centers: Calculate weighted centroids
In eliotmiller/metricTester: Test Metric and Null Model Statistical Performance

Description Usage Arguments Details Value References Examples

Calculate the weighted centroids of clouds of multivariate points.

1	centers(ordination.results, road.map)

ordination.results

Data frame of ordination results, e.g. the $x element from a prcomp object, or the $points element from a metaMDS object in vegan.

road.map

Identical to the input for the 'a' argument in the dbFD function of the FD package, and to the picante.cdm argument used elsewhere in this package. Thus, this is a matrix containing the abundance of each 'species' in the ordination results. Rows are "sites" and columns are "species". Rather than abundances, the values can simply be presence/absences. Moreover, sites could be species and species could be individuals. See details.

The definition of FDis provided by Laliberte and Legendre (2010) and implemented in the dbFD function of the FD package is geared towards calculating the functional diversity of a community, given a set of species with an array of traits. Another useful way in which FDis might be implemented is as a measure of a species' niche breadth. In this case, ordination.results would be measures (e.g. foraging observations) of multiple individuals of multiple species', and road.map would be a matrix describing which observations belong to which species. The abundances in the matrix in this case would describe how much weight to assign to each individual observation.

Matrix specifying the position of the centroids along each axis.

Miller, E. T. 2016. Random thoughts.

Laliberte, E. & P. Legendre. 2010. A distance-based framework for measuring functional diversity from multiple traits. Ecology 91:299-305.

#example of how to calculate the weighted centroids of a series of plots based on the
#traits of a set of species. begin by simulating a phylogeny with a birth-death process
tree <- geiger::sim.bdtree(b=0.1, d=0, stop="taxa", n=50)

#create a log-normal abundance distribution
sim.abundances <- round(rlnorm(5000, meanlog=2, sdlog=1)) + 1

#simulate a community data matrix, with species as columns and sites as rows
cdm <- simulateComm(tree, richness.vector=10:25, abundances=sim.abundances)

#simulate two traits, combine into a matrix, then ordinate with a PCA
traits <- evolveTraits(tree)[[2]]
ord <- prcomp(traits)

#the weighted centroids ("average traits") of the species in each plot
exCenter <- centers(ordination.results=ord$x, road.map=cdm)

#visual demonstration of how the function works. plot all of the species in the first
#three sites in the CDM according to their ordinated trait values, color the points
#according to the site (red=site1, purple=site2, blue=site3), and scale the size of the
#point to the abundance of that species in that site. centroids are plotted in the
#same color but given a thick black border.
plot(ord$x, type="n")
for(i in 1:3)
{
	#find the species and their abundances that occur in the relevant plot
	focal <- as.matrix(cdm)[i,][as.matrix(cdm)[i,]!=0]
	pointColors <- c(rgb(1, 0, 0, 0.6), rgb(0.7, 0, 1, 0.6), rgb(0, 0, 1, 0.6))
	for(j in 1:length(focal))
	{
		location <- ord$x[names(focal)[j],]
		points(x=location[1], y=location[2], col=pointColors[i], pch=20, cex=focal[j]/5)
	}
	points(x=exCenter[i,1], y=exCenter[i,2], pch=21, col="black", lwd=2, cex=2,
	bg=pointColors[i])
}