Now let us run a posteriori tests to identify the significantly concordant species
within each group:
# A posteriori tests
(spe.kendall.post2 <- kendall.post(spe.hel, clusters2,
nperm = 9999))
Look at the mean Spearman correlation coefficients of the individual species. A
group contains concordant species if each of its species has a positive mean
correlation with all the other species of its group. If a species has a negative mean
correlation with all other members of its group, this indicates that this species should
be left out of the group. Try a finer division of the groups and see if that species finds
itself in a group for which it has a positive mean correlation. This species may also
form a singleton, i.e. a group with a single species.
With 2 groups, we have in the largest group one species (Sqce) that has a
negative mean correlation with all members of its group. This indicates that we
should look for a finer partition of the species. Let us carry out a posteriori tests with
3 groups. Readers can also try with 4 groups and examine the results.
(spe.kendall.post3 <- kendall.post(spe.hel, clusters3,
nperm = 9999))
Now all species in the three groups have positive mean Spearman correlations
with the other members of their group. Sqce finds itself in a new group of 9 species
with which it has a mean positive correlation, although its contribution to the
concordance of that group is not significant. All the other species in all three groups
contribute significantly to the concordance of their group. So we can stop the
analysis and consider that three groups of species, with respectively 12, 9 and
6 species, adequately describe the species associations in the Doubs River.
Ecological theory predicts nested structures in ecological relationships. Within
communities, subgroups of species can be more or less loosely or densely associated.
One can explore such avenues by investigating smaller species groups within the
large species associations revealed by the Kendall W test results.
The groups of species defined here may be further interpreted ecologically by
different means. For instance, mapping their abundances along the river and computing summary statistics on the sites occupied by the species assemblages can help
in assessing their ecological roles. Another avenue towards interpretation is to
compute a redundancy analysis (RDA, Sect. 6.3) of the significantly associated
species with respect to a set of explanatory environmental variables.
4.10.3 Species Assemblages in Presence-Absence Data
A method exists for presence-absence data (Clua et al. 2010). It consists in computing the a component of Jaccard’s S 7 coefficient (as a measure of co-occurrence
among species) in R-mode and assessing its probability by means of a permutation
4.10 Species Assemblages
115
within each group:
# A posteriori tests
(spe.kendall.post2 <- kendall.post(spe.hel, clusters2,
nperm = 9999))
Look at the mean Spearman correlation coefficients of the individual species. A
group contains concordant species if each of its species has a positive mean
correlation with all the other species of its group. If a species has a negative mean
correlation with all other members of its group, this indicates that this species should
be left out of the group. Try a finer division of the groups and see if that species finds
itself in a group for which it has a positive mean correlation. This species may also
form a singleton, i.e. a group with a single species.
With 2 groups, we have in the largest group one species (Sqce) that has a
negative mean correlation with all members of its group. This indicates that we
should look for a finer partition of the species. Let us carry out a posteriori tests with
3 groups. Readers can also try with 4 groups and examine the results.
(spe.kendall.post3 <- kendall.post(spe.hel, clusters3,
nperm = 9999))
Now all species in the three groups have positive mean Spearman correlations
with the other members of their group. Sqce finds itself in a new group of 9 species
with which it has a mean positive correlation, although its contribution to the
concordance of that group is not significant. All the other species in all three groups
contribute significantly to the concordance of their group. So we can stop the
analysis and consider that three groups of species, with respectively 12, 9 and
6 species, adequately describe the species associations in the Doubs River.
Ecological theory predicts nested structures in ecological relationships. Within
communities, subgroups of species can be more or less loosely or densely associated.
One can explore such avenues by investigating smaller species groups within the
large species associations revealed by the Kendall W test results.
The groups of species defined here may be further interpreted ecologically by
different means. For instance, mapping their abundances along the river and computing summary statistics on the sites occupied by the species assemblages can help
in assessing their ecological roles. Another avenue towards interpretation is to
compute a redundancy analysis (RDA, Sect. 6.3) of the significantly associated
species with respect to a set of explanatory environmental variables.
4.10.3 Species Assemblages in Presence-Absence Data
A method exists for presence-absence data (Clua et al. 2010). It consists in computing the a component of Jaccard’s S 7 coefficient (as a measure of co-occurrence
among species) in R-mode and assessing its probability by means of a permutation
4.10 Species Assemblages
115