Calculate an autocorrelated kernel density estimate

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Description

This function calculates autocorrelated kernel density home-range estimates from telemetry data and a corresponding continuous-time movement model.

Usage

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akde(data,CTMM,VMM=NULL,debias=TRUE,smooth=TRUE,error=0.001,res=10,grid=NULL,...)

## S3 method for class 'telemetry'
akde(data,CTMM,VMM=NULL,debias=TRUE,smooth=TRUE,error=0.001,res=10,grid=NULL,...)

## S3 method for class 'list'
akde(data,CTMM,VMM=NULL,debias=TRUE,smooth=TRUE,error=0.001,res=10,grid=NULL,...)

## S3 method for class 'UD'
mean(x,...)

Arguments

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.

debias

Debias the distribution for area estimation (AKDEc).

smooth

"Smooth" out errors from the data.

error

Target probability error.

res

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

grid

Optional grid specification with columns labeled x and y. Not yet supported.

...

Arguments passed to all instances of bandwidth, such as weights.

x

A list of UDs calculated on the same grid.

Value

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.

For weighted AKDE, please note additional ... arguments passed to bandwidth and the weights=TRUE argument, specifically.

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 command, however this is not an optimal way to calculate population ranges.

Note

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.

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.

Author(s)

C. H. Fleming and K. Winner.

References

C. H. Fleming and W. F. Fagan and T. Mueller and K. A. Olson and P. Leimgruber and J. M. Calabrese (2015). Rigorous home-range estimation with movement data: A new autocorrelated kernel-density estimator. Ecology, 96(5), 1182-1188.

See Also

bandwidth, raster,UD-method

Examples

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# Load package and data
library(ctmm)
data(buffalo)
cilla <- buffalo[[1]]

# Fit a continuous-velocity model with tau ~ c(10 days, 1 hour)
# see help(variogram.fit)
GUESS <- ctmm(tau=c(10*24*60^2,60^2))
FIT <- ctmm.fit(cilla,GUESS)

# Compute akde object
UD <- akde(cilla,FIT)

# Plot data with AKDE contours
plot(cilla,UD=UD)