ctmm (version 1.2.0)

overlap: Calculate the overlap between two stationary distributions

Description

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.

Usage

overlap(object,method="Bhattacharyya",level=0.95,debias=TRUE,...)

Value

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.

Arguments

object

A list of ctmm fit or aligned UD objects to compare.

method

Can be "Bhattacharyya" or "Encounter" (see Details below).

level

The confidence level desired for the output.

debias

Approximate debiasing of the overlap.

...

Not currently used.

Author

C. H. Fleming and K. Winner

Details

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.

References

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) tools:::Rd_expr_doi("10.1111/2041-210X.13027").

See Also

akde, ctmm.fit, distance, encounter

Examples

# \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)

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