---
title: "3 - Parameterising landscape and dispersal"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{3 - Parameterising landscape and dispersal}
  %\VignetteEncoding{UTF-8}
  %\VignetteEngine{knitr::rmarkdown}
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---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

To simulate epidemics in a heterogeneous landscape, *landsepi* needs (among others) these three elements which are 
related one each other:  
- the spatial coordinates of fields composing the landscape (represented as polygons),  
- the allocation of croptypes in the different fields,  
- a dispersal matrix for between-field pathogen migration.  

*landsepi* includes built-in landscapes (and associated dispersal matrices for rust pathogens) and an algorithm to 
allocate croptypes, but is it possible to use your own landscape, dispersal matrix and croptype allocation. 

## Using your own landscape

Any landscape can be used to simulate epidemics in *landsepi*, provided that it is in *sp* or *sf* format and 
contains, at least, polygon coordinates.

```{r, eval=FALSE}
library(sf)
mylandscape <- st_read(dsn = "myshapefile.shp")
library(landsepi)
simul_params <- createSimulParams(outputDir = getwd())
simul_params <- setLandscape(simul_params, mylandscape)
simul_params@Landscape
```

Then you can simply call the method __allocateLandscapeCroptypes__ to allocate croptypes to the fields of 
the landscape with controlled proportions and spatio-temporal aggregation 
(*see tutorial on how to [run a simple simulation](O1-run_simple_simul.html)*). 
Otherwise, you can use your own allocation (see below).


## Using your own croptype allocation

You must define for each year of simulation the index of the croptype ("croptypeID") cultivated in each feature 
(polygons). Each feature has a field identified by "year_XX" (XX <- seq(1:Nyears+1)) and containing the croptype ID. 
Note that the allocation must contain one more year than the real number of simulated years (this is only for 
simulation purpose, the content of the allocation in year Nyears+1 does not affect the result).
  

| Features/fields | year_1 | year_2 | ... year_Nyears+1 |
|---------------- | ------ | ------ | ----------------- |
| polygons1       | 13     | 10     | 13                |
| polygonsX       | 2      | 1      | 2                 |
| ...             |        |        |                   |

An example for sf landscape:  
```{r, eval=FALSE}
mylandscape$year_1 <- c(13,2,4,1,1) # croptypes ID allocated to the different polygons
mylandscape$year_2 <- c(2,2,13,1,1)
```

Then simply add your landscape to the simulation parameters:  
```{r, eval=FALSE}
simul_params <- setLandscape(simul_params, mylandscape)
simul_params@Landscape
```


## Computing the dispersal matrix

To simulate pathogen dispersal, *landsepi* needs a vectorized matrix giving the probability 
of propagule dispersal from any field of the landscape to any other field. 
**This matrix must be computed before running any simulation with *landsepi*.** 
It is a square matrix whose size is the number of fields in the landscape and whose elements are, 
for each line $i$ and each column $i'$ the probability $\mu_{ii'}$ that propagules migrate 
from field $i$ (whose area is $A_i$) to field $i'$ (whose area is $A_{i'}$). This probability 
is computed from:  
$$\mu_{ii'} = \frac { \int_{A_i} \int_{A_{i'}} g(\mid\mid z'-z \mid\mid).dz.dz' } { A_i }$$  
with $\mid\mid z'-z \mid\mid$ the Euclidian distance between locations $z$ and $z'$ in fields $i$ and $i'$, 
respectively, and $g(.)$ the two-dimensional dispersal kernel of the propagules. Note that 
$\sum_i \mu_{ii'} = 1$.  

*landsepi* includes built-in dispersal matrices to represent rust dispersal in the 
five built-in landscapes. These have been computed from a power-law dispersal kernel:
$$g(\mid\mid z'-z \mid\mid) = \frac {(b-2).(b-1)} {2.\pi.a^2} . (1+ \frac {\mid\mid z'-z \mid\mid} {a})^{-b}$$
with $a$ the scale parameter and $b$ a parameter related to the width of the dispersal kernel.

