04. The uncompressed model output (sub-stage level)

In dynamAedes: A Unified Mechanistic Model for the Population Dynamics of Invasive Aedes Mosquitoes

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This tutorial explains step-by-step the main features of dynamAedes package, a unified modelling framework for invasive Aedes mosquitoes. Users can apply the stochastic, time-discrete and spatially-explicit population dynamical model initially developed in Da Re et al., (2021) for Aedes aegypti and then expanded for other three species: Ae. albopictus, Ae. japonicus and Ae. koreicus Da Re et al., (2022).

The model is driven by temperature, photoperiod and intra-specific larval competition and can be applied to three different spatial scales: punctual, local and regional. These spatial scales consider different degrees of spatial complexity and data availability, by accounting for both active and passive dispersal of the modelled mosquito species as well as for the heterogeneity of input temperature data.

We will describe the uncompressed model application for Ae. albopictus at the punctual and regional scales by using a simulated temperature dataset. The uncompressed model return the number of simulated individuals not only for the three main compartments, i.e. life stages (eggs, juveniles and adults), but also the number of simulated individuals within each sub-compartments, such as 2-days old eggs or host-seeking adult females.

1. Sub-compartment structure

The general structure of the compartments and sub-compartments for the four species can be inspected from the AedeslifeHistoryList object available in the package.

library(dynamAedes)
data(AedeslifeHistoryList)
knitr::kable(AedeslifeHistoryList$speciesheet, align = "ccccc")

For each species, the sub-compartments are arranges as follows.

1.1 Aedes aegypti

species_data <- data.frame(
  Species = rep("*Ae. aegypti*", 6),
  `Sub-compartments` = paste("Sub-compartment", 1:6),
  Eggs = c("New layed egg", "2 day egg", "3 day egg", ">= 4 day egg", NA, NA),
  Juveniles = c("1 day juv", "2 day juv", "3 day juv", "4 day juv", "5 day juv", ">= 6 day juv"),
  Adults = c("blood fed", "ovipositing d1", "ovipositing d2", "Host-seeking", "new emerged", NA)
)

knitr::kable(species_data, format = "markdown", align = c('c', 'c', 'c', 'c', 'c'))

1.2 Aedes albopictus

species_data <- data.frame(
  Species = rep("*Ae. albopictus*", 6),
  `Sub-compartments` = paste("Sub-compartment", 1:6),
  Eggs = c("New layed egg", "2 day egg", "3 day egg", ">= 4 day egg", NA, NA),
  Juveniles = c("1 day juv", "2 day juv", "3 day juv", "4 day juv", "5 day juv", ">= 6 day juv"),
  Adults = c("blood fed", "ovipositing d1", "ovipositing d2", "Host-seeking", "new emerged", NA),
  `Diapausing Eggs` = c("New layed degg", "2 day degg", "3 day degg", ">= 4 day degg", NA, NA)
)
knitr::kable(species_data, format = "markdown", align = c('c', 'c', 'c', 'c', 'c', 'c'))

1.3 Aedes japonicus and Ae. koreicus

species_data <- data.frame(
  Species = rep("*Ae. japonicus* or *Ae. koreicus*", 12),
  `Sub-compartments` = paste("Sub-compartment", 1:12),
  Eggs = c("New layed egg", "2 day egg", "3 day egg", "4 day egg", "5 day egg", 
           "6 day egg", "7 day egg", ">=8 day egg", NA, NA, NA, NA),
  Juveniles = c("1 day juv", "2 day juv", "3 day juv", "4 day juv", "5 day juv", 
                "6 day juv", "7 day juv", "8 day juv", "9 day juv", "10 day juv", 
                "11 day juv", ">=12 day juv"),
  Adults = c("blood fed", "ovipositing d1", "ovipositing d2", "Host-seeking", 
             "new emerged", NA, NA, NA, NA, NA, NA, NA),
  `Diapausing Eggs` = c("New layed degg", "2 day degg", "3 day degg", "4 day degg", 
                        "5 day degg", "6 day degg", "7 day degg", ">=8 day degg", 
                        NA, NA, NA, NA)
)
knitr::kable(species_data, format = "markdown", align = c('c', 'c', 'c', 'c', 'c', 'c'))

2. Punctual scale model

2.1 Input data and model settings

At the punctual scale, the model only requires a temperature time series, recorded by e.g. a weather station, provided as a numerical matrix (in degree Celsius). For the purpose of this tutorial, we simulate a 1-year long temperature time series and, for the sake of brevity, we will not discuss the chunks of code already presented in other tutorials.

#Load packages
# simulate temperatures
library(eesim)
# plotting
library(ggplot2)
Sys.setlocale("LC_TIME", "en_GB.UTF-8")  

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)

# Model settings
## Define the day of introduction (July 1st is day 1)
str <- "2000-07-01"
## Define the end-day of life cycle (August 1st is the last day)
endr <- "2000-08-01"
## Define the number of eggs to be introduced
ie <- 1000
## 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 iterations set nc=1)
cl <- 1
## convert float temperatures to integer
df_temp <- data.frame("Date" = sim_temp[[1]]$date, "temp" = sim_temp[[1]]$x)
w <- t(as.integer(df_temp$temp*1000)[format(as.Date(str)+1,"%j"):format(as.Date(endr)+1,"%j")])

2.2 Run the model

It is crucial to run the model the model specifying the argument compressed.output = FALSE. This will return the number of simulated individuals for each sub-compartments.

