# Calculate an autocorrelated kernel density estimate

### Description

This function calculates autocorrelated kernel density home-range estimates from `telemetry`

data and a corresponding continuous-time movement model.

### Usage

1 2 3 4 5 6 7 8 9 10 | ```
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 |

`CTMM` |
A |

`VMM` |
An optional vertical |

`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 |

`...` |
Arguments passed to all instances of |

`x` |
A list of |

### 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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
# 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)
``` |