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).
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, names = FALSE)
RPSV(capthist, CC = FALSE)capthist 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.
dbar is defined as --
$$
\overline{d}=\frac{\sum\limits _{i=1}^{n}
\sum\limits _{j=1}^{n_i - 1}
\sqrt{(x_{i,j}-x_{i,j+1})^2 + (y_{i,j}-y_{i,j+1})^2}}
{\sum\limits _{i=1}^{n} (n_i-1)}$$When CC = FALSE, RPSV is defined as --
$$
RPSV = \sqrt{
\frac {\sum\limits _{i=1}^{n} \sum\limits _{j=1}^{n_i} [
(x_{i,j} - \overline x_i)^2 + (y_{i,j} - \overline y_i)^2
]}{\sum\limits _{i=1}^{n} (n_i-1) - 1}}
$$.
Otherwise (CC = TRUE), RPSV uses the formula of Calhoun
and Casby (1958) with a different denominator --
$$
s = \sqrt{
\frac {\sum\limits _{i=1}^{n} \sum\limits _{j=1}^{n_i} [
(x_{i,j} - \overline x_i)^2 + (y_{i,j} - \overline y_i)^2
]}{2\sum\limits _{i=1}^{n} (n_i-1)}}
$$.
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.
If capthist comprises standalone telemetry data (all detector 'telemetry')
then calculations are performed on the telemetry coordinates.
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.
autoinidbar(captdata)
RPSV(captdata)
RPSV(captdata, CC = TRUE)
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