`akde.Rd`

These functions calculate individual and population-level autocorrelated kernel density home-range estimates from `telemetry`

data and a corresponding continuous-time movement models.

```
akde(data,CTMM,VMM=NULL,R=list(),SP=NULL,SP.in=TRUE,variable="utilization",debias=TRUE,
weights=FALSE,smooth=TRUE,error=0.001,res=10,grid=NULL,...)
pkde(data,UD,kernel="individual",weights=FALSE,ref="Gaussian",...)
```

- data
2D timeseries telemetry data represented as a

`telemetry`

object or list of objects.- CTMM
A

`ctmm`

movement model from the output of`ctmm.fit`

or list of objects.- VMM
An optional vertical

`ctmm`

object for 3D home-range calculation.

- R
A named list of raster covariates if

`CTMM`

contains an RSF model.- SP
SpatialPolygonsDataFrame object for enforcing hard boundaries.

- SP.in
Locations are assumed to be inside the

`SP`

polygons if`SP.in=TRUE`

and outside of`SP`

if`SP.in=FALSE`

.- variable
Not yet supported.

- debias
Debias the distribution for area estimation (AKDEc).

- smooth
"Smooth" out errors from the data.

- weights
Optimally weight the data to account for sampling bias (See

`bandwidth`

for`akde`

details).- error
Target probability error.

- res
Number of grid points along each axis, relative to the bandwidth.

- grid
Optional grid specification via

`raster`

,`UD`

, or list of arguments (See `Details' below).- ...
Arguments passed to

`bandwidth`

and`akde`

.- UD
A list of individual

`UD`

objects corresponding to`data`

.- kernel
Bandwidths are proportional to the individual covariances if

`kernel="individual"`

or to the population covariance if`kernel="population"`

.- ref
Include non-Gaussian overlap corrections if

`ref="AKDE"`

and`weights=TRUE`

.

For weighted AKDE, please note additional `...`

arguments passed to `bandwidth`

, which can have a large impact on computation time in certain cases.

When feeding in lists of `telemetry`

and `ctmm`

objects, all UDs will be calculated on the same grid. These UDs can be averaged with the `mean.UD`

command.

If a `UD`

or `raster`

object is supplied in the `grid`

argument, then the estimate will be calculated on the same grid. Alternatively, a list of grid arguments can be supplied, with any of the following components:

`r`

A list with vectors

`x`

and`y`

that define the grid-cell midpoints.`dr`

A vector setting the

`x`

and`y`

cell widths in meters. Equivalent to`res`

for`raster`

objects.`extent`

The \(x\)-\(y\) extent of the grid cells, formatted as from the output of

`extent`

.`align.to.origin`

Logical value indicating that cell midpoint locations are aligned to be an integer number of

`dr`

steps from the projection origin.

Returns a `UD`

object: a list with the sampled grid line locations `r$x`

and `r$y`

, the extent of each grid cell `dr`

, the probability density and cumulative distribution functions evaluated on the sampled grid locations `PDF`

& `CDF`

, the optimal bandwidth matrix `H`

, and the effective sample size of the data in `DOF.H`

.

C. H. Fleming, W. F. Fagan, T. Mueller, K. A. Olson, P. Leimgruber, J. M. Calabrese, ``Rigorous home-range estimation with movement data: A new autocorrelated kernel-density estimator'', Ecology, 96:5, 1182-1188 (2015) doi:10.1890/14-2010.1 .

C. H. Fleming, J. M. Calabrese, ``A new kernel-density estimator for accurate home-range and species-range area estimation'', Methods in Ecology and Evolution, 8:5, 571-579 (2017) doi:10.1111/2041-210X.12673 .

C. H. Fleming, D. Sheldon, W. F. Fagan, P. Leimgruber, T. Mueller, D. Nandintsetseg, M. J. Noonan, K. A. Olson, E. Setyawan, A. Sianipar, J. M. Calabrese, ``Correcting for missing and irregular data in home-range estimation'', Ecological Applications, 28:4, 1003-1010 (2018) doi:10.1002/eap.1704 .

In the case of coarse grids, the value of `PDF`

in a grid cell corresponds to the average probability density over the entire rectangular cell.

The `PDF`

estimate is not re-normalized to 1, and may fall short of this by the target numerical `error`

. If inspecting quantiles that are very far from the data, the quantiles may hit the grid boundary or become erratic, making it necessary to reduce the numerical `error`

target. However, default arguments should be able to render any quantiles of reasonable accuracy.

Prior to `ctmm`

v0.3.2, the default AKDE method was the autocorrelated Gaussian reference function bandwidth.
Starting in v0.3.2, the default AKDE method is the autocorrelated Gaussian reference function bandwidth with debiased area.

Prior to `ctmm`

v0.3.1, AKDEs included only errors due to autocorrelation uncertainty, which are insignificant in cases such as IID data.
Starting in v0.3.1, `akde`

calculated an effective sample size `DOF.H`

and used this to estimate area uncertainty under a Gaussian reference function approxmation.
In v0.3.2, this method was further improved to use `DOF.area`

from the Gaussian reference function approximation.

```
# \donttest{
# Load package and data
library(ctmm)
data(buffalo)
DATA <- buffalo$Cilla
# calculate fit guess object
GUESS <- ctmm.guess(DATA,interactive=FALSE)
# in general, you should be running ctmm.select here instead of ctmm.fit
FIT <- ctmm.fit(DATA,GUESS)
# Compute akde object
UD <- akde(DATA,FIT)
#> Default grid size of 3 minutes chosen for bandwidth(...,fast=TRUE).
# Plot data with AKDE
plot(DATA,UD=UD)
#> DOP values missing. Assuming DOP=1.
# }
```