Biological Oceanography

(^) Then Bilyard analyzed the species-by-station table using clustering and ordination
techniques. These are of many kinds, and some importance rides on the choice.
Knowing and applying the variety, advantages, drawbacks, and utility of different
methods is a discipline in itself (e.g. McCune & Grace 2002). However, virtually all
such methods can be referred to a geometric model. Generally, the data must first be
standardized, just as for the correlation matrix, so that all included species, regardless
of their absolute abundance, have roughly equal effect on the outcome. Then the
species-by-station table is taken to define either (i) the positions of stations in a space
with dimensional axes equal in number to the number of species (S) and each running
from zero to the maximum (standardized) abundance of its species, or (ii) the
positions of species in a set of axes equal in number to the count (N) of stations and
scaled in the same way. In case (i), bunches of station points result from species
whose relative abundance behaves in a similar fashion over the station set. In case (ii),
bunches define species with similar relative abundances at the different stations. Thus,
the definition of the space determines what issue is addressed: which stations have
similar species assemblages, or which species behave similarly. Of course, these two
issues are obviously tied together. The term “relative” is needed because
standardization of the data removes emphasis from absolute abundance.
(^) Since few studies would have only three species or only three stations, these spaces
generally are highly multidimensional and cannot be visualized. Spotting clusters of
points in unimaginable space is approached in one of two general modes: clustering
and ordination. Clustering methods can work in several ways. Probably the simplest
to understand are agglomerative. Distances are calculated for all possible pairs of, say,
stations in species space. The pair with the smallest separation is noted as part of a
possible cluster and replaced with a point in the middle between them (in S space). If