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Tutorial for multivariate statistics
######################################################################
# Multivariate methods tutorial
# Rob Smith, smithr2@oregonstate.edu, Oregon State Univ, 16 Nov 2017
## CC-BY-SA 4.0 License (Creative Commons Attribution-ShareAlike 4.0)
# preamble to load required packages
rm(list=ls())
pkg <- c('vegan','viridis')
has <- pkg %in% rownames(installed.packages())
if(any(!has))install.packages(pkg[!has])
lapply(pkg, require, character.only=T, quietly=T)
rm(pkg, has)
# convenience function to convert numeric vector to color vector
`colvec` <- function(x, alpha=0.8, n=99, ...){
pal <- inferno(n=n, begin=.2, end=.9, alpha=alpha, direction=1)
pal[cut(x, breaks=length(pal), include.lowest=T)]
}
# data load; y=multivariate responses, x=explanatory variables
# read from csv...
# setwd('E:/tft/oak/')
# y <- read.csv('Oakwood1.csv', stringsAsFactors=F, row.names=1)
# x <- read.csv('Oakwood2.csv', stringsAsFactors=F, row.names=1)
# or source from url connection...
u <- 'https://gist.github.com/phytomosaic/0a93ab96e49ba9f11a0cf59b8be4cf07/raw/422d4d2d67507c1c32ab74d796c977ef8bc72423/oakwood_data.txt'
source(url(u))
closeAllConnections()
rm(u)
# convert certain columns to factors
x[,c(9:13,20:24,29,30)] <- lapply(x[,c(9:13,20:24,29,30)], factor)
# examine
head(y)
head(x)
str(x)
# relativize (already done for oakwood species data)
# ym <- decostand(y, 'max', MARGIN=2) # scale species by max (0-1)
# xm <- decostand(x, 'max', MARGIN=2) # scale environ by max (0-1)
# create distance matrix D from species data
D <- vegdist(y, method='bray', binary=T)
# three kinds of ordination
m1 <- metaMDS(D, k=2, try=200, trymax=500) # NMS
m2 <- cmdscale(D, k=2, add=T) # PCoA
m3 <- prcomp(y) # PCA
# color vector for plotting
cv <- inferno(nrow(x),begin=.2,end=.9,alpha=.9,direction=1)
# compare three kinds of ordination
par(mfrow=c(1,3), bty='l', las=1)
plot(m1$points, type='n', xlab='NMDS1', ylab='NMDS2')
text(m1$points, rownames(m1$points),cex=.8, col=cv)
plot(m2$points, type='n', xlab='PCoA1', ylab='PCoA2')
text(m2$points, rownames(m2$points),cex=.8, col=cv)
plot(m3$x, type='n', xlab='PCA1', ylab='PCA2')
text(m3$x, rownames(m3$x),cex=.8, col=cv)
par(mfrow=c(1,1))
# fit btwn ordination distances vs original species dissimilarities
cor(dist(m1$points), D, method='kendall')
cor(dist(m2$points), D, method='kendall')
cor(dist(m3$x), D, method='kendall')
# NMS is almost always the best choice -- it minimizes stress
# fit btwn environmental distances vs original species dissimilarities
pc <- prcomp(x[,sapply(x, is.numeric)], scale=T) # PCA of enviro
pc <- scores(pc, display='sites', choices=1:2) # PCA scores
eD <- vegdist(pc, method='euc') # Euclidean distances of scores
mantel(D, eD) # fit = Mantel statistic r
protest(m1$points, pc) # fit = correlation in Procrustes rotation
rm(pc, eD, cv)
# find best subset of explanatory vars maximizing rank corr w/ D
best <- bioenv(D, env=x[,sapply(x, is.numeric)], upto=3, trace=T)
best
# overlay continuous gradients using point colors
par(mfrow=c(1,3), bty='l', las=1)
plot(scores(m1), pch=16, col=colvec(x$PDIR))
plot(scores(m1), pch=16, col=colvec(x$TreeHtM))
plot(scores(m1), pch=16, col=colvec(x$SppRich))
par(mfrow=c(1,1))
# overlay continuous gradients by fitting a GAM surface
f1 <- ordisurf(m1 ~ x$SppRich, plot=F)
plot(scores(m1), pch=16, col=colvec(x$SppRich))
plot(f1, add=T, col=1, lwd=2)
# clustering to form groups
cl <- hclust(D, method='ward.D2')
plot(cl, col=cutree(cl, 4), cex=0.7)
rect.hclust(cl, 4)
# overlay clusters
plot(scores(m1), pch=16, col=cutree(cl, 4))
ordicluster(m1, cl, prune=3, col=cutree(cl, 4))
# overlay other grouping variables
plot(scores(m1), pch=16, col=x$GrazCurrC)
plot(scores(m1), pch=16, col=x$GrazPastC)
plot(scores(m1), pch=16, col=x$NotLoggdC)
# test differences among groups
# permanova: test for differences in multivariate centroid
a1 <- adonis(D ~ x$NotLoggdC, permu=999)
print(a1)
# permdisp: test for differences in multivariate dispersion
b1 <- betadisper(D, x$NotLoggdC)
permutest(b1, pairwise=TRUE, permu=999)
# plot multivariate centroids per group
centr <- aggregate(scores(m1),
by=list(logged=x$NotLoggdC),
mean)[-1]
plot(m1$points, pch=16, col=x$NotLoggdC)
points(centr[1,], pch='+', col=1, cex=3)
points(centr[2,], pch='+', col=2, cex=3)
