 'Figure 12. 2: Observed (left; black=presence, light gray= absence) and potential distribution (right) of red fox modeled using random forest. The gray scale of predictions illustrates shows habitat suitability values between 0 (light, unsuitable) and 1 (dark, highly suitable)'}
RF.pred = predict(RF, type="prob")[,2]

par(mfrow=c(1,2))
level.plot(mammals_data$VulpesVulpes, XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3,show.scale=F, title="Original data")
level.plot(RF.pred, XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3,show.scale=F, title="RF")
par(mfrow=c(1,1))
```


```{r RF_b11 12.3, opts.label = 'fig_quarter_page', fig.cap = 'Figure 12. 3: RF response curve for the red fox.'}
rp <- response.plot2(models = c('RF'),
                     Data = mammals_data[,c("bio3", "bio7", "bio11", "bio12")],
                     show.variables = c("bio3",  "bio7", "bio11", "bio12"),
                     fixed.var.metric = 'mean', plot = FALSE, use.formal.names = TRUE)

gg.rp <- ggplot(rp, aes(x = expl.val, y = pred.val, lty = pred.name)) +
  geom_line() + ylab("prob of occ") + xlab("") + 
  rp.gg.theme + 
  facet_grid(~ expl.name, scales = 'free_x')
print(gg.rp)
```
 

### 12.3	Boosted Regression Trees

```{r code_12.3_Boosted_Regression_Trees_b1}
library(gbm)
### Note that this line of code takes quite a longbit of time to run.
GBM.mod <- gbm(VulpesVulpes~ bio3+bio7+bio11+bio12, data=mammals_data, distribution = "bernoulli", n.trees = 10000, 	interaction.depth = 3, shrinkage = 0.01, bag.fraction = 0.5, cv.folds=10)
```


```{r GBM_b2 12.4, opts.label = 'fig_quarter_page', fig.cap = 'Figure 12. 4:  Optimal number of iterations (trees) for the GBM object. The Y-axis represents the error of the model in function of the total number of trees (X-axis). The black line represents the error of the calibrated model with all data, while the green line represents the error from the cross-validation runs.'}
gbm.mod.perf = gbm.perf(GBM.mod, method = "cv", plot.it = T)
```


```{r code_12.3_Boosted_Regression_Trees_b3}
summary(GBM.mod, method=relative.influence, plotit=F)
summary(GBM.mod, method=permutation.test.gbm, plotit=F)
```

```{r GBM_b4 12.5, opts.label = 'fig_half_page', fig.cap = 'Figure 12. 5: Response curves of Vulpes vulpes as a function of the explanatory variables built using the plot.gbm function in the GBM package.'}
par(mfrow=c(2,2)) 
for(i in 1:ncol(mammals_data[,c("bio3",  "bio7", "bio11", "bio12")]))
plot(GBM.mod, n.trees =gbm.mod.perf, i.var=i)
par(mfrow=c(1,1)) 
```


```{r GBM_b5 12.6, opts.label = 'fig_whole_page', fig.cap = 'Figure 12. 6: Response curves of red fox as a function of one (a) or two (b) explanatory variables at a time.'}
library(cowplot)

# Univariate response curves
rp <- response.plot2(models = c('GBM.mod'),
                     Data = mammals_data[,c("bio3", "bio7", "bio11", "bio12")],
                     show.variables = c("bio3",  "bio7", "bio11", "bio12"),
                     fixed.var.metric = 'mean', plot = FALSE, use.formal.names = TRUE)

gg.rp <- ggplot(rp, aes(x = expl.val, y = pred.val, lty = pred.name)) +
  geom_line() + ylab("prob of occ") + xlab("") + 
  rp.gg.theme + 
  facet_grid(~ expl.name, scales = 'free_x')

# Bivariate response curves
rp.2D <- response.plot2( models = c('GBM.mod'),
                         Data = mammals_data[,c("bio3", "bio7", "bio11", "bio12")],
                         show.variables = c("bio3",  "bio7", "bio11", "bio12"),
                         fixed.var.metric = 'median', 
                         do.bivariate=T,
                         plot = FALSE, use.formal.names = TRUE )

gg.rp.2D <- ggplot(rp.2D, aes(x = expl1.val, y = expl2.val, fill = pred.val)) +
  geom_raster() + rp.gg.theme  + ylab("") + xlab("") + theme(legend.title = element_text()) +
  scale_fill_gradient(name = "prob of occ.", low = "#f0f0f0", high = "#000000") + 
  facet_grid(expl2.name ~ expl1.name, scales = 'free')

plot_grid(gg.rp, gg.rp.2D, labels=c("(a)", "(b)"), ncol = 1, nrow = 2, rel_heights = c(1,2))
```


