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H24_DENSITIES.R
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H24_DENSITIES.R
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################################################################################
# Article: Using inlabru to predict and map wildlife densities in heterogenous
# landscapes
# Contact: Andrew Houldcroft
# Notes: Please replace "..." with your own values.
################################################################################
library(INLA)
library(INLAspacetime)
library(inlabru)
library(fmesher)
library(sf)
library(terra)
# Set INLA mode
bru_options_set(inla.mode = "experimental")
# Import data
data <- readRDS("data.rds")
# Unwrap covariates
covariate.1 <- unwrap(data$covariates$covariate.1)
covariate.2 <- unwrap(data$covariates$covariate.2)
# Define key parameters
max.dist <- max(data$points$distance)
max.cluster <- max(data$points$cluster)
# Hazard-rate detection model
log_hr <- function(distance, log.sigma, log.gamma) {
log1p(-exp(-(distance/exp(log.sigma))^-exp(log.gamma)))
}
# Discretized truncated log-Normal cluster size distribution
log_pd <- function(cluster, meanlog, log.sdlog) {
bounds <- c(0, 1:max.cluster)
log(plnorm(bounds[cluster+1], meanlog = meanlog, sdlog = exp(log.sdlog)) -
plnorm(bounds[cluster], meanlog = meanlog, sdlog = exp(log.sdlog))) -
plnorm(max(bounds), meanlog = meanlog, sdlog = exp(log.sdlog), log.p = TRUE)
}
# Define barrier SPDE Matérn models
barrier.matern <- barrierModel.define(data$mesh,
data$barrier,
prior.sigma = c("...", "..."),
prior.range = c("...", "..."))
# Define the model components
components <- ~ 0 +
BSPDE(main = geometry, model = barrier.matern) +
meanlog(main = geometry, model = barrier.matern) +
beta.cov.1(covariate.1, model = "linear") +
beta.cov.2(covariate.2, model = "linear") +
beta.cluster(seq_len(max.cluster), model = "linear") +
log.sigma(1) +
log.gamma(1) +
log.sdlog(1) +
intercept(1) +
intercept.2(1)
# Define the model formula
formula <- geometry + distance + cluster ~
BSPDE +
log_hr(distance, log.sigma + beta.cluster[cluster], log.gamma) +
log_pd(cluster, meanlog + intercept.2, log.sdlog) +
beta.cov.1 +
beta.cov.2 +
intercept +
log(2)
# Run the model
model <- lgcp(
components = components,
data = data$points,
samplers = data$samplers,
domain = list(
geometry = data$mesh,
distance = fm_mesh_1d(seq(0, max.dist, length.out = 30)),
cluster = seq_len(max.cluster)),
formula = formula,
options = list(
bru_initial = list(beta.cov.1 = "...",
beta.cov.2 = "...",
beta.cluster = "...",
log.sigma = "...",
log.gamma = "...",
log.sdlog = "...",
intercept = "...",
intercept.2 = "..."),
bru_verbose = 4,
bru_method = list(rel_tol = 0.15),
control.compute = list(dic = TRUE)))
# View model summary
summary(model)
# Define integration points
pred.points <- fm_int(data$mesh, data$site, format = "sf")
# Predict individual abundance
abundance <- predict(model, pred.points, ~ {
bounds <- c(0, 1:max.cluster)
cluster <- 1:max.cluster
cluster.expectation <- vapply(
seq_along(meanlog),
function(k){
prob.vector <- plnorm(
bounds[cluster + 1],
meanlog = meanlog[k] + intercept.2,
sdlog = exp(log.sdlog)) -
plnorm(bounds[cluster],
meanlog = meanlog[k] + intercept.2,
sdlog = exp(log.sdlog))
prob.vector <- prob.vector/plnorm(max(bounds),
meanlog = meanlog[k] + intercept.2,
sdlog = exp(log.sdlog))
sum((1:max.cluster) * prob.vector)
}, 0.0)
sum(weight * exp(BSPDE + beta.cov.1 + beta.cov.2 + intercept) *
cluster.expectation)
},
n.samples = "...")
abundance
# Predict individual abundance
average.density <- predict(model, pred.points, ~ {
bounds <- c(0, 1:max.cluster)
cluster <- 1:max.cluster
cluster.expectation <- vapply(
seq_along(meanlog),
function(k){
prob.vector <- plnorm(
bounds[cluster + 1],
meanlog = meanlog[k] + intercept.2,
sdlog = exp(log.sdlog)) -
plnorm(bounds[cluster],
meanlog = meanlog[k] + intercept.2,
sdlog = exp(log.sdlog))
prob.vector <- prob.vector/plnorm(max(bounds),
meanlog = meanlog[k] + intercept.2,
sdlog = exp(log.sdlog))
sum((1:max.cluster) * prob.vector)
}, 0.0)
sum(weight * exp(BSPDE + beta.cov.1 + beta.cov.2 + intercept) *
cluster.expectation) / sum(weight)
},
n.samples = "...")