# permanova works as 'regular' ANOVA when using Euclidean distances...
De <- vegdist(x$SppRich, 'euc')
adonis(De ~ x$NotLoggdC, perm=999) # examine F and SS
anova(lm(x$SppRich ~ x$NotLoggdC)) # expect identical F and SS
# blocked design: permutations must occur within strata
blk <- factor(sample(rep(1:12,len=nrow(x)))) # make arbitrary 'blocks'
plot(scores(m1), pch=16, col=colvec(x$SppRich))
ordiellipse(m1, blk, label=TRUE)
customperm <- how(nperm=999)
setBlocks(customperm) <- blk
adonis(D ~ x$NotLoggdC, permutations=customperm)
### END ####
y <-
structure(list(ALL = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L,
1L, 0L, 0L, 0L, 0L), Abgr.t = c(0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.4, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0), Acar = c(0,
0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.5, 0, 0,
0, 0, 0, 0, 0, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0), Acma.t = c(0, 0.01851852, 0, 0, 1, 0.07407407,
0.01851852, 0, 0, 0, 0, 0.01851852, 0, 0.1111111, 0.1481482,
0, 0, 0, 0, 0.01851852, 0.1111111, 0, 0, 0, 0, 0.1111111, 0.03703704,
0.1111111, 0, 0, 0.1481482, 0, 0, 0, 0, 0, 0, 0.2222222, 0, 0.6666667,
0, 0.1111111, 0.1111111, 0, 0, 0.01851852, 0.07407407), Acma.s = c(0,
0.03333334, 0.01333333, 0, 0.03333334, 0.3333333, 0.06666667,
0, 0, 0.01333333, 0.3333333, 0, 0.03333334, 0.06666667, 0.4666667,
0.2666667, 0, 0, 0, 0, 1, 0, 0, 0, 0.03333334, 0.03333334, 0.03333334,
0.03333334, 0.01333333, 0.03333334, 0.8666667, 0.2, 0, 0, 0,
0, 0, 0.6666667, 0.01333333, 0.03333334, 0.01333333, 0.9333333,
0.2, 0.03333334, 0, 0.03333334, 0.3333333), Acmi = c(1, 1, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0.4, 0, 1, 0, 1, 0,
0, 0, 0), Adbi = c(0, 0.1666667, 0.1666667, 0, 0, 1, 0.1666667,
0.1666667, 0, 0, 0, 0, 0.06666667, 0.06666667, 0, 0, 0, 0, 0,
0.1666667, 0.1666667, 0, 0, 0, 0, 0.1666667, 0, 0.1666667, 0.6666667,
0.1666667, 0.1666667, 0, 0, 0, 0, 0, 0.1666667, 0.1666667, 0.1666667,
0.3333333, 0, 0, 0, 0, 0, 0, 0), Agha = c(0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0.2, 0.04, 0, 0, 0, 0, 0, 0, 0, 0, 0),
Agse = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0,
1, 0, 0, 0, 0, 0.4, 0, 0, 0, 0, 0, 0), Agte = c(0.125, 0.0625,
0.125, 0.0625, 0, 0.0625, 0.0625, 0.0625, 0, 0, 0, 0.0625,
0.0625, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0625, 0, 0.0625,
0, 0, 0.0625, 0, 0, 0.0625, 0, 0.0625, 1, 0, 0, 0, 0, 0.25,
0.025, 0.0625, 0.0625, 0.0625, 0.0625, 0.0625), Aica = c(0L,
1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L), Amal.s = c(0.04477612, 0.02985075, 0.04477612, 0.3432836,
0.04477612, 0.1791045, 0.00746269, 0.04477612, 0.1492537,
0.04477612, 0.00746269, 0.02985075, 0, 0.00746269, 0.5671642,
0.3731343, 0.07462686, 0.2985075, 0.119403, 0.05970149, 0.1492537,
1, 0.00746269, 0.9701493, 0.3432836, 0, 0.00746269, 0.00746269,
0, 0.00298508, 0.00746269, 0, 0.04477612, 0.6716418, 0.1492537,
0.00746269, 0.04477612, 0.00298508, 0, 0.04477612, 0, 0.00298508,
0.00298508, 0.1044776, 0.07462686, 0.07462686, 0.1343284),
Apan = c(0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0.4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), Aqfo = c(0L, 1L, 0L,
0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L),
Arel = c(0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 1L, 0L, 1L, 0L), Arme.s = c(0, 0, 0, 0, 0, 0, 1, 0, 0,
0, 0, 0, 0, 0.1666667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.06666667,
0.06666667, 0, 0, 0), Beaq = c(0, 0, 0, 0, 0.5, 0, 0, 0,
0, 0, 0, 0, 0.5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0.5, 0, 0, 0, 0.2, 0, 0.5, 0,
0, 1, 0), Brla = c(0.25, 0.25, 0.25, 0.25, 0, 0.25, 0.25,
0.25, 0.25, 0.25, 0.25, 0, 0.25, 0.25, 0.25, 0.25, 0, 0,
0, 0.25, 0, 0, 0, 0, 0.25, 0.25, 0.25, 0, 0.25, 0.5, 0.25,
0, 0.25, 0, 0.25, 0.5, 0.25, 0.25, 0.25, 0.25, 0.25, 0.1,
0.25, 0, 0, 0.25, 1), Brpu = c(1, 0, 1, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0.4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
Brri = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.5, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0.5, 0, 0, 0.5, 0,
0, 0.5, 0, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0), CAR = c(0, 0,
0.5, 0.5, 0, 0.5, 0, 0, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0.5, 0, 0, 0.5, 0.2, 0, 0, 0, 0, 0, 0, 0, 0, 0.5, 0, 0, 1,
0, 0, 0, 0.5, 0.5, 0, 0.5, 0.5, 0.2, 0.5, 0), Cato = c(0,
0, 0, 0.4, 0, 0.4, 0, 0, 0, 1, 0, 0, 0, 0, 0.4, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0), Cipa = c(0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0.1, 0, 1, 0.2, 0, 0.4, 0, 0.1, 0, 0.1, 0, 0,
0, 0, 0, 0.1, 0.04, 0.1, 0.4, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0), Coco.s = c(0.00694444, 0, 0.2083333,
0.00694444, 0.3055556, 0, 0.02777778, 0.00277778, 0, 0.1388889,
1, 0.02777778, 0.1666667, 0.02777778, 0.02777778, 0.1944444,
0.4027778, 0.2916667, 0.5833333, 0.4305556, 0.02777778, 0,
0, 0, 0, 0.04166667, 0.01388889, 0.5138889, 0.08333334, 0.00694444,
