simOccSpatial {AHMbook}  R Documentation 
Simulate replicated detection/nondetection data under a spatial, static occupancy model
Description
Simulates replicated detection/nondetection data under a spatial, static occupancy model for a semirealistic landscape in a square of 50x50 km in the Bernese Oberland around Interlaken, Switzerland. Unit of the data simulation is a 1km2 quadrat, hence, there are 2500 units. It uses the data set BerneseOberland
, which has covariates for elevation and forest cover.
For occupancy, the function allows you to specify a quadratic effect of elevation. Then, a Gaussian spatial random field (s) with negative exponential correlation function is simulated using simExpCorrRF
; you can set the variance and the range (scale) parameter theta. Basically, the larger the value of theta.RF, the bigger are the 'islands' simulated in the random field. The abundance in each quadrat (i) is built up via the following linear predictor:
psi[i] < qlogis(beta0 + beta[1] * elev[i] + beta[2] * elev[i]^2 + s[i])
z[i] ~ Bernoulli(psi[i])
Replicated detection/nondetection data are simulated as usual under a Bernoulli observation model, and detection probability is allowed to vary by one site and one observational covariate: respectively quadrat forest cover (in the BerneseOberland data set), and windspeed, which is invented data. Counts at each site (i) and for each occasion (j) are then produced according to the following model:
p[i,j] < plogis(alpha0 + alpha[1] * forest[i] + alpha[2] * wind[i,j])
y[i,j] ~ Bernoulli(z[i] * p[i,j])
Finally, we assume that only a subset of the 2500 quadrats is surveyed. Hence, we allow you to choose the number of quadrats that are surveyed and these will then be randomly placed into the landscape. We then assume that counts will only be available for these surveyed quadrats, i.e., detection/nondetection data from all nonsurveyed quadrats will be replaced with NA.
To recreate the data sets used in the book with R 3.6.0 or later, call RNGversion="3.5.3"
before the call to simOccSpatial
. This should only be used for reproduction of old results.
Usage
simOccSpatial(nsurveys = 3, mean.psi = 0.6, beta = c(2, 2),
mean.p = 0.4, alpha = c(1, 1), sample.size = 500, variance.RF = 1, theta.RF = 10,
seeds = c(10, 100), show.plots = TRUE, verbose = TRUE)
Arguments
nsurveys 
number of surveys per quadrat. 
mean.psi 
probability of occupancy at a quadrat with mean values of all covariates; 
beta 
vector of length 2, the linear and quadratic coefficients for the effect of elevation on occupancy. 
mean.p 
Expected detection at the average value of all detection covariates (and ignoring all random effects): detection model 
alpha 
vector of length 2, the coefficients for the effect of forest and wind on detection. 
sample.size 
the number of quadrats surveyed. 
variance.RF 
variance of the random field. 
theta.RF 
parameter governing spatial correlation (=1/phi); the larger the value of theta.RF, the bigger are the 'islands' simulated in the random field. 
seeds 
vector of length 2; random seeds used for the random field and the selection of quadrats surveyed respectively. 
show.plots 
if TRUE, plots of the data will be displayed; set to FALSE if you are running simulations. 
verbose 
if TRUE, output will be written to the console. 
Value
A list with the arguments input and the following additional elements:
xcoord , ycoord 
The x and y coordinates from the 
elevation 
The elevation covariate from the 
forest 
The forest cover covariate from the 
elevationS 
The elevation covariate standardized to mean 0, SD 1. 
forestS 
The forest cover covariate standardized to mean 0, SD 1. 
wind 
The wind covariate, generated internally. 
field 
The spatiallyautocorrelated covariate, generated internally. 
alpha0 
Intercept for the detection model, equal to 
beta0 
Intercept for the abundance model, equal to 
z 
True occupancy in each quadrat. 
trueNocc 
True number of occupied sites. 
obsNocc 
Number of sites where the species was detected. 
true_psi_fs 

obs_psi_fs 

p 
probability of detection for each survey. 
y 
detected/nondetected data for each quadrat. 
surveyed.sites 
the IDs of the quadrats surveyed. 
yobs 
detected/nondetected data for each quadrat surveyed, NA for quadrats not surveyed. 
Author(s)
Marc Kéry & Andy Royle
References
Kéry, M. & Royle, J.A. (2021) Applied Hierarchical Modeling in Ecology AHM2  9.2.
Examples
# Generate data with the default arguments and look at the structure
str(dat < simOccSpatial())
str(dat < simOccSpatial(show.plots=FALSE))
# More surveys
str(dat< simOccSpatial(nsurveys = 10))
# Minimal number of surveys is 1
str(dat< simOccSpatial(nsurveys = 1))
# A truly ubiquitous species
str(dat < simOccSpatial(mean.psi = 1))
# Only negative linear effect of elevation
str(dat < simOccSpatial(beta = c(2, 0)))
# No effect of elevation at all (see effects of spatial field now clearly)
str(dat < simOccSpatial(beta = c(0, 0)))
# Perfect detection (p = 1)
str(dat < simOccSpatial(mean.p = 1))
# No effect in detection of forest cover
str(dat < simOccSpatial(alpha = c(0, 1)))
# No effect in detection of wind speed (see neatly forest effect now)
str(dat < simOccSpatial(alpha = c(1, 0)))
# Sample only 100 quadrats
str(dat < simOccSpatial(sample.size = 100))
# Sample all 2500 quadrats
str(dat < simOccSpatial(sample.size = 2500))
# Larger variance of the multivariate Gaussian Random variable in the random field
# (this will increase the effect of the field on occupancy and detection)
str(dat < simOccSpatial(variance.RF = 10))
# No spatial autocorrelation (Variant 1: set variance to 0)
str(dat < simOccSpatial(variance.RF = 0))
# No spatial autocorrelation (Variant 2: set theta very close to 0,
# but not quite 0, otherwise function breaks)
str(dat < simOccSpatial(theta.RF = 0.0001))
# Larger value of theta.RF gives larger 'islands'
#try(str(dat < simOccSpatial(theta.RF = 100))) # Works with RandomFields