Estimate population density by simulation and inverse prediction (Efford 2004; Efford, Dawson & Robbins 2004). A restricted range of SECR models may be fitted (detection functions with more than 2 parameters are not supported, nor are covariates).
ip.secr (capthist, predictorfn = pfn, predictortype = "null", detectfn = 0,
mask = NULL, start = NULL, boxsize = 0.2, boxsize2 = boxsize, centre = 3,
min.nsim = 10, max.nsim = 2000, CVmax = 0.002, var.nsim = 1000, maxbox = 5,
maxtries = 2, ncores = 1, seed = NULL, trace = TRUE, ...)pfn(capthist, N.estimator = c("n", "null","zippin","jackknife") )
boxsize; used from second box onwardsip.secr, a list comprising
For pfn, a vector of numeric values corresponding to \(\hat{N}\), \(\hat{p}\), and
RPSV, a measure of the spatial scale of individual detections.
`Inverse prediction' uses methods from multivariate calibration (Brown
1982). The goal is to estimate population density (D) and the parameters
of a detection function (usually g0 and sigma) by `matching' statistics
from predictorfn(capthist) (the target vector) and statistics
from simulations of a 2-D population using the postulated detection
model. Statistics (see Note) are defined by the predictor function,
which should return a vector equal in length to the number of parameters
(np = 3). Simulations of the 2-D population use sim.popn.
The simulated population is sampled with sim.capthist
according to the detector type (e.g., `single' or `multi') and detector
layout specified in traps(capthist), including allowance for varying
effort if the layout has a usage attribute.
… may be used to control aspects of the simulation by passing named
arguments (other than D) to sim.popn. The most important arguments of
sim.popn to keep an eye on are `buffer' and `Ndist'. `buffer'
defines the region over which animals are simulated (unless mask
is specified) - the region should be large enough to encompass all
animals that might be caught. `Ndist' controls the number of individuals
simulated within the buffered or masked area. The default is `poisson'.
Use `Ndist = fixed' to fix the number in the buffered or masked area
\(A\) at \(N = DA\). This conditioning reduces the estimated
standard error of \(\hat{D}\), but conditioning is not always
justified - seek advice from a statistician if you are unsure.
The simulated 2-D distribution of animals is Poisson by default. There is no `even' option as in Density.
Simulations are conducted on a factorial experimental design in
parameter space - i.e. at the vertices of a cuboid `box' centred on the
working values of the parameters, plus an optional number of centre
points. The size of the `box' is specified as a fraction of the working
values, so for example the limits on the density axis are D*(1--boxsize)
and D*(1+boxsize) where D* is the working value of D. For g0, this
computation uses the odds transformation (g0/(1--g0)). boxsize
may be a vector defining different scaling on each parameter dimension.
A multivariate linear model is fitted to predict each set of simulated statistics from the known parameter values. The number of simulations at each design point is increased (doubled) until the residual standard error divided by the central value is less than CVmax for all parameters. An error occurs if max.nsim is exceeded.
Once a model with sufficient precision has been obtained, a new working vector of parameter estimates is `predicted' by inverting the linear model and applying it to the target vector. A working vector is accepted as the final estimate when it lies within the box; this reduces the bias from using a linear approximation to extrapolate a nonlinear function. If the working vector lies outside the box then a new design is centred on value for each parameter in the working vector.
Once a final estimate is accepted, further simulations are conducted to estimate the variance-covariance matrix. These also provide a parametric bootstrap sample to evaluate possible bias. Set var.nsim = 0 to suppress the variance step.
See Efford et al. (2004) for another description of the method, and Efford et al. (2005) for an application.
The value of predictortype is passed as the second argument of
the chosen predictorfn. By default this is pfn, for which
the second argument (N.estimator) is a character value from
c("n", "null","zippin","jackknife"), corresponding respectively to the
number of individuals caught (Mt+1), and \(\hat{N}\) from
models M0, Mh and Mb of Otis et al. (1978).
If not provided, the starting values are determined automatically
with autoini.
Linear measurements are assumed to be in metres and density in animals per hectare (10 000 \(\mbox{m}^2\)).
If ncores > 1 the parallel package is used to create
processes on multiple cores (see Parallel for more).
Brown, P. J. (1982) Multivariate calibration. Journal of the Royal Statistical Society, Series B 44, 287--321.
Efford, M. G. (2004) Density estimation in live-trapping studies. Oikos 106, 598--610.
Efford, M. G., Borchers D. L. and Byrom, A. E. (2009) Density estimation by spatially explicit capture--recapture: likelihood-based methods. In: D. L. Thompson, E. G. Cooch and M. J. Conroy (eds) Modeling Demographic Processes in Marked Populations. Springer. Pp. 255--269.
Efford, M. G., Dawson, D. K. and Robbins C. S. (2004) DENSITY: software for analysing capture-recapture data from passive detector arrays. Animal Biodiversity and Conservation 27, 217--228.
Efford, M. G., Warburton, B., Coleman, M. C. and Barker, R. J. (2005) A field test of two methods for density estimation. Wildlife Society Bulletin 33, 731--738.
Otis, D. L., Burnham, K. P., White, G. C. and Anderson, D. R. (1978) Statistical inference from capture data on closed animal populations. Wildlife Monographs 62.
capthist, secr.fit, RPSV, autoini,
sim.popn, Detection functions
## Not run: ------------------------------------
# ## these calculations may take several minutes
#
# ## default settings
# ip.secr (captdata)
#
# ## coarse initial fit, no variance step
# ip1 <- ip.secr (captdata, boxsize = 0.2, CVmax=0.01, var=0)
# ## refined fit
# ip2 <- ip.secr (captdata, start = ip1$IP[,"estimate"],
# boxsize = 0.1, CVmax=0.002, var=1000)
# ip2
#
# ## compare to MLE of same data using multi-catch assumption
# predict(secrdemo.0)
#
# ## improvise another predictor function (dbar instead of RPSV)
# pfn2 <- function (capthist, v) { ## v is not used
# sumni <- sum(capthist!=0) ## total detections
# n <- nrow(capthist) ## number of individuals
# nocc <- ncol(capthist) ## number of occasions
# c(N = n, p = sumni/n/nocc, dbar = dbar(capthist))
# }
# ip.secr (captdata, predictorfn = pfn2)
## ---------------------------------------------
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