0.5972222, 0.05555556, 0, 0, 0, 0, 0.1527778, 0.06944445,
0.00694444, 0.08333334, 0, 0.1527778, 0, 0, 0.00277778, 0.4583333,
0.05555556), Conu = c(0, 0, 0, 0, 0, 0.5, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0.25, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.1, 0, 0, 0, 0),
Crdo.s = c(0.125, 0.125, 0.05, 0, 0.125, 0.25, 0.05, 0, 0,
1, 0, 0.125, 0, 0, 0.5, 0, 0, 1, 0, 0, 0.05, 0.125, 0, 0,
0, 0.05, 0, 0, 0, 0.125, 0.5, 0, 0.05, 0, 0, 0, 0.125, 0,
0, 0, 0, 0.125, 0.125, 0.125, 0, 0.25, 0.05), Crox = c(0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0.4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.4, 1, 0, 0,
0, 0, 0, 0, 0, 0.4, 0, 0, 0), Cyec = c(0, 0.08333334, 0,
0, 0, 0.08333334, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.03333334, 0, 0,
0, 0, 0, 0.08333334, 0, 1, 0, 0.08333334, 0, 0, 0, 0), Daca = c(0,
0, 0, 0, 0, 0, 0, 0, 0.25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0.5, 0, 0, 0, 0, 0, 0, 0.25, 0, 0, 0.25, 0, 0.25,
0.25, 0, 0, 0, 0, 1, 0, 0.25, 0, 0, 0, 0), Dacar = c(0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0.4, 0, 1, 0.4, 1, 0, 0), Dagl = c(0.02380952, 0.02380952,
0.0952381, 0.0952381, 0, 0.04761905, 0, 0.00952381, 0, 0,
0, 0, 0, 0, 0.02380952, 0, 0, 0, 0, 0.02380952, 0, 0, 1,
0, 0, 0.00952381, 0, 0, 0, 0, 0, 0, 0.02380952, 0, 0, 0.2857143,
0.00952381, 0, 0.02380952, 0, 0, 0, 0.02380952, 0.02380952,
0.00952381, 0, 0), Drar = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0.7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0.05, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
Elgl = c(0.1, 0.1, 0.1, 0.1, 0, 0, 0.1, 0.1, 0, 0.1, 0.1,
0.1, 0.1, 0.1, 0.1, 0.04, 0, 0, 0, 0, 0, 0, 0.4, 0, 0, 0.1,
0.04, 0, 0.1, 0.1, 0, 0, 0.1, 0, 0.1, 1, 0.1, 0, 0.1, 0,
0, 0, 0.1, 0.1, 0.04, 0.1, 0.1), Erla = c(0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.5, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0.5, 0, 0.5,
0, 0, 0, 0), Erog = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0.4, 0, 1, 0, 0,
0, 1, 0, 0.4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), Feca = c(0.5,
0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0.5, 0, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.2,
0, 0, 0, 0, 0, 0.2, 1, 0, 0, 0), Feoc = c(0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0.4, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0), Feru = c(0, 0.04166667, 0, 0.04166667, 0, 0.04166667,
0, 0, 0, 0, 0, 0.04166667, 0.04166667, 0, 0.04166667, 0,
0, 0, 0, 0, 0, 0, 0.6666667, 0, 0, 0, 0.04166667, 0, 0, 0.04166667,
0, 0, 0.04166667, 0, 0, 1, 0, 0, 0.04166667, 0, 0.5833333,
0, 0.04166667, 0, 0, 0, 0.04166667), Frbr = c(0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L),
Frla = c(0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
1L, 0L, 0L, 0L, 0L), Frla.s = c(0.1, 0.1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.04,
0, 0, 0, 0, 0, 0, 0, 0, 0.4, 0, 0, 0, 0.04, 0.04, 0, 0, 0,
1, 0.2, 0, 0.04, 0), Frvi = c(1, 1, 1, 1, 0, 1, 1, 0, 1,
0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0.4, 0, 0, 0, 1, 1, 0, 1, 1
), GAL = c(0.07142857, 0.07142857, 0.2857143, 0.07142857,
0, 0.07142857, 0.07142857, 1, 0.07142857, 0.07142857, 0.4285714,
0.07142857, 0.4285714, 0.2857143, 0.07142857, 0.1428571,
0.07142857, 0.07142857, 0, 0.07142857, 0.07142857, 0.07142857,
0.07142857, 0.5714286, 0.07142857, 0.07142857, 0.07142857,
0, 0.07142857, 0.07142857, 0.07142857, 0.07142857, 0.07142857,
0.02857143, 0.07142857, 0.07142857, 0.07142857, 0.07142857,
0.2857143, 0, 0, 0.07142857, 0, 0.07142857, 0.4285714, 0.2857143,
0.2857143), Geog = c(0, 0, 0, 0, 0, 1, 0, 0.4, 0, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0.4,
0, 0, 0, 0, 0, 0, 0, 0.4, 0, 0, 0, 0, 0, 0, 0, 0), Gepu = c(0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0.02857143, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.07142857,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), Hodi = c(0, 0,
0.02702703, 0, 0.1891892, 0, 0, 0, 0, 0, 0, 0, 0.1891892,
0.3513514, 0, 0, 0, 0, 0.5675676, 0.05405406, 0, 0, 0, 0,
0.7567568, 0.00540541, 0, 0, 0.9459459, 0, 0, 0.08108108,
0.00540541, 0, 0, 0, 1, 0, 0.05405406, 0, 0, 0, 0, 0.00540541,
0.1081081, 0, 0), Hola = c(0.1, 0.05, 0.2, 0.05, 0, 0.1,
0.05, 0, 0, 0.05, 0, 0, 0, 0, 0, 0.02, 0, 0, 0, 0, 0, 0,
0.2, 0, 0, 0.05, 0.05, 0, 0, 0.4, 0.05, 0, 0.05, 0, 0.05,
0.05, 0.05, 0.05, 1, 0.05, 0.3, 0, 0.05, 0.05, 0, 0, 0),
Hype = c(0, 0.25, 0.25, 0.5, 0, 0.25, 0, 0.25, 0.25, 0.25,
0.1, 0.25, 0, 0.1, 0.25, 0.25, 0, 0, 0, 0.1, 0, 0.25, 0.25,
0.25, 0, 0.25, 0.25, 0, 0, 0.25, 0.25, 0, 1, 0, 0, 0.25,
0.25, 0.1, 0.25, 0, 0.25, 0.25, 0.25, 0.5, 0, 0.1, 0.25),
Irte = c(0, 0, 0, 0.25, 0, 0.25, 0, 0, 0, 0.25, 0, 0, 0,
0, 0.25, 0, 0, 0, 0, 0.25, 0, 0, 1, 0, 0, 0.25, 0, 0, 0,
0.25, 0, 0, 0.25, 0, 0, 0, 0.25, 0, 0.25, 0, 0, 0, 0.25,
0, 0, 0, 0), Kocr = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0.4, 0, 1, 0, 0, 0, 0), Lapo = c(0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L,
