3 - Parameterising landscape and dispersal

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.

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). 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).

An example for sf landscape:

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:

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.

install.packages("RCALI")
library(RCALI)
library(landsepi)
landscape <- landscapeTEST1
Npoly <- length(landscape)
Npoly
plot(landscape)

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")

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)

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)

## 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=",")

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():

landscape <- landscapeTEST1
plot(landscape)
plotland(landscape)

To highlight a specific field:

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:

## 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:

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())