```{r GBM_b6 12.7, opts.label = 'fig_quarter_page', fig.cap = 'Figure 12. 7: Observed (left; black=presence, light gray= absence) and potential distributions (right) of the red fox modelled using a boosted regression tree approach. The gray scale of predictions showsshows habitat suitability values between 0 (light, unsuitable) and 1 (dark, highly suitable)'}
GBM.pred <- predict(GBM.mod, newdata=mammals_data[,c("bio3",  "bio7", "bio11", "bio12")], type="response", n.trees=gbm.mod.perf)

par(mfrow=c(1,2))
level.plot(mammals_data$VulpesVulpes, XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3,show.scale=F, title="Original data")
level.plot(GBM.pred, XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3,show.scale=F, title="GBM")
```


## Chapter 13: Maximum Entropy
### 13.2	Maxent in R


Maxent.jar should be placed in the same directory as the R workspace (getwd())

```{r code_13.2_Maxent_in_R_b1}
## The folders 'book.data' should be in the a directory just a before your working directory
## test if the data directory is well located (i.e. in dirname(getwd()))
parent.dir <- dirname(getwd()) ## get the name of the directory where data dir should be
any(file.exists('data', parent.dir)) ## ok if return TRUE
dir.create("MaxEnt.res")
MaxEnt.layers.dir <- "../data/tabular/bioclim"
MaxEnt.samples.dir <- "../data/tabular/species"
MaxEnt.out.dir <- "MaxEnt.res"
MaxEnt.soft.path <- "../data/maxent.jar" ## the path to maxent.jar file
Java.soft.path <- "C:/Program Files (x86)/Java/jre1.8.0_101/bin/java.exe" #
# the path to java software binaries => to be adapted according to your computer settings
```

```{r code_13.2_Maxent_in_R_b2}
list.files(MaxEnt.layers.dir, pattern=".asc", recursive=T)
```


```{r code_13.2_Maxent_in_R_b3}
list.files(MaxEnt.samples.dir, pattern=".csv")
```



```{r code_13.2_Maxent_in_R_b4}
## define the shell command we want to execute
maxent.cmd <- paste0('"', Java.soft.path, '" -mx512m -jar "', MaxEnt.soft.path, '" environmentallayers="', 
                     file.path(MaxEnt.layers.dir, 'current', 'ascii'), '" samplesfile="', 
                     file.path(MaxEnt.samples.dir, 'VulpesVulpes.csv'), '" projectionlayers="', 
                     file.path(MaxEnt.layers.dir, 'current', 'bioclim_table.csv'), '" outputdirectory="', 
                     MaxEnt.out.dir, '"  outputformat=logistic maximumiterations=500 jackknife visible=FALSE redoifexists autorun nowarnings notooltips')
## run Maxent
system(command = maxent.cmd)
#system(command = maxent.cmd,  wait = TRUE, intern = TRUE, ignore.stdout = FALSE, ignore.stderr = FALSE)
```

```{r code_13.2_Maxent_in_R_b5}
list.files(MaxEnt.out.dir)
```


```{r code_13.2_Maxent_in_R_b6}
Maxent.pred_AllFeatures <- read.csv(file.path(MaxEnt.out.dir, 'VulpesVulpes_bioclim_table.csv'))
```


```{r Maxent_b7 13.1, opts.label = 'fig_quarter_page', fig.cap = 'Figure 13. 1: Observed (left; black=presence, light gray= absence) and potential distribution (right) of the red fox modeled using Maxent in batch mode from R. The gray scale of predictions shows habitat suitability values between 0 (unsuitable) and 1 (highly suitable).'}
par(mfrow=c(1,2))
level.plot(mammals_data$VulpesVulpes, XY=mammals_data[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3, level.range=c(0,1), show.scale=F, title="Original data")
level.plot(Maxent.pred_AllFeatures[,3], XY=Maxent.pred_AllFeatures[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3,show.scale=F, title="MAXENT", level.range=c(0,1))
```

```{r code_13.2_Maxent_in_R_b8}
Maxent.results <- read.csv("MaxEnt.res/maxentResults.csv")
names(Maxent.results)
```