0L), Lasa = c(0, 0, 0, 0, 0, 0, 0, 0.5, 0, 0.5, 0.5, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.5, 0, 0, 0, 0.5, 0,
0, 0, 0, 0.5, 0.2, 0, 0.2, 0, 0, 1, 0, 0, 0, 0, 0.2, 0),
Liap = c(0, 0, 0, 0.01785714, 0, 0, 0, 0.01785714, 0.2142857,
0, 1, 0.01785714, 0.1785714, 0.03571429, 0.01785714, 0.01785714,
0, 0, 0, 0.01785714, 0.01785714, 0, 0, 0, 0.1071429, 0.01785714,
0.01785714, 0.01785714, 0.01785714, 0, 0, 0, 0, 0.00714286,
0.2142857, 0, 0, 0.01785714, 0, 0, 0, 0, 0, 0, 0, 0.2857143,
0), Loci = c(0, 0.1666667, 0, 0, 0, 0.1666667, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.1666667, 0, 0,
0, 0, 0, 0.1666667, 0, 0.1666667, 0, 0, 0, 0.1666667, 0,
0, 0, 0.1666667, 0.6666667, 0.3333333, 0, 0, 0, 0.1666667
), Lope = c(1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L), MAL.s = c(0, 0, 0, 0, 0, 0.6666667,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.06666667, 0, 0, 0, 1,
0, 0.6666667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.1666667,
0, 0, 0, 0, 0, 0, 0.1666667, 0, 0, 0), Mebu = c(0, 0, 1,
0, 0, 0, 0, 0, 0, 1, 1, 0, 0.4, 1, 1, 0, 0, 0, 0, 0, 0.4,
0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1,
0, 0, 0, 0, 0, 0, 0), Mope = c(0, 0, 0, 0, 0, 0, 0, 1, 0.25,
0, 0.25, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0.1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0), Mosi = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0.4,
0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), Nepa = c(0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 0L,
1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L
), Osce.s = c(0, 0, 0, 0.04761905, 0.1904762, 0.04761905,
0, 0.00952381, 0.02380952, 0.00952381, 0.00952381, 0, 0,
0.02380952, 0.0952381, 0, 0.3333333, 0.3333333, 0.9047619,
0, 0.02380952, 0, 0, 0, 1, 0, 0, 0, 0.02380952, 0, 0, 0.00952381,
0, 0.5238095, 0.04761905, 0.02380952, 0, 0, 0, 0.02380952,
0, 0, 0, 0.02380952, 0, 0.04761905, 0.00952381), Osnu = c(0.25,
0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0,
0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0, 0, 0.25, 0.25, 0,
0.25, 0.1, 0.1, 0.25, 1, 0.1, 0.25, 0.25, 0.25, 0, 0.25,
0, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0, 0.25, 0.25, 0.25,
0.5, 0, 0.25), Phle = c(0, 0, 0, 0, 0.2857143, 0, 0, 0, 0,
0, 0, 0, 0.2857143, 0.07142857, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0.4285714, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0), Phpr = c(0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0.4, 0, 0, 0, 0
), Plla = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L,
1L, 0L, 0L, 0L, 0L), Poco = c(0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0.4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
Pogl = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L,
0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 1L), Pogr = c(0, 0, 0, 0, 0, 1, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0.4, 0, 0, 0, 0, 0, 0, 0.4, 0, 0, 0,
0), Pomu = c(0, 0.00617284, 0.00617284, 0.00617284, 0.0617284,
0.1358025, 0.00617284, 0.00246914, 0.07407407, 0, 0.2098765,
0, 0.1975309, 0.09876543, 0.1234568, 0.00617284, 0.308642,
0.1481482, 0.8148148, 0.5679013, 0.2222222, 0, 0, 0.00246914,
0.03703704, 0.7654321, 0.1111111, 0.9876543, 0.5679013, 0.04938272,
0.4691358, 1, 0, 0.03703704, 0.04938272, 0, 0.1604938, 1,
0.02469136, 0.7160494, 0, 0.00617284, 0, 0.00617284, 0.00617284,
0.1234568, 0.03703704), Popr = c(0.02272727, 0.02272727,
0.02272727, 0.02272727, 0, 0.02272727, 0.02272727, 0.02272727,
0.02272727, 0, 0, 0.02272727, 0, 0, 0.02272727, 0, 0, 0,
0, 0, 0, 0, 0.1818182, 0, 0, 0, 0.02272727, 0, 0, 0, 0, 0,
0.6363636, 0, 0.02272727, 1, 0.02272727, 0.02272727, 0.02272727,
0, 0.8636364, 0, 0.2727273, 0.02272727, 0.02272727, 0, 0),
Povu = c(0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0, 0.4, 0.4,
0.4, 0.4, 0.4, 0, 0.4, 1, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0,
0.4, 0, 1, 0.4, 0.4, 0.4, 0, 1, 0.4, 0.4, 0.4, 0.4, 0.4,
1, 0.4, 0.4, 0.4, 0.4, 0.4, 0, 0.4, 0.4, 0.4, 0.4), Prav.t = c(0,
0, 0, 0.1555556, 0, 0.04444445, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0.2888889, 0.06666667, 0.3777778, 0.01111111, 0.4, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01111111,
0, 0.06666667, 0, 0, 0, 0, 0.06666667), Prav.s = c(0, 0,
0, 0.2266667, 0.01333333, 0.00666667, 0.00666667, 0.01333333,
0, 0.05333333, 0, 0, 0, 0, 0.08, 0.00266667, 0.5733333, 0.3733333,
0.4266667, 0.16, 0.6266667, 0.00266667, 0, 0.00666667, 0.05333333,
0, 1, 0.02666667, 0.00666667, 0, 0.00266667, 0.00266667,
0.00266667, 0.02666667, 0.00666667, 0.00266667, 0.04, 0.00266667,
0.00266667, 0.02666667, 0, 0.06666667, 0, 0, 0.00266667,
0.00266667, 0.7333333), Psme.t = c(0, 0.7692308, 0, 0, 0.3846154,
0, 0.03846154, 0, 0.2307692, 0, 0, 0, 0, 0.03846154, 0, 0,
0.03846154, 0, 0, 0, 0, 0, 0, 0, 0.3846154, 0.03846154, 0.2307692,
0, 1, 0.03846154, 0.1538462, 0, 0, 0, 0, 0, 0, 0.5384616,
0, 0, 0, 0.6923077, 0.03846154, 0, 0, 0, 0.7692308), Psme.s = c(0,
