Punctual scale model
At punctual scale, the model only requires a weather station temperature time series provided as a numerical matrix (in degree Celsius). For the purpose of this tutorial, we simulate a 1-year long temperature time series.
Simulate temperature data with seasonal trend
We first simulate a 1-year temperature time series with seasonal trend. For the time series we consider a mean value of 16°C and standard deviation of 2°C.
ndays = 365*1 #length of the time series in days
set.seed(123)
sim_temp <- create_sims(n_reps = 1,
n = ndays,
central = 16,
sd = 2,
exposure_type = "continuous",
exposure_trend = "cos1", exposure_amp = -1.0,
average_outcome = 12,
outcome_trend = "cos1",
outcome_amp = 0.8,
rr = 1.0055)A visualisation of the distribution of temperature values and temporal trend.
plot(sim_temp[[1]]$date,
sim_temp[[1]]$x,
main="Simulated temperatures seasonal trend",
xlab="Date", ylab="Temperature (°C)"
)
Format the simulated input datasets and run the model
Model settings
Float numbers in the temperature matrix would slow the computational speed, they must be multiplied by 1000 and then transformed in integer numbers. We also transpose the matrix from long to wide format, since we conceptualised the model structure considering the rows as the spatial component (e.g. observations; here = 1) and the columns as the temporal one (e.g. variables).
df_temp <- data.frame("Date" = sim_temp[[1]]$date, "temp" = sim_temp[[1]]$x)
w <- t(as.integer(df_temp$temp*1000))We are now left with a few model parameters which need to be defined by the user.
## Define the day of introduction (August 1st is day 1)
str = 213
## Define the end-day of life cycle (September 1st is the last day)
endr = 213+31
## Define the number of eggs to be introduced
ie = 100
## Define the number of model iterations
it = 1 # The higher the number of simulations the better
## Define the number of liters for the larval density-dependent mortality
habitat_liters=1
#Define latitude and longitude for the diapause process
myLat=42
myLon=7
## Define the number of parallel processes (for sequential itarations set nc=1)
cl = 1
## Set output name for the *.RDS output will be saved
#outname= paste0("dynamAedes_albo_ws_dayintro_",str,"_end",endr,"_niters",it,"_neggs",ie)Run the model
Running the model with the settings specified in this example takes about 2 minutes.
Analyse the results
We first explore the model output structure: the simout object is a nested list.
The first level corresponds to the number of model iterations
# [1] 1# [1] 1The second level corresponds to the simulated days. So if we inspect the first iteration, we observe that the model has computed 62 days, as we had specified above in the object endr.
# [1] 32The third level corresponds to the amount of individuals for each stage (rows). So if we inspect the 1st and the 62th day within the first iteration, we obtain a matrix having
# [1] 4 1# [,1]
# egg 100
# juvenile 34
# adult 0
# diapause_egg 0# [,1]
# egg 783
# juvenile 1726
# adult 240
# diapause_egg 0We can now use the auxiliary functions of the package to analyse the results.
Derive probability of a successfull introduction at the end of the simulated period
First, we can retrieve the “probability of successful introduction”, computed as the proportion of model iterations that resulted in a viable mosquito population at a given date.
# Days_after_intro p_success stage
# 1 Day 31 1 PopulationDerive abundance 95% CI for each life stage and in each day
We now compute the interquantile range abundance for all the stages of the simulated population using the function adci.
dd <- max(sapply(simout, function(x) length(x)))#retrieve the maximum number of simulated days
egg <- as.data.frame(adci(simout, eval_date=1:dd, breaks=c(0.25,0.50,0.75), st=1))
juv <- as.data.frame(adci(simout, eval_date=1:dd, breaks=c(0.25,0.50,0.75), st=2))
ad <- as.data.frame(adci(simout, eval_date=1:dd, breaks=c(0.25,0.50,0.75), st=3))
eggd <- as.data.frame(adci(simout, eval_date=1:dd, breaks=c(0.25,0.50,0.75), st=4))
egg$myStage="Egg"
egg$Date=seq.Date(sim_temp[[1]]$date[str], sim_temp[[1]]$date[endr], by="day")
juv$myStage="Juvenile"
juv$Date=seq.Date(sim_temp[[1]]$date[str], sim_temp[[1]]$date[endr], by="day")
ad$myStage="Adult"
ad$Date=seq.Date(sim_temp[[1]]$date[str], sim_temp[[1]]$date[endr], by="day")
eggd$myStage="Diapausing egg"
eggd$Date=seq.Date(sim_temp[[1]]$date[str], sim_temp[[1]]$date[endr], by="day")
outdf=bind_rows(egg, juv, ad, eggd) %>%
as_tibble()
outdf %>%
mutate(myStage=factor(myStage, levels= c("Egg", "Diapausing egg", "Juvenile", "Adult"))) %>%
ggplot( aes(y=(`50%`),x=Date, group=factor(myStage),col=factor(myStage))) +
ggtitle("Ae. albopictus Interquantile range abundance")+
geom_line(size=1.2)+
geom_ribbon(aes(ymin=`25%`,ymax=(`75%`),fill=factor(myStage)),
col="white",
alpha=0.2,
outline.type="full")+
labs(x="Date", y="Interquantile range abundance", col="Stage", fill="Stage")+
facet_wrap(~myStage, scales = "free")+
theme_light()+
theme(legend.pos="bottom", text = element_text(size=14) , strip.text = element_text(face = "italic"))
# Local scale model The “local scale” means that the model accounts for both active and passive dispersal of the mosquitoes. With this setting, the model requires three input datasets: a numerical temperature matrix (in degree Celsius) defined in space and time (space in the rows, time in the columns), a two-column numerical matrix reporting the coordinates (in meters) of each space-unit (cell) and a numerical distance matrix which reports the distance in meters between the cells connected through a road network. For the purpose of this tutorial, we will use the following simulated datasets:
- A 5 km lattice grid with 250 m cell size;
- A 1-year long spatially and temporally correlated temperature time series;
- A matrix of distances between cells connected through a simulated road network;
Prepare input data
Create lattice arena
First, we define the physical space into which the introduction of our mosquitoes will happen. We define a squared lattice arena having 5 km side and 250 m resolution (20 colums and 20 rows, 400 total cells).