```{r code_13.2_Maxent_in_R_b9, opts.label = 'fig_quarter_page', fig.cap = 'Figure 13. 2: Heuristic estimate of relative contributions of the four environmental variables to the Maxent model using a jackknife procedure.'}
par(mfrow=c(1,1))
barplot(as.matrix(Maxent.results[1,c(8:11)]), horiz = F, cex.names = 1, names = sub(".contribution$", "", names(Maxent.results[1,c(8:11)])), xlab = "Jackknife importance")
``` 
 
 
```{r code_13.2_Maxent_in_R_b10}
## define the shell command we want to execute
maxent.cmd <- paste0('"', Java.soft.path, '" -mx512m -jar "', MaxEnt.soft.path, '" environmentallayers="', 
                     file.path(MaxEnt.layers.dir, 'current', 'ascii'), '" samplesfile="', 
                     file.path(MaxEnt.samples.dir, 'VulpesVulpes.csv'), '" projectionlayers="', 
                     file.path(MaxEnt.layers.dir, 'current', 'bioclim_table.csv'), '" outputdirectory="', 
                     MaxEnt.out.dir, '"  outputformat=logistic nowarnings nolinear noquadratic nothreshold noproduct maximumiterations=500 jackknife visible=FALSE redoifexists autorun nowarnings notooltips')
## run Maxent
system(command = maxent.cmd)

Maxent.pred_Hinge <- read.csv('MaxEnt.res/VulpesVulpes_bioclim_table.csv')
```

```{r Maxent_b11 13.3, opts.label = 'fig_quarter_page', fig.cap = 'Figure 13.3 Comparison between the potential distribution (right) of the red fox modeled using Maxent with all feature (by default) and the one from Maxent with only the hinge feature selected. The gray scale of predictions shows habitat suitability values between 0 (unsuitable) and 1 (highly suitable).'}
par(mfrow=c(1,2))
level.plot(Maxent.pred_AllFeatures[,3], XY=Maxent.pred_AllFeatures[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3, level.range=c(0,1), show.scale=F, title="MAXENT - all features")
level.plot(Maxent.pred_Hinge[,3], XY=Maxent.pred_Hinge[,c("X_WGS84", "Y_WGS84")], color.gradient = "grey", cex=0.3,show.scale=F, title="MAXENT - hinge feature", level.range=c(0,1))
```


## Chapter 14: Ensemble modeling and modeling averaging 

```{r code_14_Ensemble_modeling_and_modeling_averaging_b1}
library(biomod2)
### Load species and environmental data at lower resolution (100x100km)
DataSpecies <- read.csv(system.file("external/species/mammals_table.csv", package="biomod2"))

require(raster)
myExpl = stack( system.file( "external/bioclim/current/bio3.grd",package="biomod2"), system.file( "external/bioclim/current/bio4.grd", package="biomod2"), system.file( "external/bioclim/current/bio7.grd", package="biomod2"), system.file( "external/bioclim/current/bio11.grd", package="biomod2"), system.file( "external/bioclim/current/bio12.grd", package="biomod2"))
```

Extract the environmental layers for the presence and absence points. 

```{r code_14_Ensemble_modeling_and_modeling_averaging_b2}
Env <- extract(myExpl,DataSpecies[,c(2,3)])
```

Combine the presence/absence data and the extracted environmental data.
```{r code_14_Ensemble_modeling_and_modeling_averaging_b3}
DataSpecies <- cbind(DataSpecies,Env)
```

Load the required packages
```{r code_14_Ensemble_modeling_and_modeling_averaging_b4}
library(MASS); library(mgcv); library(earth); library(rpart);library(mda)
library(Hmisc)  # would be used for model evaluation using the AUC approach
```

```{r code_14_Ensemble_modeling_and_modeling_averaging_b5}
nCV <- 20 # Number of cross-validations
nRow <- nrow(DataSpecies)
```

```{r code_14_Ensemble_modeling_and_modeling_averaging_b6}
Test_results <- as.data.frame(matrix(0,ncol=nCV,nrow=5, dimnames=list(c("GLM","GAM","MARS","FDA","RF"), NULL)))
```

```{r code_14_Ensemble_modeling_and_modeling_averaging_b7}
Pred_results <- array(0,c(nRow, 5,nCV), dimnames=list(seq(1:nRow), c("GLM","GAM","MARS","FDA","RF"), seq(1:nCV)))
```


```{r code_14_Ensemble_modeling_and_modeling_averaging_b8}
for(i in 1:nCV){
#separate the original data in one sub set for calibration and the other for evaluation. 
  a <- SampleMat2(ref=DataSpecies$VulpesVulpes, ratio=0.7) # function from the biomod2 package
  calib <- DataSpecies[a$calibration,]
  eval <- DataSpecies[a$evaluation,]
  
  ###  GLM ###
  glmStart <- glm(VulpesVulpes~1, data=calib, family=binomial)
  glm.formula <- makeFormula("VulpesVulpes",DataSpecies[,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 on the evaluation data and evaluation using the AUC approach
  Pred_test <-  predict(glmModAIC, eval, type="response") 
  Test_results["GLM",i] <- somers2(Pred_test,eval$VulpesVulpes)["C"]

