Fit the integrated distance sampling model of Kery et al. (2022).

Model abundance using a combination of distance sampling data (DS) and other similar data types, including simple point counts (PC) and occupancy/detection-nondetection (OC/DND) data.

IDS(lambdaformula = ~1, detformulaDS = ~1, detformulaPC = NULL, detformulaOC = NULL,
    dataDS, dataPC = NULL, dataOC = NULL, availformula = NULL,
    durationDS = NULL, durationPC = NULL, durationOC = NULL, keyfun = "halfnorm",
    maxDistPC, maxDistOC, K = 100, unitsOut = "ha", 
    starts = NULL, method = "BFGS", ...)

Arguments

lambdaformula: Formula for abundance
detformulaDS: Formula for distance-based (DS) detection probability
detformulaPC: Formula for point count detection probability. If NULL, will share a model with DS detection probability
detformulaOC: Formula for occupancy/detection-nondetection detection probability. If NULL, will share a model with DS detection probability
dataDS: An object of class unmarkedFrameDS. Required
dataPC: An object of class unmarkedFramePCount. If NULL, no PC data will be used in the model
dataOC: An object of class unmarkedFrameOccu. If NULL, no OC/DND data will be used in the model
availformula: Optional. If specified, formula for availability. Only possible to use if you have variable detection survey lengths (see below)
durationDS: Optional. Vector of survey durations at each distance sampling site
durationPC: Optional. Vector of survey durations at each PC site
durationOC: Optional. Vector of survey durations at each OC/DND site
keyfun: Distance sampling key function; either "halfnorm" or "exp"
maxDistPC: Maximum observation distance for PC surveys; defaults to maximum of distance bins from the distance sampling data
maxDistOC: Maximum observation distance for OC/DND surveys; defaults to maximum of distance bins from the distance sampling data
K: Integer, upper bound for integrating out latent abundance. Only used if you have included OC/DND data
unitsOut: Units of density for output. Either "ha" or "kmsq" for hectares and square kilometers, respectively
starts: A numeric vector of starting values for the model parameters
method: Optimization method used by optim
...: Additional arguments to optim, such as lower and upper bounds

Value

An object of class unmarkedFitIDS

Details

This function facilitates a combined analysis of distance sampling data (DS) with other similar data types, including simple point counts (PC) and occupancy/detection-nondetection (OC/DND) data. The combined approach capitalizes on the strengths and minimizes the weaknesses of each type. The PC and OC/DND data are viewed as latent distance sampling surveys with an underlying abundance model shared by all data types. All analyses must include some distance sampling data, but can include either PC or DND data or both. If surveys are of variable duration, it is also possible to estimate availability.

Input data must be provided as a series of separate unmarkedFrames: unmarkedFrameDS for the distance sampling data, unmarkedFramePCount for the point count data, and unmarkedFrameOccu for OC/DND data. See the help files for these objects for guidance on how to organize the data.

Note

Simulations indicated estimates of availability were very unreliable when including detection/non-detection data, so the function will not allow you to use DND data and estimate availability at the same time. In general estimation of availability can be difficult; use simulations to see how well it works for your specific situation.

References

Kery M, Royle JA, Hallman T, Robinson WD, Strebel N, Kellner KF. 2024. Integrated distance sampling models for simple point counts. Ecology.

Author

Ken Kellner contact@kenkellner.com

Examples


if (FALSE) { # \dontrun{

# Simulate data based on a real dataset

# Formulas for each model
formulas <- list(lam=~elev, ds=~1, phi=~1)

# Sample sizes
design <- list(Mds=2912, J=6, Mpc=506)

# Model parameters
coefs <- list(lam = c(intercept=3, elev=-0.5),
              ds = c(intercept=-2.5),
              phi = c(intercept=-1.3))

# Survey durations
durs <- list(ds = rep(5, design$Mds), pc=runif(design$Mpc, 3, 30))

set.seed(456)
sim_umf <- simulate("IDS", # name of model we are simulating for
                    nsim=1, # number of replicates
                    formulas=formulas, 
                    coefs=coefs,
                    design=design,
                    # arguments used by unmarkedFrameDS
                    dist.breaks = seq(0, 0.30, length.out=7),
                    unitsIn="km", 
                    # arguments used by IDS
                    # could also have e.g. keyfun here
                    durationDS=durs$ds, durationPC=durs$pc, durationOC=durs$oc,
                    maxDistPC=0.5, maxDistOC=0.5,
                    unitsOut="kmsq")

# Look at the results
lapply(sim_umf, head)

# Fit a model
(mod_sim <- IDS(lambdaformula = ~elev, detformulaDS = ~1,
                dataDS=sim_umf$ds, dataPC=sim_umf$pc,
                availformula = ~1, durationDS=durs$ds, durationPC=durs$pc,
                maxDistPC=0.5,
                unitsOut="kmsq"))

# Compare with known parameter values
# Note:  this is an unusually good estimate of availability
# It is hard to estimate in most cases
cbind(truth=unlist(coefs), est=coef(mod_sim))

# Predict density at each distance sampling site
head(predict(mod_sim, 'lam'))

} # }