**A new dispersal matrix must be computed to run simulations with a different landscape or a 
different dispersal kernel.**  

The computation of $\mu_{ii'}$ is performed using the CaliFloPP algorithm from the R package *RCALI*.
The *RCALI* package has a limited number of built-in dispersal kernels. 
However, users can code for their own dispersal kernel. 
See section "Details" in the documentation of the function `califlopp` to learn how to implement 
your own kernel.   
 
***

#### An example

Here is an example illustrating the computation of the dispersal matrix on the first landscape supplied in *landsepi*.
```{r, eval=FALSE}
install.packages("RCALI")
library(RCALI)
library(landsepi)
landscape <- landscapeTEST1
Npoly <- length(landscape)
Npoly
plot(landscape)
```

For compatibility with the function `califlopp`, the landscape can be modified with specific functions 
of package *sf* relative to geographic projection (`st_transform`), polygon simplification (`st_simplify`).

The function `califlopp` needs a specific format for the coordinates of each polygon 
(i.e. fields) composing the landscape.
```{r, eval=FALSE}
file_land <- "land_rcali.txt"  ## input for califlopp
file_disp <- "disp_rcali.txt"  ## output for califlopp (DO NOT WRITE A PATH)

## Formatting the polygons-file for califlopp
cat(Npoly, file=file_land)
for (k in 1:Npoly) {
  ## extract coordinates of polygon vertices
  coords <- landscape@polygons[[k]]@Polygons[[1]]@coords 
  ## alternatively:
  # coords <- as.data.frame(landscape$geometry[[k]][[1]])
  n <- nrow(coords)
  cat(NULL, file=file_land, append=T, sep="\n")
  cat(c(k,k,n), file=file_land, append=T, sep="\t")
  cat(NULL, file=file_land, append=T, sep="\n")
  cat(coords[1:n,1], file=file_land, append=T, sep="\t")
  cat(NULL,file=file_land,append=T,sep="\n")
  cat(coords[1:n,2], file=file_land, append=T, sep="\t")
}
cat(NULL, file=file_land, append=T, sep="\n")
```

Then the function `califlopp` calculates the flow of particles between polygons 
using an integration method. Here we use the dispersal kernel of oilseed rape pollen 
(available in *RCALI*: use `dispf=1` in the arguments of function `califlopp`, 
see `?califlopp` for details).
```{r, eval=FALSE}
param <- list(input=2, output=0, method="cub", dp=6000, dz=6000
              , warn.poly=FALSE, warn.conv=FALSE, verbose=FALSE)
califlopp(file=file_land, dispf=1, param=param, resfile=file_disp)
```

The *RCALI* package has a limited number of built-in dispersal kernels (dispf = 1 in our example). 
However, users can code for their own dispersal kernel (let say the name of your kernel is `f`) 
using `dispf=f` in the function `califlopp`:
```{r, eval=FALSE}
my_df <-function(x, a=40, b=7) ((b-2)*(b-1)/(2*a^2*pi)*(1+(abs(x)/a))^(-b))

param <- list(input=2, output=0, method="cub", dp=6000, dz=6000, warn.poly=FALSE,
              warn.conv=FALSE, verbose=FALSE)
califlopp(file=file_land, dispf=my_df, param=param, resfile=file_disp)
```
However, if there are many polygons in the landscape, computations may be long. 
In this situation, we recommend to replace one of the built-in functions of RCALI by your own function 
in the source code, and to recompile RCALI. 
See paragraph "The individual dispersion functions" in the details of the documentation of the 
califlopp function (`?califlopp`). 