  # prediction on the total dataset
  Pred_results[,"GLM",i] <- predict(glmModAIC, DataSpecies, type="response")
  
  ### 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 AUC approach
  Pred_test <-  predict(gam_mgcv, eval, type="response")
  Test_results["GAM",i] <- somers2(Pred_test,eval$VulpesVulpes)["C"]
  
# prediction on the total dataset
  Pred_results[,"GAM",i] <- predict(gam_mgcv, DataSpecies, type="response")
  
  ### 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 AUC approach
  Pred_test <-  predict(Mars_int2, eval, type="response")
  Test_results["MARS",i] <- somers2(Pred_test, eval$VulpesVulpes)["C"]

  # prediction on the total dataset
  Pred_results[,"MARS",i] <- predict(Mars_int2, DataSpecies, type="response")
  
  ### FDA ###
  fda_mod = fda(VulpesVulpes ~ 1+bio3+bio7+bio11+bio12, data=calib,method=mars)
  # prediction on the evaluation data and evaluation using the AUC approach
  Pred_test <-  predict(fda_mod, eval, type = "posterior")[,2]
  Test_results["FDA",i] <- somers2(Pred_test, eval$VulpesVulpes)["C"]

  # prediction on the total dataset
  Pred_results[,"FDA",i] = predict(fda_mod, DataSpecies[,c("bio3",  "bio7", "bio11", "bio12")], type = "posterior")[,2]
  
  ### Random Forest ###  
    RF_mod = randomForest(x = calib[,c("bio3",  "bio7", "bio11", "bio12")],y = as.factor(calib$VulpesVulpes), ntree = 1000, importance = TRUE)
  # prediction on the evaluation data and evaluation using the AUC approach
  Pred_test <-  predict(RF_mod, eval, type="prob")[,2]
  Test_results["RF",i] <- somers2(Pred_test,eval$VulpesVulpes)["C"]  

  # prediction on the total dataset
  Pred_results[,"RF",i] = predict(RF_mod, DataSpecies, type="prob")[,2]
}  
```


```{r EM_b9 14.1, opts.label = 'fig_quarter_page', fig.cap = 'Figure 14. 1: Variation in the area under the receiver operating characteristic curve (AUC) amongst the cross-validation runs and between the different models.'}
library(ggplot2)
AUC <- unlist(Test_results)
AUC <- as.data.frame(AUC)
Test_results_ggplot <- cbind(AUC, model=rep(rownames(Test_results), times=20))

p <- ggplot(Test_results_ggplot, aes(model, AUC))
p + geom_boxplot()
```



```{r EM_b10 14.2, opts.label = 'fig_quarter_page', fig.cap = 'Figure 14.2: Probability density functions of the habitat suitability obtained for a given pixel across the different cross-validation runs, for each of the five modeling techniques.'}
Pred_results[143,,] # select pixel 143 for which the species is predicted present by all models. 

HSM <- unlist(as.data.frame(Pred_results[143,,]))
HSM <- as.data.frame(HSM)
Prob_density_ggplot <- cbind(HSM, model=rep(rownames(Pred_results[143,,]), times=20))

ggplot(Prob_density_ggplot, aes(x=HSM, fill=model)) +  geom_density(alpha=0.5) 
```

```{r EM_b11 , opts.label = 'fig_quarter_page', fig.cap = 'Figure: Probability density functions of the habitat suitability obtained for a given pixel across the different cross-validation runs, for each of the five modeling techniques.'}
### Average prediction (mean and median) and variance
Pred_total_mean <- apply(Pred_results,1,mean)
Pred_total_median <- apply(Pred_results,1,median)
Pred_total_sd <- apply(Pred_results,1,sd)
```

 

```{r EM_b12 14.3, opts.label = 'fig_half_page', fig.cap = 'Figure 13. 6: Observed presence and absence of Vulpes vulpes at the global scale (top left), together with the two model averaging predictions (mean and median; top right and bottom-left) and the ensemble modeling uncertainty (sd; bottom-right).'}
Obs <- rasterFromXYZ(DataSpecies[,c("X_WGS84", "Y_WGS84", "VulpesVulpes")])
Pred_total_mean_r <- rasterFromXYZ(cbind(DataSpecies[,c("X_WGS84", "Y_WGS84")],Pred_total_mean))
Pred_total_median_r <- rasterFromXYZ(cbind(DataSpecies[,c("X_WGS84", "Y_WGS84")],Pred_total_median))
Pred_total_sd_r <- rasterFromXYZ(cbind(DataSpecies[,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")

plot(Out)
```