simout <- dynamAedes.m(species="albopictus", 
 scale="ws",  
 jhwv=habitat_liters,  
 temps.matrix=w,  
 startd=str, 
 endd=endr,  
 n.clusters=cl, 
 iter=it,  
 intro.eggs=ie,  
 compressed.output=FALSE, 
 lat=myLat, 
 long=myLon,
 verbose=FALSE,
 seeding=TRUE)

2.3 Analyse the results

A first summary of simulations can be obtained with:

summary(simout)

The simout object is a S4 object where the outputs of the model and related details are saved in different slot. For example, the number of model iterations is saved in:

simout@n_iterations

The model output, i.e. the number of simulated individuals, is stored in simout@simulation. For the uncompressed model, simout@simulation is a list where the first level stores the simulation of different iteration, while the second corresponds to the simulated days in the corresponding iteration. If we inspect the first iteration, we observe that the model has computed length(simout[[1]]) days, since we have started the simulation on the 1st of July and ended on the 1st of August.

length(simout@simulation[[1]])

The third level corresponds to an array reporting, for a given iteration and a given day, the number of individuals belonging to each compartment (rows) for each sub-compartment (the third dimension of the array, noted as sc1-...-scN in the print). As example, if we inspect the 1st and the 15th day within the first iteration, we obtain a matrix having:

class(simout@simulation[[1]][[1]])
simout@simulation[[1]][[1]]
simout@simulation[[1]][[15]]

2.4 Derive abundance 95% CI for a specific sub-compartment

We can use the auxiliary functions of the package to analyse the results. We now compute the interquantile range abundance for the host-seeking sub-compartment of the simulated population using the function adci.

# Retrieve the maximum number of simulated days
dd <- max(simout)
# Compute the inter-quartile of abundances along the iterations
breaks <- c(0.25,0.50,0.75)
ed <- 1:dd
hs <- adci(simout, eval_date=ed, breaks=breaks, 
           stage="Adults",
           sub_stage = "Host-seeking" ) 
head(hs)
tail(hs)

We can now simply plot it.

ggplot(hs, aes(x=day, y=X50., group=factor(stage), col=factor(stage))) +
ggtitle("Host-seeking Ae. albopictus Interquantile range abundance") +
geom_ribbon(aes(ymin=X25., ymax=X75., fill=factor(stage)), 
  col="white", 
  alpha=0.2, 
  outline.type="full") +
geom_line(linewidth=0.8) +
ylim(0,10)+
labs(x="Date", y="Interquantile range abundance", col="Stage", fill="Stage") +
theme_classic() +
theme(legend.position="bottom",  
  text = element_text(size=16), 
  strip.text = element_text(face = "italic"))

3. Regional scale model

We can now repeat the exercise for a regional scale model.

library(gstat)
library(terra)
gridDim <- 20 # 5000m/250 m = 20 columns and rows
xy <- expand.grid(x=1:gridDim, y=1:gridDim)
varioMod <- vgm(psill=0.5, 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)
utm32N <- "+proj=utm +zone=32 +ellps=WGS84 +datum=WGS84 +units=m +no_defs"
r <- terra::rast(nrow=gridDim, ncol=gridDim, crs=utm32N, ext=terra::ext(1220000,1225000, 5700000,5705000))
terra::values(r) <- xyz$sim1
# plot(r, main="SAC landscape")

# convert to a data.frame
df <- data.frame("id"=1:nrow(xyz), terra::crds(r))
bbox <- terra::as.polygons(terra::ext(r), crs=utm32N)

# Store Parameters for autocorrelation
autocorr_factor <- terra::values(r)

# "expand onto space" the temperature time series by multiplying it with the autocorrelated surface simulated above. 
mat <- do.call(rbind, lapply(1:ncell(r), function(x) {
    d_t <- sim_temp[[1]]$x*autocorr_factor[[x]]
    return(d_t)
}))

# format simulated temperature
names(mat) <- paste0("d_", 1:ndays)
df_temp <- cbind(df, mat)
w <- sapply(df_temp[,-c(1:3)], function(x) as.integer(x*1000))
# define a two-column matrix of coordinates to identify each cell in the lattice grid.
cc <- df_temp[,c("x","y")]

We run now the regional model keeping the same settings defined for the punctual scale model.

simout <- dynamAedes.m(species="albopictus", 
            scale="rg",  
            jhwv=habitat_liters,  
            temps.matrix=w[,as.numeric(format(as.Date(str),"%j")):as.numeric(format(as.Date(endr),"%j"))],
            coords.proj4=utm32N,
            cells.coords=as.matrix(cc),
            startd=str,
            endd=endr,
            n.clusters=cl,
            iter=it,
            intro.eggs=ie,
            compressed.output=FALSE,
            seeding=TRUE,
            verbose=FALSE)

summary(simout)

# Retrieve the maximum number of simulated days
dd <- max(simout)

# Compute a raster with the  median of the iterations
breaks <- c(0.50)
ed <- 1:dd
hs.r <- adci(simout, eval_date=ed, breaks=breaks, 
     stage="Adults",
     sub_stage = "Host-seeking", type="N")

# inspect the raster
hs.r$`Host-seeking_q_0.5`

# plot the raster with the median host-seeking abundace
plot(hs.r$`Host-seeking_q_0.5`$day30)

dynamAedes documentation built on May 29, 2024, 2:18 a.m.