through a clustering method and look for species that are more present, abundant or
specific in each cluster of sites. Here is an example.
# Compute mean species abundances in the four groups from the
# optimized Ward clustering
groups <- as.factor(spech.ward.gk)
spe.means <- matrix(0, ncol(spe), length(levels(groups)))
row.names(spe.means) <- colnames(spe)
for (i in 1:ncol(spe)) {
spe.means[i, ] <- tapply(spe[, i], spech.ward.gk, mean)
}
group1 <- round(sort(spe.means[, 1], decreasing = TRUE), 2)
group2 <- round(sort(spe.means[, 2], decreasing = TRUE), 2)
group3 <- round(sort(spe.means[, 3], decreasing = TRUE), 2)
group4 <- round(sort(spe.means[, 4], decreasing = TRUE), 2)
# Species with abundances greater than group mean species abundance
group1.domin <- which(group1 > mean(group1))
group1
group1.domin
#... same for other groups
4.10.2 Kendall’s W Coefficient of Concordance
Legendre (2005) proposed to use Kendall’s W coefficient of concordance, together
with permutation tests, to identify species assemblages in abundance data (this
method cannot be applied to presence-absence data): “An overall test of independence of all species is first carried out. If the null hypothesis is rejected, one looks for
groups of correlated species and, within each group, tests the contribution of each
species to the overall statistic, using a permutation test.” In this method, the search
for species associations is done without any reference to a typology of the sites
known a priori or computed from other data, for example environmental. The
method aims at finding the most encompassing assemblages, i.e., the smallest
number of groups containing the largest number of positively and significantly
associated species.
The package kendall.W has been written to carry out these computations. Its
functions are now part of vegan. The simulation results accompanying the Legendre (2005) paper show that “when the number of judges [¼ species] is small, which
is the case in most real-life applications of Kendall’s test of concordance, the
classical χ
2 test is overly conservative, whereas the permutation test has correct
Type I error; power of the permutation test is thus also higher.” The kendall.
global() function also includes a parametric F-test which does not suffer from
the problems of the χ
2 test and has correct Type I error (Legendre 2010).
As a simple example, let us classify the fish species into several groups using
k-means partitioning (Fig. 4.25), and run a global test (kendall.global()) to
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4 Cluster Analysis
specific in each cluster of sites. Here is an example.
# Compute mean species abundances in the four groups from the
# optimized Ward clustering
groups <- as.factor(spech.ward.gk)
spe.means <- matrix(0, ncol(spe), length(levels(groups)))
row.names(spe.means) <- colnames(spe)
for (i in 1:ncol(spe)) {
spe.means[i, ] <- tapply(spe[, i], spech.ward.gk, mean)
}
group1 <- round(sort(spe.means[, 1], decreasing = TRUE), 2)
group2 <- round(sort(spe.means[, 2], decreasing = TRUE), 2)
group3 <- round(sort(spe.means[, 3], decreasing = TRUE), 2)
group4 <- round(sort(spe.means[, 4], decreasing = TRUE), 2)
# Species with abundances greater than group mean species abundance
group1.domin <- which(group1 > mean(group1))
group1
group1.domin
#... same for other groups
4.10.2 Kendall’s W Coefficient of Concordance
Legendre (2005) proposed to use Kendall’s W coefficient of concordance, together
with permutation tests, to identify species assemblages in abundance data (this
method cannot be applied to presence-absence data): “An overall test of independence of all species is first carried out. If the null hypothesis is rejected, one looks for
groups of correlated species and, within each group, tests the contribution of each
species to the overall statistic, using a permutation test.” In this method, the search
for species associations is done without any reference to a typology of the sites
known a priori or computed from other data, for example environmental. The
method aims at finding the most encompassing assemblages, i.e., the smallest
number of groups containing the largest number of positively and significantly
associated species.
The package kendall.W has been written to carry out these computations. Its
functions are now part of vegan. The simulation results accompanying the Legendre (2005) paper show that “when the number of judges [¼ species] is small, which
is the case in most real-life applications of Kendall’s test of concordance, the
classical χ
2 test is overly conservative, whereas the permutation test has correct
Type I error; power of the permutation test is thus also higher.” The kendall.
global() function also includes a parametric F-test which does not suffer from
the problems of the χ
2 test and has correct Type I error (Legendre 2010).
As a simple example, let us classify the fish species into several groups using
k-means partitioning (Fig. 4.25), and run a global test (kendall.global()) to
112
4 Cluster Analysis