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

data and a corresponding continuous-time movement model.

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,...)
``` |

`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 |

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.

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.

C. H. Fleming and K. Winner.

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.

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, DOI:10.1111/2041-210X.12673 (2016).

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)
``` |

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