0.2, 0, 0.02, 0.7, 0, 0.05, 0, 0.3, 0.02, 0, 0, 0, 0.05,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.05, 0.2, 0, 0.02, 0.6, 0.02,
0.7, 0.2, 0.05, 0, 0, 0, 0, 0.3, 0, 0, 0.05, 1, 0.05, 0.05,
0, 0.05, 0.05), Ptaq = c(0, 0, 0.6666667, 0.1111111, 0.05555556,
0.6666667, 0.05555556, 0, 0, 0, 0.05555556, 0, 0, 0, 0, 0.3333333,
0.05555556, 0, 0, 0.7777778, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
0.4444444, 0.05555556, 0, 0, 0, 0, 0, 0.2222222, 0.05555556,
0.02222222, 0, 0, 0, 0, 0.05555556, 0.05555556, 0), Pyco.t = c(0,
0, 0, 0, 0, 0, 0, 0, 0, 0.6666667, 0, 0, 0, 0, 0, 0, 0, 0.06666667,
0, 0, 0, 0.06666667, 0, 0, 0.1666667, 0, 0, 0, 0, 0, 0, 0,
0.1666667, 0, 0, 0.06666667, 0.06666667, 0, 0, 0, 0.06666667,
0, 1, 0, 0, 0.6666667, 0), Pyfu.s = c(0.125, 0, 0, 0, 0,
0.05, 0.125, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0.125, 0.125, 0,
0, 0.05, 0, 0, 0.05, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.125,
0, 0, 0, 0, 0, 0.125, 0, 0, 0.05, 0.125, 0, 0), Quga.t = c(0.6867924,
0.5320755, 1, 0.5320755, 0.4075472, 0.5056604, 0.490566,
0.9584906, 0.5886792, 0.6716981, 0.6075472, 0.4075472, 0.6415094,
0.6867924, 0.5320755, 0.5584906, 0.5584906, 0.5660377, 0.4528302,
0.7849057, 0.909434, 0.5660377, 0.4830189, 0.7396227, 0.6528302,
0.4377359, 0.509434, 0.5320755, 0.5962264, 0.9886792, 0.4641509,
0.9849057, 0.6264151, 0.6603774, 0.5584906, 0.3773585, 0.445283,
0.6867924, 0.8226415, 0.7735849, 0.5584906, 0.5849057, 0.5207547,
0.4641509, 0.7056604, 0.954717, 0.6037736), Quga.s = c(0.05263158,
0.05263158, 0.02631579, 0.2105263, 0.02631579, 0.4210526,
0.1578947, 0.02631579, 0, 0, 0.02631579, 0.02631579, 0.02631579,
0, 0.05263158, 0.02631579, 0.02631579, 0, 0, 0.02631579,
0.02631579, 0.02631579, 0.5789474, 0.02631579, 0.05263158,
0.05263158, 0.02631579, 0, 0.01052632, 0.02631579, 0, 0,
1, 0.02631579, 0.02631579, 0.4736842, 0.02631579, 0.01052632,
0.1052632, 0.02631579, 0.3157895, 0.02631579, 0.05263158,
0.05263158, 0.05263158, 0.05263158, 0.02631579), Rhdi = c(0.6162791,
0.5, 0.3604651, 0.2906977, 0.00581395, 0.1511628, 0.2790698,
0.255814, 0.3837209, 0.3139535, 0.3139535, 0.9069768, 0.5581396,
0.4534884, 0.5116279, 0.7906977, 0.05813954, 0.2209302, 0.1976744,
0.4302325, 0.1860465, 0.1860465, 0.2790698, 0.1744186, 0.2906977,
0.372093, 0.08139535, 0.05813954, 0.127907, 0.255814, 0.06976745,
0.255814, 0.6860465, 0.09302326, 0.5116279, 0.03488372, 0.2906977,
0.2093023, 1, 0.1046512, 0.03488372, 0.4069767, 0.255814,
0.3604651, 0.1860465, 0.3372093, 0.3023256), Rhpu.t = c(0,
0, 0, 0, 0.3333333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0.06666667, 0, 1, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0.1666667, 0, 0, 0, 0, 0, 0, 0, 0, 0), Rhpu.s = c(0.04545455,
0, 0.04545455, 0, 0.2727273, 0, 0.04545455, 0, 0.04545455,
0.04545455, 0.04545455, 0, 0, 0.04545455, 0.04545455, 0,
0, 0, 1, 0.09090909, 0.04545455, 0, 0, 0, 0, 0, 0.01818182,
0, 0.1818182, 0, 0.2727273, 0.1818182, 0, 0.1818182, 0.01818182,
0, 0.09090909, 0.6363636, 0.01818182, 0.01818182, 0, 0.01818182,
0.01818182, 0.5454546, 0, 0.04545455, 0.04545455), Rodu = c(0.25,
0.25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0), Roeg = c(0.1304348, 0.08695652,
0.08695652, 0.3478261, 0.1304348, 0.3043478, 0.00869565,
0, 0.08695652, 0.4782609, 0.1304348, 0.7391304, 0.1304348,
1, 0.1739131, 0.08695652, 0, 0.02173913, 0.00869565, 0.08695652,
0.02173913, 0.2608696, 0.1304348, 0.1304348, 0, 0, 0.02173913,
0, 0, 0.02173913, 0.04347826, 0.00869565, 0.8695652, 0, 0.02173913,
0.04347826, 0.08695652, 0.02173913, 0.02173913, 0.00869565,
0.02173913, 0.02173913, 0.2608696, 0.08695652, 0.2608696,
0.2173913, 0.00869565), Rogy = c(0.125, 0.125, 0, 0, 0, 0.125,
0, 0.5, 0, 0.75, 0.125, 0, 0.5, 1, 0.5, 0.75, 0, 0.25, 0.25,
0.25, 0.75, 0.25, 0, 0.25, 1, 0.05, 0.125, 0, 0, 0.75, 0.125,
0.05, 0.5, 0, 0.125, 0, 0.75, 0.05, 0, 0.05, 0, 0, 0, 0.5,
0, 0.25, 0), Ronu = c(0, 0, 0.0625, 0.25, 0.0625, 0.125,
0, 0, 0.5, 0, 0, 0, 0, 0, 0.0625, 0, 0.25, 1, 0.125, 0, 0.0625,
0.625, 0, 0.25, 0.0625, 0, 0, 0, 0, 0, 0.0625, 0, 0, 0.5,
0, 0, 0.0625, 0, 0, 0, 0, 0, 0.0625, 0.25, 0.375, 0.375,
0), Ropi = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.4,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0.4, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0), Rula = c(0, 0, 0,
0, 0, 0, 0, 0, 0, 0.125, 0, 0.125, 0, 0.125, 0, 0, 0.125,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0.05, 1, 0, 0, 0), Rupa = c(0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0.00625, 0, 0, 0, 0, 0.00625, 0, 0.00625,
0.375, 0, 0, 0, 0, 0, 0, 0, 0, 0.59375, 0, 0, 0.0625, 0,
0, 0, 0, 0, 0, 0, 0, 0.28125, 0, 0, 0, 0, 0, 0, 0), Rupr = c(0,
0, 0, 0, 0, 0, 0, 0.01818182, 0.01818182, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.04545455, 0,
0, 0, 0, 0.01818182, 0.04545455, 0, 0, 0, 0, 0, 0.01818182,
0, 0.09090909, 1, 0, 0.09090909, 0), Ruur = c(0, 0.01754386,
0.8596491, 0, 0.00877193, 0.05263158, 0.03508772, 0, 0.07017544,
0.122807, 0.07017544, 0, 0.122807, 0.4035088, 0, 0.5438597,
