ipsecr-package {ipsecr}

Spatially Explicit Capture–Recapture by Inverse Prediction

Description

Functions to estimate the density of a spatially distributed animal population sampled with an array of passive detectors, such as traps. ipsecr addresses ‘difficult’ models that strictly cannot be fitted by maximum likelihood in the package secr (Efford 2022). The classic example concerns discrete-time data from single-catch traps.

Details

Package:	ipsecr
Type:	Package
Version:	1.4.1
Date:	2024-01-15
License:	GNU General Public License Version 2 or later

Spatially explicit capture–recapture is a set of methods for studying marked animals distributed in space. Data comprise the locations of detectors (described in an object of class ‘traps’), and the detection histories of individually marked animals. Individual histories are stored in an object of class ‘capthist’ that includes the relevant ‘traps’ object.

Models for population density (animals per hectare) and detection are defined in ipsecr using symbolic formula notation. The set of possible models overlaps with secr (some models for varying detection parameters are excluded, e.g., ~t, ~b). Density models may include spatial trend. Habitat is distinguished from nonhabitat with an object of class ‘mask’.

Models are fitted in ipsecr by simulation and inverse prediction (Efford 2004, 2023). A model fitted with ipsecr.fit is an object of class ipsecr. Generic methods (plot, print, summary, etc.) are provided.

A link at the bottom of each help page takes you to the help index. The vignette includes worked examples.

The analyses in ipsecr extend those available in the software Density (see www.otago.ac.nz/density/ for the most recent version of Density). Help is available on the ‘DENSITY | secr’ forum at www.phidot.org and the Google group secrgroup. Feedback on the software is also welcome, including suggestions for additional documentation or new features consistent with the overall design.

‘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 or lambda0 and sigma) by ‘matching’ statistics from proxyfn(capthist) (the target vector) to statistics from simulations of a 2-D population using the postulated detection model. Statistics (see Note) are defined by the proxy function, which should return a vector equal in length to the number of parameters (default np = 3). Simulations of the 2-D population use either internal C++ code or sim.popn. The simulated 2-D distribution of animals is Poisson by default.

The simulated population is sampled with internal C++ code, sim.capthist, or a user-specified function. Simulations match 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.

Simulations are usually 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.

A multivariate linear model is fitted to predict each vector of simulated proxies from the known parameter values. Simulations are performed at each design point until a specified precision is reached, up to a user-specified maximum number.

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.

See Efford et al. (2004) for an early description of the method, and Efford et al. (2005) for an application.

If not provided, the starting values are determined automatically with the **secr** function makeStart.

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 worker processes on multiple cores (see Parallel for more).

Author(s)

Murray Efford [e-mail]

References

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. (2022) secr: Spatially explicit capture–recapture models. R package version 4.5.8. https://CRAN.R-project.org/package=secr/

Efford, M. G. (2023) ipsecr: An R package for awkward spatial capture–recapture data. Methods in Ecology and Evolution In review.

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.

See Also

proxy.ms ipsecr.fit, secr.fit, capthist, mask