this removes a small amount of the overall separation among stations, then the pairing
is given a high rating, if not, then it is rated weak. This procedure is repeated over and
over (perhaps weighting new positions according to how many stations are on each
side of the new pairing) until all stations are in one cluster. The sequence is examined
to find a stopping place that defines a convenient number of clusters, or (better) at
which the reductions in remaining intergroup distance jump to large values (as distant
clusters are combined). Clusters of stations defined at this stopping place might then
be mapped or examined for commonalities in sediment type or factors likely to
differentiate the habitat made “visible” by the species clusters.
(^) Ordination techniques establish the coordinates of, for example, stations in species
space, then progressively fit axes through that space with minimum total distance
(usually a sum of distances squared, Σ D^2 , is minimized) to the station points. In the
simplest versions, all related to principal-component analysis, the axes are taken to be
at right angles (orthogonal) to each other. Thus, the first axis would be the line
through the S-dimensional space with minimal Σ D^2 , and the second the line at right
angles to the first chosen by the same criterion. Those together would define a plane.
If the stations define three main clusters in S-space, then they will all be near that
plane and obvious when their positions are projected onto it and plotted. Lines and
planes can be added, showing the positions of additional clusters. Some stations with
nearly unique species assemblages will be isolated.
(^) Most workers use methods popular in their organization, with which good
familiarity is available locally. On that basis, Bilyard selected a clustering technique
called “CLUSB” developed at Oregon State University by D. McIntire and S.
Overton. CLUSB puts cluster centers into a geometric model of the data and then
assigns stations to centers so as to minimize the summed squares of distances of
station points from their cluster centers. Clusterings are tried with more and more
centers, stopping when the sum of squares is no longer much reduced by adding
another. Bilyard found four station groups that were well separated, and for which no
stations included in any cluster were far in species space from their designated center.
He plotted the cluster designations A to D at each station location on the isobath map
(Fig. 14.6).
Fig. 14.6 Locations of stations in each of four clusters (A, B, C, and D) identified by
both CLUSB and canonical correlation analysis. Stations in the clusters have high
similarity in polychaete species composition.
(^) (After Bilyard & Carey 1979.)