`overlap.Rd`

This function calculates a useful measure of similarity between distributions known as the *Bhattacharyya coefficient* in statistics and simply the *fidelity* or *overlap* in quantum and statistical mechanics. It is roughly speaking the ratio of the intersection area to the average individual area, but it is a direct comparison between the density functions and does not require an arbitrary quantile to be specified. When applied to `ctmm`

objects, this function returns the overlap of the two Gaussian distributions. When applied to aligned `UD`

objects with corresponding movement models, this function returns the overlap of their (autocorrelated) kernel density estimates.

overlap(object,level=0.95,debias=TRUE,...)

object | A |
---|---|

level | The confidence level desired for the output. |

debias | Approximate debiasing of the overlap. |

... | Not currently used. |

A table of confidence intervals on the overlap estimate. A value of `1`

implies that the two distributions are identical, while a value of `0`

implies that the two distributions share no area in common.

K. Winner, M. J. Noonan, C. H. Fleming, K. Olson, T. Mueller, D. Sheldon, J. M. Calabrese. ``Statistical inference for home range overlap'', Methods in Ecology and Evolution, 9:7, 1679-1691 (2018) doi: 10.1111/2041-210X.13027 .

C. H. Fleming and K. Winner

In `ctmm`

v0.5.2, direct support for `telemetry`

objects was dropped and the `CTMM`

argument was depreciated for `UD`

objects, simplifying usage.

Uncertainties in the model fits are propagated into the overlap estimate under the approximation that the Bhattacharyya distance is a chi-square random variable. Debiasing makes further approximations noted in Winner & Noonan et al (2018).

# \donttest{ # Load package and data library(ctmm) data(buffalo) # fit models for first two buffalo GUESS <- lapply(buffalo[1:2], function(b) ctmm.guess(b,interactive=FALSE) ) # using ctmm.fit here for speed, but you should almost always use ctmm.select FITS <- lapply(1:2, function(i) ctmm.fit(buffalo[[i]],GUESS[[i]]) ) names(FITS) <- names(buffalo[1:2]) # Gaussian overlap between these two buffalo overlap(FITS)#> , , low #> #> Cilla Gabs #> Cilla 1.000000 0.898462 #> Gabs 0.898462 1.000000 #> #> , , est #> #> Cilla Gabs #> Cilla 1.0000000 0.9987807 #> Gabs 0.9987807 1.0000000 #> #> , , high #> #> Cilla Gabs #> Cilla 1 1 #> Gabs 1 1 #># AKDE overlap between these two buffalo # create aligned UDs UDS <- akde(buffalo[1:2],FITS) # evaluate overlap overlap(UDS)#> , , low #> #> Cilla Gabs #> Cilla 1.0000000 0.8957911 #> Gabs 0.8957911 1.0000000 #> #> , , est #> #> Cilla Gabs #> Cilla 1.0000000 0.9958115 #> Gabs 0.9958115 1.0000000 #> #> , , high #> #> Cilla Gabs #> Cilla 1 1 #> Gabs 1 1 #># }