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).
moves reports the distance between successive detections of each animal.
centroids reports the averaged coordinates of each animal's detections
ORL reports the observed range length of each animal, the maximum
distance between any two detections.
trapsPerAnimal tabulates the number of animals recorded at 1, 2, ..., K detectors
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)
ORL(capthist, userdist = NULL, mask = NULL)
centroids(capthist)
trapsPerAnimal(capthist)
For dbar, MMDM, ARL and RPSV --
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.
For moves --
List with one component for each animal, a vector of distances, or numeric(0) if the animal is detected only once. A list of such lists if capthist is a multi-session list.
For centroids --
For a single-session capthist, a matrix of two columns, the x- and y-coordinates of the centroid of the detections of each animal. The number of detections is returned as the attribute `Ndetections', a 1-column matrix.
For a multi-session capthist, a 3-D array as before, but with a third dimension for the session. Centroid coordinates are missing (NA) if the animal was not detected in a session. The attribute `Ndetections' with the number of detections per animal and session is a matrix.
For trapsPerAnimal --
A vector with the number of animals detected at k detectors.
object of class capthist
function or matrix with user-defined distances
habitat mask passed to userdist function, if required
logical; should results be ordered alphanumerically by row names?
integer minimum number of recaptures for a detection history to be used
logical; if TRUE observed range length is plotted against number of recaptures
logical; set to TRUE for detailed output
logical for whether to use Calhoun and Casby formula
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.
RPSV has a specific role as a proxy for
detection scale in inverse-prediction estimation of density (Efford
2004, 2023).
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. If capthist
combines telemetry data and conventional detections (`multi', `proximity' etc.)
then only the conventional data are summarised.
Movements are reliably reported by moves only if there is a maximum of one detection per animal per occasion. The sequence of detections within any occasion is not known; where these occur the sequence used by moves is arbitrary (sequence follows detector index).
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.
Efford, M. G. (2023) ipsecr: An R package for awkward spatial capture--recapture data. Methods in Ecology and Evolution In press.
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.
autoini
dbar(captdata)
RPSV(captdata)
RPSV(captdata, CC = TRUE)
centr <- centroids(captdata)
plot(traps(captdata), border = 20 )
text(centr[,1], centr[,2], attr(centr, 'Ndetections'))
text(centr[,1]+2, centr[,2]+3, rownames(captdata), cex = 0.6,
adj = 0)
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