Biology Reference
In-Depth Information
based on the observed values, the range of
P
mean
invariably includes zero and, for that
reason, we cannot rule out the Gaussian null model.
Cluster Analysis
The test for clustering in the nearest-neighbor analysis tells us that species tend to be
closer together than expected for a random distribution, but it does not tell us if there is
one large cluster, or several smaller ones. In other words, it does not tell us about the
homogeneity of the clustering. Several methods have been developed to identify groups
or clusters based on the distances between species, and to depict that clustering in a
dendrogram showing nested sets of species. Below, we present a few of these methods to
illustrate their variety and discuss their limitations. Each method will be used to analyze
the same data set: mean shapes of mandibles from 31 squirrel species, including tree
squirrels, ground squirrels and flying squirrels (
Figure 10.11A
). Scores on the first two
principal components of these data (
Figure 10.11B
), which account for 60% of the varia-
tion, suggest there may be some hierarchical structure in the data; but that structure
appears to be more consistent with ecological similarity than with the phylogenetic
relationships that have been inferred (
Figure 10.11C
).
The simplest clustering approach is called, appropriately enough, single linkage. The
first link connects the two closest taxa. The second link connects the next two closest taxa,
which may be a different pair, or it may connect a third taxon to a member of the first
pair. It often occurs that the first pair forms a nucleus and other species are successively
linked to this growing core; because they are on the periphery of the core, they tend to be
closer to a species that is already in the group than to another species that is still on the
outside. Consequently, this method tends to link taxa in long chains, successively linking sin-
gletons in a comb-like dendrogram that suggests little hierarchical structure (
Figure 10.12A
).
In those cases where two groups of several species are linked, they are linked through the
one species in each group that are closest to each other (like the tips of two ellipses aligned
on the same axis). There is no implication of any general similarity among the other mem-
bers of the group.
A somewhat more complicated method is the average linkage method, or unweighted
pair-group method with arithmetic means (UPGMA). Again, the two closest taxa are
linked first. At each successive step, the taxa that are joined are the ones that would have
the smallest increase in average linkages. This is analogous to linking two ellipses that are
side-by-side before linking ones that are tip-to-tip. The average of the linkages between
the side-by-side pair will tend to be smaller than the average between the tip-to-tip pair
unless the tips are very much closer than the sides. Similarly, this method will tend to
avoid creating groups that are elliptical or making them more eccentric than they already
are. This tends to create a more tree-like dendrogram (more hierarchical structure) than
single-linkage does. In the UPGMA dendrogram (see
Figure 10.12B
), less than
1
4
of the
species were linked as singletons to existing clusters, in contrast to more than
2
3
linked as
singletons in the single linkage dendrogram.
A still more complicated method is
Ward's (1963)
minimum variance. In this method,
the taxa that are joined are the ones that create the smallest increase in variance in the new