average.density
# Predict cluster abundance
cluster.abundance <- predict(model, pred.points, ~ {
sum(weight * exp(BSPDE + beta.cov.1 + beta.cov.2 + intercept))
},
n.samples = "...")
cluster.abundance
# Predict mean cluster density
average.cluster.density <- predict(model, pred.points, ~ {
sum(weight * exp(BSPDE + beta.cov.1 + beta.cov.2 + intercept)) / sum(weight)
},
n.samples = "...")
average.cluster.density
# Predict cluster expectation
average.cluster.size <- predict(model, pred.points, ~ {
bounds <- c(0, 1:max.cluster)
cluster <- 1:max.cluster
cluster.expectation <- vapply(
seq_along(meanlog),
function(k){
prob.vector <- plnorm(
bounds[cluster + 1],
meanlog = meanlog[k] + intercept.2,
sdlog = exp(log.sdlog)) -
plnorm(bounds[cluster],
meanlog = meanlog[k] + intercept.2,
sdlog = exp(log.sdlog))
prob.vector <- prob.vector/plnorm(max(bounds),
meanlog = meanlog[k] + intercept.2,
sdlog = exp(log.sdlog))
sum((1:max.cluster) * prob.vector)
}, 0.0)
sum(weight * cluster.expectation) / sum(weight)
},
n.samples = "...")
average.cluster.size
# Define prediction grid
grid <- fm_pixels(data$mesh, mask = TRUE)
# Predict individual density surface
density.surface <- predict(model, grid, ~ {
bounds <- c(0, 1:max.cluster)
cluster <- 1:max.cluster
cluster.expectation <- vapply(
seq_along(meanlog),
function(k){
prob.vector <- plnorm(
bounds[cluster + 1],
meanlog = meanlog[k] + intercept.2,
sdlog = exp(log.sdlog)) -
plnorm(bounds[cluster],
meanlog = meanlog[k] + intercept.2,
sdlog = exp(log.sdlog))
prob.vector <- prob.vector/plnorm(max(bounds),
meanlog = meanlog[k] + intercept.2,
sdlog = exp(log.sdlog))
sum((1:max.cluster) * prob.vector)
}, 0.0)
exp(BSPDE + beta.cov.1 + beta.cov.2 + intercept) * cluster.expectation
},
n.samples = "...")
ggplot() + gg(density.surface, geom = "tile")
# Predict cluster density surface
cluster.density.surface <- predict(model, grid, ~ {
exp(BSPDE + beta.cov.1 + beta.cov.2 + intercept)
},
n.samples = "...")
ggplot() + gg(cluster.density.surface, geom = "tile")
# Predict spatial cluster distribution
cluster.size.surface <- predict(model, grid, ~ {
bounds <- c(0, 1:max.cluster)
cluster <- 1:max.cluster
cluster.expectation <- vapply(
seq_along(meanlog),
function(k){
prob.vector <- plnorm(
bounds[cluster + 1],
meanlog = meanlog[k] + intercept.2,
sdlog = exp(log.sdlog)) -
plnorm(bounds[cluster],
meanlog = meanlog[k] + intercept.2,
sdlog = exp(log.sdlog))
prob.vector <- prob.vector/plnorm(max(bounds),
meanlog = meanlog[k] + intercept.2,
sdlog = exp(log.sdlog))
sum((1:max.cluster) * prob.vector)
}, 0.0)
cluster.expectation
},
n.samples = "...")
ggplot() + gg(cluster.size.surface, geom = "tile")
# Predict barrier SPDE spatial effect
BSPDE.spatial.effect <- predict(model, grid, ~ {
exp(BSPDE)
},
n.samples = "...")
ggplot() + gg(BSPDE.spatial.effect, geom = "tile")
# Predict covariate.1 spatial effect
cov.1.spatial.effect <- predict(model, grid, ~ {
exp(beta.cov.1)
},
n.samples = "...")
ggplot() + gg(cov.1.spatial.effect, geom = "tile")
# Predict covariate.2 spatial effect
cov.2.spatial.effect <- predict(model, grid, ~ {
exp(beta.cov.2)
},
n.samples = "...")
ggplot() + gg(cov.2.spatial.effect, geom = "tile")