0.2631579, 0, 0.03508772, 0.00877193, 0.1754386, 0, 0, 0,
0, 0.1578947, 0.3684211, 0.07017544, 0.00877193, 0.6842105,
0.6666667, 0.2631579, 0, 0.00350877, 0.00877193, 0, 0.3859649,
0.2280702, 0.4561403, 0, 0, 0.9649123, 0, 1, 0, 0.1578947,
0.122807), Sacr = c(0, 0, 0, 0, 0, 0, 0, 1, 0.5, 0.5, 1,
0.5, 0.5, 0.5, 0, 0, 0, 0, 0, 0.5, 0.5, 0, 0.5, 0, 0.2, 0.5,
0.5, 0.5, 0, 0.5, 0, 0, 0.5, 0, 0.2, 0.5, 0, 0, 0.2, 0.2,
0.5, 0, 0, 0, 0.5, 0.5, 0), Sado = c(0.25, 0.5, 0.25, 0,
0, 0.25, 0.25, 0, 0.25, 0, 0.25, 0.25, 0.25, 0.25, 0.5, 0.25,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0.25, 0.25, 0, 0, 0, 0.25, 0,
0.25, 0, 0, 0.25, 0.25, 0.25, 0.5, 0.25, 0.1, 0.25, 0.25,
1, 0, 0.5, 0.5), Syal = c(0.01388889, 0.1666667, 0.05555556,
0.4027778, 0.2916667, 0.25, 0.00277778, 0.6944444, 0.8888889,
0.7777778, 0.4027778, 0, 0.1666667, 0.5277778, 0.2916667,
0.00694444, 0.7777778, 0.9166667, 0.1527778, 0.3194444, 0.4722222,
0.8055556, 0.04166667, 0.8333333, 0.2222222, 0.3194444, 0.625,
0.2777778, 0.2222222, 0.9027778, 0.5138889, 0.8333333, 0.01388889,
1, 0.7638889, 0.00694444, 0.2222222, 0.02777778, 0.00694444,
0.08333334, 0.00277778, 0.1527778, 0.00277778, 0.4027778,
0.9861111, 0.6527778, 0.3472222), Taof = c(0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0.4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0.4, 0, 0, 0, 0,
0, 0, 0, 0), Tegr = c(0, 0, 0, 0, 0.125, 0.125, 0, 0, 0,
0.125, 0.125, 0, 1, 1, 0.125, 0.75, 0.125, 0, 0.125, 0.125,
0, 0, 0, 0, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125,
0.125, 0, 0, 0, 0, 0.125, 0.125, 0.125, 0.5, 0, 0, 0, 0.125,
0, 0, 0), Thoc = c(0.5, 0.5, 0, 0, 0, 0, 0, 0, 0.5, 0, 1,
0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.5, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
Toar = c(0.05555556, 0.05555556, 0.05555556, 0.05555556,
0.05555556, 0.05555556, 0.05555556, 0.7777778, 0.05555556,
0.2222222, 0.05555556, 0.1111111, 0.1111111, 0.05555556,
0.05555556, 0.05555556, 0.02222222, 0, 0, 0.05555556, 0.05555556,
0.05555556, 1, 0.05555556, 0, 0, 0.05555556, 0, 0, 0.05555556,
0, 0, 0.05555556, 0, 0.05555556, 0.2222222, 0.05555556, 0,
0.05555556, 0, 0.05555556, 0.05555556, 0.05555556, 0, 0.1111111,
0, 0.1111111), Trla = c(1L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 0L,
0L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L,
1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L), Trov = c(0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0.4, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0), Viam = c(0.08333334, 0.08333334, 0.08333334,
0.08333334, 0.08333334, 0.08333334, 0.08333334, 0.1666667,
0, 0.08333334, 0, 0, 0, 0, 0.03333334, 0.08333334, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0.08333334, 0, 0, 0.3333333,
0, 0.08333334, 0.08333334, 0, 0, 0.08333334, 0.08333334,
0.08333334, 0.08333334, 0.08333334, 0.03333334, 0, 0.08333334,
0.08333334), Vinu = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L)), .Names = c("ALL", "Abgr.t",
"Acar", "Acma.t", "Acma.s", "Acmi", "Adbi", "Agha", "Agse", "Agte",
"Aica", "Amal.s", "Apan", "Aqfo", "Arel", "Arme.s", "Beaq", "Brla",
"Brpu", "Brri", "CAR", "Cato", "Cipa", "Coco.s", "Conu", "Crdo.s",
"Crox", "Cyec", "Daca", "Dacar", "Dagl", "Drar", "Elgl", "Erla",
"Erog", "Feca", "Feoc", "Feru", "Frbr", "Frla", "Frla.s", "Frvi",
"GAL", "Geog", "Gepu", "Hodi", "Hola", "Hype", "Irte", "Kocr",
"Lapo", "Lasa", "Liap", "Loci", "Lope", "MAL.s", "Mebu", "Mope",
"Mosi", "Nepa", "Osce.s", "Osnu", "Phle", "Phpr", "Plla", "Poco",
"Pogl", "Pogr", "Pomu", "Popr", "Povu", "Prav.t", "Prav.s", "Psme.t",
"Psme.s", "Ptaq", "Pyco.t", "Pyfu.s", "Quga.t", "Quga.s", "Rhdi",
"Rhpu.t", "Rhpu.s", "Rodu", "Roeg", "Rogy", "Ronu", "Ropi", "Rula",
"Rupa", "Rupr", "Ruur", "Sacr", "Sado", "Syal", "Taof", "Tegr",
"Thoc", "Toar", "Trla", "Trov", "Viam", "Vinu"), class = "data.frame", row.names = c("Stand01",
"Stand02", "Stand03", "Stand04", "Stand05", "Stand06", "Stand07",
"Stand08", "Stand09", "Stand10", "Stand11", "Stand12", "Stand13",
"Stand14", "Stand15", "Stand16", "Stand17", "Stand18", "Stand19",
"Stand20", "Stand21", "Stand22", "Stand23", "Stand24", "Stand25",
"Stand26", "Stand27", "Stand28", "Stand29", "Stand30", "Stand31",
"Stand32", "Stand33", "Stand34", "Stand35", "Stand36", "Stand37",
"Stand38", "Stand39", "Stand40", "Stand41", "Stand42", "Stand43",
"Stand44", "Stand45", "Stand46", "Stand47"))
x <-
structure(list(Elev.m = c(91L, 106L, 152L, 91L, 152L, 91L, 213L,
106L, 167L, 167L, 182L, 121L, 152L, 152L, 121L, 198L, 76L, 137L,
91L, 91L, 91L, 121L, 106L, 91L, 91L, 121L, 106L, 76L, 152L, 198L,
182L, 198L, 243L, 121L, 137L, 182L, 152L, 228L, 182L, 304L, 182L,
152L, 182L, 85L, 198L, 91L, 213L), LatAppx = c(44.4831, 44.6613,
44.7625, 45.0081, 45.1381, 44.3974, 43.9023, 45.3837, 45.3982,
45.3259, 45.1526, 45.167, 45.1526, 45.1526, 45.1237, 45.2104,
44.9936, 44.9936, 44.9936, 45.0081, 45.0081, 45.0081, 45.0081,
45.0081, 44.583, 44.7625, 44.8781, 44.8492, 44.9647, 44.8492,
