spatialCorrForPointsPlot: Plot spatial autocorrelation for geographic points

In adamlilith/enmSdm: Tools for Modeling Niches and Distributions of Species

Plot spatial autocorrelation for geographic points

Description

This function plots output from the function spatialCorrForPoints which estimates a null distribution of pairwise distances between points for an observed set of points. In the plot the lines and points represent the observed pairwise distance distribution and the polygon represents the randomized distribution with maximum values representing the upper n-th (usually 95th) percentile of the null distribution. Points falling above the polygon indicate the observed set of points has more pairwise distances than expected by chance at the given distance interval.

Usage

spatialCorrForPointsPlot(
  x,
  perc = 95,
  rescale = 1,
  nullCol = "gray",
  arrow = TRUE,
  leg = TRUE,
  xlab = "Distance",
  ylab = "Proportion of distances",
  ...
)

Arguments

x	Matrix generated by the function spatialCorrForPoints.
perc	Numeric value in the range [0, 100], indicates the upper quantile of randomized distance frequencies above which observed distance frequencies are considered significant. Default is 95.
rescale	Numeric, value by which to multiply distances. For example, if distances are in meters, but it is visually more appealing to display them in kilometers, then rescale should equal 0.001 (km / m). Default is 1 (no re-scaling).
nullCol	Character or non-negative integer indicating fill color for null distribution.
arrow	Logical, if TRUE then add an arrow indicating the interval at which the observed distance distribution is first insignificantly different from the null distribution.
leg	Logical, if TRUE (default) then include legend.
xlab, ylab	x- and y-axis labels.
...	Arguments to pass to plot.

Details

The idea behind this measure of spatial autocorrelation is that a set of geographic points is "independent" of one another if their pairwise distances are indistinguishable from pairwise distances of the same number of points randomly located across a landscape. Typically a set of points displays clustering (non-independence) across some distances but not all distances. Thus to identify the scale of clustering pairwise distances are tabulated into bins. (We suggest using overlapping bins, e.g., from 0 to 20000 m, 10000 to 30000 m, 20000 to 40000 m, etc. See the example below for how to do this). The function spatialCorrForPoints first calculates the observed distance distribution and tabulates the frequency of distances into bins. Then, it generates a set of randomly located points equal to the same number of points as in the observed set. It then calculates the randomized distance distribution and tabulates the distances. The randomization is repeated a large number of times (the default is 100). The observed frequency of distances can be compared to the set of random distances using spatialCorrForPointsSummary and spatialCorrForPointsPlot. The default values in those functions assume that clustering occurs if the observed pairwise distance is > the 95th quantile of the null frequency distribution for that bin (i.e., a 1-tailed test), but users can specify a different percentile to demarcate significance. In practice a series of distance bins often show clustering, but the one usually of interest is the first distance bin (the one closest to 0) that has a non-significant difference between observed and expected distances. This is the characteristic diameter of a cluster of points. Points closer than this distance can be considered non-independent of one another. Alternatively, one can specify a set of points using the fixed argument. In this case, the "observed" pairwise distance distribution is tabulated from the set of pairwise distances between the points specified by argument pts and fixed. The randomized distance distribution is calculated by randomly re-locating points in pts and calculating distances to fixed. The function spatialCorrForPointsWeight calculates weights for a set of points based on the characteristic scale of spatial autocorrelation.

See Also

spatialCorrForPoints, spatialCorrForPointsSummary, spatialCorrForPointsWeight

Examples

## Not run: 
# create raster of Madagascar
data(mad0)
rast <- raster::raster(mad0, res=c(1/12, 1/12))
rast[] <- 1
rast <- raster::crop(rast, mad0)
mad0rast <- raster::rasterize(mad0, rast)
rast <- rast * mad0rast

# lemur point data
data(lemurs)
fulvus <- lemurs[lemurs$species == 'Eulemur fulvus', c('longitude', 'latitude')]

# create overlapping bins for tabulating pairwise distances
ext <- extent(rast)
southwest <- c(ext@xmin, ext@ymin)
northeast <- c(ext@xmax, ext@ymax)
maxDist <- geosphere::distGeo(southwest, northeast)

binLength <- 60000 # in meters
maxDist <- binLength * ceiling(maxDist / binLength)

breaks <- data.frame(
	lower=seq(0, maxDist - binLength, by=binLength / 2),
	upper=seq(binLength, maxDist, by=binLength / 2)
)

# compare observed pairwise distance distribution to null distribution
# of pairwise values from randomly located points
obsAndNullDistrib <- spatialCorrForPoints(
	pts = fulvus,
	rast = rast,
	breaks = breaks,
	iters = 100,
	verbose = TRUE
)

# summary and plot
sacDist <- spatialCorrForPointsSummary(obsAndNullDistrib)
main <- paste('Characteristic cluster size:', sacDist, 'meters')
spatialCorrForPointsPlot(obsAndNullDistrib, xlab='Distance (m)', main=main)

# calculate weights
weight <- 4 * spatialCorrForPointsWeight(x=obsAndNullDistrib, pts=fulvus)
plot(mad0, main='Point size represents weight')
points(fulvus, pch=1, cex=weight)

## End(Not run)

adamlilith/enmSdm documentation built on Jan. 6, 2023, 11 a.m.