We then add a spatial pattern into the lattice area. This spatial pattern will be used later to add spatial correllation (SAC) to the temperature time series. The spatial autocorrelated pattern will be obtained using a semivariogram model with defined sill (value that the semivarion attains at the range) and range (distance of 0 spatial correlation) and then predicting the semivariogram model over the lattice grid using unconditional Gaussian simulation.
varioMod <- vgm(psill=0.005, range=100, model='Exp') # psill = partial sill = (sill-nugget)
# Set up an additional variable from simple kriging
zDummy <- gstat(formula=z~1,
locations = ~x+y,
dummy=TRUE,
beta=1,
model=varioMod,
nmax=1)
# Generate a randomly autocorrelated predictor data field
set.seed(123)
xyz <- predict(zDummy, newdata=xy, nsim=1)# [using unconditional Gaussian simulation]We generate a spatially autocorrelated raster adding the SA variable (xyz$sim1) to the RasterLayer object. The autocorrelated surface could for example represent the distribution of vegetation cover in a urban landscape.
utm32N <- "+proj=utm +zone=32 +ellps=WGS84 +datum=WGS84 +units=m +no_defs"
r <- raster(nrow=gridDim, ncol=gridDim, crs=utm32N, ext=extent(0,5000, 0,5000))
values(r)=xyz$sim1
plot(r)
Simulate temperature data with seasonal trend
We take advantage of the temperature dataset simulated for the punctual scale modelling exercise. We can then “expand onto space” the temperature time series by multiplying it with the autocorrelated surface simulated above.
mat <- lapply(1:ncell(r), function(x) {
d_t <- sim_temp[[1]]$x*autocorr_factor[[x]]
return(d_t)
})
mat <- do.call(rbind,mat)A comparison between the distribution of the initial temperature time series and autocorrelated temperature surface
par(mfrow=c(2,1))
hist(mat, xlab="Temperature (°C)", main="Histogram of simulated spatial autocorreled temperature")
hist(sim_temp[[1]]$x, xlab="Temperature (°C)", main="Histogram of simulated temperatures", col="red")
Simulate an arbitrary road segment for medium-range dispersal
In the model we have considered the possiblity of medium-range passive dispersal. Thus, we will simulate an arbitrary road segment along which adult mosquitoes can disperse passively (i.e., through car traffic).
set.seed(123)
pts <- spsample(bbox, 5, type="random")
roads <- spLines(pts)
# Check simulated segment
raster::plot(r)
raster::plot(roads, add=T)
After defining the road segment we add a “buffer” of 250 m around the road segment. Adult mosquitoes that reach or develop into cells comprised in the 250 m buffer around roads are thus able to undergo passive dispersal.
buff <- buffer(roads, width=250)
crs(buff) <- crs(r)
# Check grid, road segment and buffer
raster::plot(r)
raster::plot(buff, add=T)
raster::plot(roads, add=T, col="red")
Next, we derive a distance matrix between cells comprised in the spatial buffer along the road network. First, we select the cells.
df_sp <- df
coordinates(df_sp)=~x+y
df_sp <- raster::intersect(df_sp,buff)
# Check selected cells
raster::plot(r)
raster::plot(buff, add=T)
raster::plot(df_sp, add=T, col="red")
Then, we compute the Euclidean distance between each selected cell.
At local scale, the interpretation of this output is more nuanced than for the other scales: a pixel having psi=0 can be a pixel where all the simulations resulted in an extinction or where the species has not yet arrived through dispersal.
Note that if only a small number of mosquitoes are present in a pixel over many iterations, quantiles may be 0 (especially for low quantiles) and you may see a series of empty rasters!
### Derive abundance 95% CI for each life stage and in each day We can now compute the interquantile range abundance of the simulated population using the function adci over the whole landscape.