44.8492, 44.8492, 45.0225, 45.0081, 45.0225, 44.9792, 44.9792,
44.8781, 44.8781, 44.4973, 44.5116, 44.4259, 44.2648, 44.3369,
44.5687, 44.5259, 44.9647), LongAppx = c(123.3618, 123.2029,
123.2641, 123.2233, 123.3355, 123.3215, 123.3353, 123.1825, 123.2029,
123.1417, 123.2641, 123.2845, 123.2845, 123.2845, 123.2029, 123.2641,
123.1825, 123.1825, 123.1825, 123.2233, 123.2233, 123.2233, 123.2233,
123.2233, 123.3014, 123.3049, 123.2641, 123.2845, 123.3049, 123.3049,
123.3049, 123.3049, 123.1621, 123.3253, 123.3049, 123.2233, 123.2437,
123.3049, 123.3049, 122.9393, 122.9594, 122.9796, 122.994, 123.2145,
123.3417, 123.3215, 123.1417), SlopeDeg = c(1L, 7L, 6L, 5L, 10L,
5L, 6L, 11L, 10L, 7L, 22L, 14L, 22L, 19L, 20L, 11L, 3L, 17L,
23L, 4L, 9L, 1L, 7L, 1L, 22L, 14L, 10L, 14L, 29L, 2L, 14L, 22L,
9L, 6L, 14L, 2L, 11L, 11L, 3L, 27L, 10L, 2L, 24L, 0L, 22L, 1L,
17L), AspClass = c(3L, 3L, 2L, 4L, 4L, 4L, 3L, 3L, 3L, 1L, 4L,
3L, 4L, 3L, 2L, 4L, 4L, 2L, 5L, 5L, 3L, 4L, 3L, 3L, 5L, 3L, 5L,
3L, 3L, 5L, 3L, 3L, 2L, 3L, 5L, 2L, 5L, 3L, 3L, 4L, 3L, 2L, 1L,
0L, 3L, 4L, 2L), AspDeg = c(315L, 315L, 180L, 90L, 0L, 0L, 135L,
315L, 315L, 250L, 90L, 110L, 90L, 315L, 270L, 90L, 0L, 270L,
65L, 45L, 120L, 90L, 160L, 345L, 35L, 320L, 60L, 315L, 350L,
45L, 275L, 305L, 270L, 340L, 35L, 180L, 55L, 330L, 315L, 90L,
135L, 270L, 200L, 0L, 340L, 0L, 270L), PDIR = c(0.910663, 0.8528266,
0.9441805, 0.8973573, 0.7900158, 0.8649957, 0.9387315, 0.8067303,
0.8180456, 0.9056402, 0.816286, 0.8979344, 0.816286, 0.7181216,
0.8256099, 0.8700042, 0.8721656, 0.8466234, 0.7330847, 0.8753292,
0.9191313, 0.9088469, 0.9459497, 0.8980643, 0.6752424, 0.7725364,
0.8400729, 0.77854, 0.5442948, 0.8972169, 0.8510198, 0.7165647,
0.8832078, 0.8483517, 0.7636641, 0.9205946, 0.8182663, 0.7917117,
0.8817961, 0.7929193, 0.9410934, 0.9116634, 0.9963973, 0.9169162,
0.6537821, 0.9025471, 0.8469195), HeatLoad = c(0.9140712, 0.8932892,
0.9300866, 0.8701203, 0.8150123, 0.8762777, 0.9047057, 0.8704287,
0.8750353, 0.9406292, 0.6895504, 0.8085389, 0.6895504, 0.8308181,
0.943758, 0.8032951, 0.880631, 0.9444098, 0.6364894, 0.8654551,
0.8648359, 0.9054387, 0.9138882, 0.9025555, 0.6455517, 0.8519068,
0.8025213, 0.8612094, 0.6398448, 0.8929822, 0.936359, 0.8504906,
0.9338031, 0.8732331, 0.744297, 0.9163601, 0.7794704, 0.8489962,
0.9022334, 0.6403902, 0.8841037, 0.9218866, 0.9897917, 0.9169162,
0.7464579, 0.9053704, 0.9447058), Landform = c(4L, 3L, 4L, 3L,
3L, 3L, 3L, 3L, 3L, 4L, 3L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 4L, 3L, 3L, 3L, 2L, 3L, 3L, 2L, 3L, 3L, 3L, 4L, 3L, 3L, 4L,
2L, 3L, 4L, 2L, 4L, 3L, 3L, 1L, 3L, 1L, 3L), TopoClas = c(6L,
6L, 7L, 8L, 5L, 5L, 6L, 6L, 4L, 8L, 5L, 6L, 5L, 4L, 7L, 5L, 5L,
7L, 5L, 5L, 4L, 8L, 6L, 6L, 6L, 4L, 5L, 6L, 6L, 4L, 6L, 6L, 8L,
6L, 6L, 9L, 5L, 6L, 8L, 5L, 8L, 4L, 8L, 1L, 6L, 2L, 7L), Drainage = c(1L,
2L, 4L, 2L, 3L, 3L, 3L, 3L, 2L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 1L,
4L, 4L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 3L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 3L, 4L, 4L, 4L, 4L, 2L, 4L, 4L, 1L, 4L, 1L, 4L), SoilSer = c(7L,
2L, 2L, 2L, 4L, 4L, 2L, 5L, 5L, 1L, 4L, 3L, 4L, 1L, 1L, 6L, 5L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 5L, 1L, 5L, 5L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 2L, 6L, 3L, 3L, 3L, 7L, 3L, 7L, 1L), SoilGrp = c(3L,
1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 2L, 3L, 1L), A.horiz = c(5L,
20L, 18L, 5L, 20L, 28L, 5L, 8L, 43L, 13L, 13L, 13L, 13L, 28L,
13L, 8L, 23L, 27L, 8L, 8L, 18L, 28L, 24L, 18L, 5L, 10L, 10L,
33L, 33L, 13L, 30L, 13L, 9L, 18L, 15L, 36L, 18L, 15L, 23L, 8L,
3L, 30L, 4L, 3L, 52L, 8L, 13L), B1.horiz = c(18L, 0L, 0L, 0L,
30L, 0L, 32L, 0L, 0L, 28L, 13L, 33L, 13L, 23L, 0L, 15L, 23L,
0L, 23L, 23L, 19L, 13L, 0L, 18L, 10L, 18L, 15L, 28L, 0L, 20L,
0L, 43L, 0L, 33L, 0L, 0L, 0L, 0L, 15L, 0L, 15L, 0L, 38L, 18L,
0L, 0L, 15L), B2.horiz = c(86L, 15L, 53L, 25L, 15L, 64L, 79L,
30L, 76L, 0L, 91L, 30L, 64L, 0L, 38L, 41L, 25L, 81L, 152L, 51L,
38L, 30L, 28L, 0L, 33L, 15L, 79L, 56L, 30L, 25L, 33L, 66L, 28L,
43L, 104L, 15L, 15L, 15L, 41L, 23L, 36L, 3L, 0L, 76L, 23L, 51L,
20L), B3.horiz = c(51L, 0L, 0L, 107L, 0L, 51L, 51L, 76L, 51L,
30L, 0L, 0L, 51L, 152L, 74L, 46L, 46L, 0L, 0L, 0L, 0L, 30L, 0L,
38L, 0L, 157L, 0L, 51L, 56L, 51L, 132L, 0L, 46L, 0L, 51L, 0L,
0L, 130L, 51L, 41L, 0L, 0L, 15L, 91L, 51L, 0L, 0L), B.horiz = c(155L,
15L, 53L, 132L, 46L, 114L, 161L, 107L, 127L, 58L, 104L, 64L,
127L, 175L, 112L, 102L, 94L, 81L, 175L, 74L, 57L, 74L, 28L, 56L,
43L, 191L, 94L, 135L, 86L, 97L, 165L, 109L, 74L, 76L, 155L, 15L,
15L, 145L, 107L, 64L, 51L, 3L, 53L, 185L, 74L, 51L, 36L), GrazCurr = c(1L,
0L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L,
0L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 0L), GrazCurrC = c("grazed",
"ungrazed", "grazed", "ungrazed", "ungrazed", "grazed", "grazed",
"ungrazed", "ungrazed", "ungrazed", "grazed", "grazed", "grazed",
"grazed", "ungrazed", "ungrazed", "ungrazed", "ungrazed", "ungrazed",
