Calculates the overlap between the volumes defined by two sets of points in cartesian space.

voloverlap(tcsres1, tcsres2, plot = FALSE, interactive = FALSE,
col = c("blue", "red", "darkgrey"), fill = FALSE, new = TRUE,
montecarlo = FALSE, nsamp = 1000, psize = 0.001, lwd = 1, ...)

## Arguments

tcsres1, tcsres2 (required) data frame, possibly a result from the colspace function, containing values for the 'x', 'y' and 'z' coordinates as columns (labeled as such) logical. Should the volumes and points be plotted? (defaults to FALSE) logical. If TRUE, uses the rgl engine for interactive plotting; if FALSE then a static plot is generated. a vector of length 3 with the colors for (in order) the first volume, the second volume, and the overlap. logical. should the two volumes be filled in the plot? (defaults to FALSE) logical. Should a new plot window be called? If FALSE, volumes and their overlap are plotted over the current plot (defaults to TRUE). logical. If TRUE, Monte Carlo simulation is used instead of exact solution (not recommended; defaults to FALSE) if montecarlo = TRUE, determines the number of points to be sampled. if montecarlo = TRUE and plot = TRUE, sets the size to plot the points used in the Monte Carlo simulation. if plot = TRUE, sets the line width for volume grids. additional arguments passed to the plot. See vol

## Value

Calculates the overlap between the volumes defined by two set of points in colorspace. The volume from the overlap is then given relative to:

• vsmallest the volume of the overlap divided by the smallest of that defined by the the two input sets of color points. Thus, if one of the volumes is entirely contained within the other, this overlap will be vsmallest = 1.

• vboth the volume of the overlap divided by the combined volume of both input sets of color points.

The Monte Carlo solution is available mostly for legacy and benchmarking, and is not recommended (see notes). If used, the output will be different:

• s_in1, s_in2 the number of sampled points that fall within each of the volumes individually.

• s_inboth the number of sampled points that fall within both volumes.

• s_ineither the number of points that fall within either of the volumes.

• psmallest the proportion of points that fall within both volumes divided by the number of points that fall within the smallest volume.

• pboth the proportion of points that fall within both volumes divided by the total number of points that fall within both volumes.

If the Monte Carlo solution is used, a number of points much greater than the default should be considered (Stoddard & Stevens(2011) use around 750,000 points, but more or fewer might be required depending on the degree of overlap).

## Note

Stoddard & Stevens (2011) originally obtained the volume overlap through Monte Carlo simulations of points within the range of the volumes, and obtaining the frequency of simulated values that fall inside the volumes defined by both sets of color points.

Here we present an exact solution based on finding common vertices to both volumes and calculating its volume. However, we also the Monte Carlo solution is available through the montecarlo=TRUE option.

Stoddard & Stevens (2011) also return the value of the overlap relative to one of the volumes (in that case, the host species). However, for other applications this value may not be what one expects to obtain if (1) the two volumes differ considerably in size, or (2) one of the volumes is entirely contained within the other. For this reason, we also report the volume relative to the union of the two input volumes, which may be more adequate in most cases.

## References

Stoddard, M. C., & Prum, R. O. (2008). Evolution of avian plumage color in a tetrahedral color space: A phylogenetic analysis of new world buntings. The American Naturalist, 171(6), 755-776.

Stoddard, M. C., & Stevens, M. (2011). Avian vision and the evolution of egg color mimicry in the common cuckoo. Evolution, 65(7), 2004-2013.

Villeger, S., Novack-Gottshall, P. M., & Mouillot, D. (2011). The multidimensionality of the niche reveals functional diversity changes in benthic marine biotas across geological time. Ecology Letters, 14(6), 561-568.

Maia, R., White, T. E., (2018) Comparing colors using visual models. Behavioral Ecology, ary017 doi: 10.1093/beheco/ary017

## Examples

# NOT RUN {
data(sicalis)
tcs.sicalis.C <- subset(colspace(vismodel(sicalis)), 'C')
tcs.sicalis.T <- subset(colspace(vismodel(sicalis)), 'T')
tcs.sicalis.B <- subset(colspace(vismodel(sicalis)), 'B')
voloverlap(tcs.sicalis.T, tcs.sicalis.B)
voloverlap(tcs.sicalis.T, tcs.sicalis.C, plot = T)
voloverlap(tcs.sicalis.T, tcs.sicalis.C, plot = T, col = 1:3)
# }