overlap | R Documentation |

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,method="Bhattacharyya",level=0.95,debias=TRUE,...) `

`object` |
A |

`method` |
Can be |

`level` |
The confidence level desired for the output. |

`debias` |
Approximate debiasing of the overlap. |

`...` |
Not currently used. |

The default `method="Bhattacharyya"`

estimates the standard overlap measure `\int\int \sqrt{p(x,y) \, q(x,y)} \, dx \, dy`

between the distributions `p(x,y)`

and `q(x,y)`

,
while `method="encounter"`

estimates the non-standard measure `\frac{\int\int p(x,y) \, q(x,y) \, dx \, dy}{\sqrt{\int\int p(x',y')^2 \, dx' dy' \int\int q(x'',y'')^2 \, dx'' dy''}}`

,
which has a numerator proportional to the uncorrelated encounter probability.
Both measures lie between 0 and 1, where 0 indicates no shared support and 1 indicates identical distributions.

An object with slots `DOF`

, containing the effective sample sizes, and `CI`

containing a table of confidence intervals on the overlap estimates. 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.

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).

C. H. Fleming and K. Winner

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) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/2041-210X.13027")}.

`akde`

, `ctmm.fit`

, `distance`

, `encounter`

```
# 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)
# AKDE overlap between these two buffalo
# create aligned UDs
UDS <- akde(buffalo[1:2],FITS)
# evaluate overlap
overlap(UDS)
```

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