secr (version 2.9.4)

homerange: Home Range Statistics

Description

Some ad hoc measures of home range size may be calculated in secr from capture--recapture data: dbar is the mean distance between consecutive capture locations, pooled over individuals (e.g. Efford 2004). moves returns the raw distances. MMDM (for `Mean Maximum Distance Moved') is the average maximum distance between detections of each individual i.e. the observed range length averaged over individuals (Otis et al. 1978). ARL or `Asymptotic Range Length') is obtained by fitting an exponential curve to the scatter of observed individual range length vs the number of detections of each individual (Jett and Nichols 1987: 889). RPSV (for `Root Pooled Spatial Variance') is a measure of the 2-D dispersion of the locations at which individual animals are detected, pooled over individuals (cf Calhoun and Casby 1958, Slade and Swihart 1983).

Usage

dbar(capthist, userdist = NULL, mask = NULL)
MMDM(capthist, min.recapt = 1, full = FALSE, userdist = NULL, mask = NULL)
ARL(capthist, min.recapt = 1, plt = FALSE, full = FALSE, userdist = NULL, mask = NULL)
moves(capthist, userdist = NULL, mask = NULL)
RPSV(capthist, CC = FALSE)

Arguments

capthist

object of class capthist

userdist

function or matrix with user-defined distances

mask

habitat mask passed to userdist function, if required

min.recapt

integer minimum number of recaptures for a detection history to be used

plt

logical; if TRUE observed range length is plotted against number of recaptures

full

logical; set to TRUE for detailed output

CC

logical for whether to use Calhoun and Casby formula

Value

• Scalar distance in metres, or a list of such values if capthist is a multi-session list. The full argument may be used with MMDM and ARL to return more extensive output, particularly the observed range length for each detection history.

Details

dbar is defined as -- $$\bar{d}=\frac{\sum _{i=1}^n\sum _{j=1}^{n_i-1}\sqrt{(x_{i,j}-x_{i,j+1}{)}^2+(y_{i,j}-y_{i,j+1}{)}^2}}{\sum _{i=1}^n(n_i-1)}$$ When CC = FALSE, RPSV is defined as -- $$RPSV=\sqrt{\frac{\sum _{i=1}^n\sum _{j=1}^{n_i}[(x_{i,j}-{\bar{x}}_i{)}^2+(y_{i,j}-{\bar{y}}_i{)}^2]}{\sum _{i=1}^n(n_i-1)-1}}$$. Otherwise (CC = TRUE), RPSV uses the formula of Calhoun and Casby (1958) with a different denominator -- $$s=\sqrt{\frac{\sum _{i=1}^n\sum _{j=1}^{n_i}[(x_{i,j}-{\bar{x}}_i{)}^2+(y_{i,j}-{\bar{y}}_i{)}^2]}{2\sum _{i=1}^n(n_i-1)}}$$. The Calhoun and Casby formula (offered from 2.9.1) correctly estimates $\sigma$ when trapping is on an infinite, fine grid, and is preferred for this reason. The original RPSV (CC = FALSE) is retained as the default for compatibility with previous versions of secr. dbar and RPSV have a specific role as proxies for detection scale in inverse-prediction estimation of density (Efford 2004; see ip.secr). RPSV is used in autoini to obtain plausible starting values for maximum likelihood estimation. MMDM and ARL discard data from detection histories containing fewer than min.recapt+1 detections. The userdist option is included for exotic non-Euclidean cases (see e.g. secr.fit details). RPSV is not defined for non-Euclidean distances.

References

Calhoun, J. B. and Casby, J. U. (1958) Calculation of home range and density of small mammals. Public Health Monograph. No. 55. U.S. Government Printing Office. Efford, M. G. (2004) Density estimation in live-trapping studies. Oikos 106, 598--610. Jett, D. A. and Nichols, J. D. (1987) A field comparison of nested grid and trapping web density estimators. Journal of Mammalogy 68, 888--892. 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, 1--135. Slade, N. A. and Swihart, R. K. (1983) Home range indices for the hispid cotton rat (Sigmodon hispidus) in Northeastern Kansas. Journal of Mammalogy 64, 580--590.

See Also

autoini

Examples

dbar(captdata)
RPSV(captdata)
RPSV(captdata, CC = TRUE)