The output of califlopp must then be reformatted to generate the dispersal matrix that will 
be further used in *landsepi*. 
The vector of field areas can also be generated.
```{r, eval=FALSE}
## Import califlopp results
disp_df <- getRes(file_disp)
## Double the table because only half of the flows have been calculated
emitter <- c(disp_df$poly1, disp_df$poly2)
receiver <- c(disp_df$poly2, disp_df$poly1)

## Write a text file containing a vector of areas of all polygons
area_e <- c(disp_df$area1, disp_df$area2)
area_r <- c(disp_df$area2, disp_df$area1)
area <- as.vector(by(area_e, emitter, mean))
write(area, file="area.txt", sep=",")

## Generation of the dispersal matrix
name_f <- "mean.flow"
flow_mean <- c(disp_df[,name_f], disp_df[,name_f])
flow_f <- cbind(emitter, receiver, flow_mean, area_e, area_r)

## Remove the doublons (i.e. half the lines where emitter == receiver)
flow_f[1:nrow(disp_df),][(disp_df$poly2 - disp_df$poly1) == 0,] <- NA
flow_f <- flow_f[is.na(apply(flow_f, 1, sum)) == F,]
flow_f <- as.data.frame(flow_f)
colnames(flow_f) <- c("emitter", "receiver", "flow", "area_e", "area_r")
flow_f <- flow_f[order(flow_f$emitter),]

## lines: emitter
## columns: receiver
matrix_f <- NULL
for(k in 1:Npoly){
  ## flow divided by the emitter area
  matrix_f <- cbind(matrix_f, flow_f$flow[flow_f$receiver==k] / area)
}

## Normalisation of the matrix (reflecting boundaries)
## (do not normalise for absorbing boundaries)
flowtot_f <- apply(matrix_f,1,sum)
for(k in 1:Npoly){
  matrix_f[k,] <- (matrix_f[k,] / flowtot_f[k]) ## In order to have sum == 1
}

write(as.vector(matrix_f), file="dispersal.txt", sep=",")
```

Then, to read the file, use:
```{r, eval=FALSE}
disp_patho <- scan("dispersal.txt", sep=",")
```

## Plotting landscape and dispersal

Landscape structure can be plotted using the basic function `plot()`, or using the landsepi function 
`plotland()`:
```{r, eval=FALSE}
landscape <- landscapeTEST1
plot(landscape)
plotland(landscape)
```

To highlight a specific field:
```{r, eval=FALSE}
poly <- 10
colFields <- rep("white", length(landscape))
colFields[poly] <- "red"
plot(landscape, col = colFields)
```

To check the dispersal matrix and represent in a graphic the flow emitted by a specific polygon, use:
```{r, eval=FALSE}
## convert dispersal in matrix
mat <- matrix(disp_patho, nrow=sqrt(length(disp_patho)))
poly <- 1
dispToPlot <- log10(mat[poly,] +1E-20)  ## 1E-20 to avoid log(0)

## Colour palette
nCol <- 11
whiteYellowRed <- colorRampPalette(c("white", "#FFFF99", "#990000"))
col_disp <- whiteYellowRed(nCol)
intvls <- seq(min(dispToPlot) - 1, max(dispToPlot) + 1, length.out=nCol)
intvls_disp <- findInterval(dispToPlot, intvls)

## Plot
plot(landscape, col = col_disp[intvls_disp], main=paste("Dispersal from polygon", poly))
```

With package *ggplot2*:
```{r, eval=FALSE}
library(ggplot2)
ggplot(landscape) + ggtitle(paste("Dispersal from polygon", poly)) +
    geom_sf(colour="black", aes(fill = dispToPlot)) + 
    scale_fill_gradientn(name="Prob. of\ndispersal", colours=rev(heat.colors(10)), breaks=-1:-10, labels=10^(-1:-10)) +
    # theme_classic() +
    theme(axis.line=element_blank(),axis.text.x=element_blank(),
          axis.text.y=element_blank(),axis.ticks=element_blank(),
          axis.title.x=element_blank(),
          axis.title.y=element_blank(),
          panel.background=element_blank(),panel.border=element_blank(),panel.grid.major=element_blank(),
          panel.grid.minor=element_blank(),plot.background=element_blank())
```