# homerange: Home Range Statistics In secr: Spatially Explicit Capture-Recapture

## 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).

`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.

## Usage

 ```1 2 3 4 5 6 7``` ```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) ```

## Arguments

 `capthist` object of class `capthist` `userdist` function or matrix with user-defined distances `mask` habitat mask passed to userdist function, if required `names` logical; should results be ordered alphanumerically by row names? `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

## Details

`dbar` is defined as –

see pdf manual

When `CC = FALSE`, `RPSV` is defined as –

see pdf manual

.

Otherwise (`CC = TRUE`), `RPSV` uses the formula of Calhoun and Casby (1958) with a different denominator –

see pdf manual

.

The Calhoun and Casby formula (offered from 2.9.1) correctly estimates σ 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.

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).

## Value

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.

## Note

All measures are affected by the arrangement of detectors. `dbar` is also affected quite strongly by serial correlation in the sampled locations. Using `dbar` with ‘proximity’ detectors raises a problem of interpretation, as the original sequence of multiple detections within an occasion is unknown. RPSV is a value analogous to the standard deviation of locations about the home range centre.

The value returned by `dbar` for ‘proximity’ or ‘count’ detectors is of little use because multiple detections of an individual within an occasion are in arbitrary order.

Inclusion of these measures in the secr package does not mean they are recommended for general use! It is usually better to use a spatial parameter from a fitted model (e.g., sigma of the half-normal detection function). Even then, be careful that sigma is not ‘contaminated’ with behavioural effects (e.g. attraction of animal to detector) or ‘detection at a distance’.

The argument 'names' was added in 3.0.1. The default `names = FALSE` causes a change in behaviour from that version onwards.

## 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.

`autoini`
 ```1 2 3 4 5 6 7 8 9``` ```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) ```