"ungrazed", "ungrazed", "ungrazed", "ungrazed", "ungrazed", "ungrazed",
"ungrazed", "ungrazed", "ungrazed", "grazed", "ungrazed", "ungrazed",
"ungrazed", "grazed", "ungrazed", "grazed", "grazed", "grazed",
"ungrazed", "ungrazed", "grazed", "grazed", "grazed", "grazed",
"ungrazed", "ungrazed", "ungrazed", "ungrazed"), GrazPast = c(1L,
1L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L,
0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 0L, 0L), GrazPastC = c("grazedpast",
"grazedpast", "grazedpast", "ungrazedpast", "ungrazedpast", "grazedpast",
"grazedpast", "ungrazedpast", "ungrazedpast", "ungrazedpast",
"grazedpast", "grazedpast", "grazedpast", "grazedpast", "grazedpast",
"grazedpast", "ungrazedpast", "ungrazedpast", "ungrazedpast",
"ungrazedpast", "ungrazedpast", "ungrazedpast", "ungrazedpast",
"ungrazedpast", "ungrazedpast", "ungrazedpast", "ungrazedpast",
"ungrazedpast", "grazedpast", "ungrazedpast", "ungrazedpast",
"ungrazedpast", "grazedpast", "ungrazedpast", "grazedpast", "grazedpast",
"grazedpast", "grazedpast", "grazedpast", "grazedpast", "grazedpast",
"grazedpast", "grazedpast", "ungrazedpast", "grazedpast", "ungrazedpast",
"ungrazedpast"), NotLoggd = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L,
1L, 1L, 0L, 1L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 1L, 1L, 1L, 0L), NotLoggdC = c("logged", "logged",
"logged", "logged", "logged", "logged", "logged", "logged", "logged",
"logged", "logged", "logged", "logged", "logged", "logged", "logged",
"notlogged", "notlogged", "notlogged", "notlogged", "notlogged",
"notlogged", "logged", "notlogged", "notlogged", "notlogged",
"logged", "notlogged", "logged", "notlogged", "notlogged", "notlogged",
"logged", "logged", "notlogged", "logged", "logged", "logged",
"logged", "logged", "logged", "logged", "logged", "notlogged",
"notlogged", "notlogged", "logged"), Que.60cm = c(5L, 0L, 9L,
0L, 2L, 1L, 6L, 2L, 1L, 5L, 2L, 1L, 1L, 1L, 6L, 14L, 9L, 6L,
2L, 1L, 10L, 2L, 0L, 10L, 0L, 8L, 14L, 17L, 22L, 10L, 10L, 9L,
6L, 15L, 4L, 10L, 4L, 11L, 14L, 2L, 0L, 13L, 4L, 19L, 19L, 15L,
4L), LogQ.60 = c(0.78, 0, 1, 0, 0.48, 0.3, 0.85, 0.48, 0.3, 0.78,
0.48, 0.3, 0.3, 0.3, 0.85, 1.18, 1, 0.85, 0.48, 0.3, 1.04, 0.48,
0, 1.04, 0, 0.95, 1.18, 1.26, 1.36, 1.04, 1.04, 1, 0.85, 1.2,
0.7, 1.04, 0.7, 1.08, 1.18, 0.48, 0, 1.15, 0.7, 1.3, 1.3, 1.2,
0.7), TreeHtM = c(13.71533, 16.76318, 22.24931, 15.84883, 24.38281,
18.89668, 18.28711, 22.24931, 15.84883, 22.5541, 22.85888, 14.62969,
17.98232, 14.93447, 21.03017, 21.94453, 21.63974, 19.81103, 19.20146,
19.50625, 21.03017, 18.28711, 9.448339, 19.50625, 10.97226, 15.23926,
20.72539, 21.63974, 21.33496, 18.59189, 20.72539, 18.89668, 14.3249,
19.50625, 14.02012, 13.41055, 12.19141, 15.84883, 15.84883, 14.93447,
6.705273, 18.59189, 10.66748, 20.4206, 17.67754, 20.72539, 15.54404
), SppRich = c(32L, 41L, 35L, 33L, 32L, 51L, 37L, 30L, 29L, 38L,
35L, 33L, 38L, 45L, 41L, 34L, 23L, 22L, 22L, 32L, 29L, 18L, 51L,
20L, 32L, 36L, 40L, 26L, 34L, 35L, 32L, 18L, 46L, 16L, 38L, 49L,
40L, 33L, 41L, 28L, 38L, 33L, 61L, 44L, 27L, 38L, 33L), ThilType = c(4L,
4L, 1L, 3L, 1L, 3L, 4L, 3L, 3L, 1L, 1L, 4L, 1L, 1L, 3L, 3L, 2L,
2L, 1L, 1L, 2L, 3L, 4L, 3L, 3L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 4L,
3L, 3L, 4L, 1L, 1L, 4L, 1L, 4L, 1L, 4L, 3L, 3L, 1L, 2L), FlxB..25 = c(1L,
1L, 1L, 1L, 5L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 17L,
17L, 5L, 1L, 1L, 17L, 23L, 17L, 5L, 5L, 1L, 5L, 5L, 1L, 5L, 5L,
1L, 17L, 1L, 23L, 1L, 5L, 1L, 5L, 23L, 5L, 23L, 1L, 17L, 1L,
1L)), .Names = c("Elev.m", "LatAppx", "LongAppx", "SlopeDeg",
"AspClass", "AspDeg", "PDIR", "HeatLoad", "Landform", "TopoClas",
"Drainage", "SoilSer", "SoilGrp", "A.horiz", "B1.horiz", "B2.horiz",
"B3.horiz", "B.horiz", "GrazCurr", "GrazCurrC", "GrazPast", "GrazPastC",
"NotLoggd", "NotLoggdC", "Que.60cm", "LogQ.60", "TreeHtM", "SppRich",
"ThilType", "FlxB..25"), class = "data.frame", row.names = c("Stand01",
"Stand02", "Stand03", "Stand04", "Stand05", "Stand06", "Stand07",
"Stand08", "Stand09", "Stand10", "Stand11", "Stand12", "Stand13",
"Stand14", "Stand15", "Stand16", "Stand17", "Stand18", "Stand19",
"Stand20", "Stand21", "Stand22", "Stand23", "Stand24", "Stand25",
"Stand26", "Stand27", "Stand28", "Stand29", "Stand30", "Stand31",
"Stand32", "Stand33", "Stand34", "Stand35", "Stand36", "Stand37",
"Stand38", "Stand39", "Stand40", "Stand41", "Stand42", "Stand43",
"Stand44", "Stand45", "Stand46", "Stand47"))
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@phytomosaic phytomosaic commented Nov 7, 2017

This is a brief tutorial of multivariate methods commonly used in ecological analysis of community (multi-species) data. Methods include relativization, ordination, clustering, group discrimination, and visualizations of those methods. Data are from PC-ORD version 7, originally from: Thilenius, J. F. 1968. The Quercus garryana forests of the Willamette Valley, Oregon. Ecology 49: 1124-1133.

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