Data from: "Size" and "shape" in the measurement of multivariate proximity

1. Ordination and clustering methods are widely applied to ecological data
that are nonnegative, for example species abundances or biomasses. These
methods rely on a measure of multivariate proximity that quantifies
differences between the sampling units (e.g. individuals, stations, time
points), leading to results such as: (i) ordinations of the units, where
interpoint distances optimally display the measured differences; (ii)
clustering the units into homogeneous clusters; or (iii) assessing
differences between pre-specified groups of units (e.g., regions, periods,
treatment-control groups). 2. These methods all conceal a fundamental
question: To what extent are the differences between the sampling units,
computed according to the chosen proximity function, capturing the
"size" in the multivariate observations, or their
"shape"? "Size" means the overall level of the
measurements: for example, some samples contain higher total abundances or
more biomass, others less. "Shape" means the relative levels of
the measurements: for example, some samples have different relative
abundances, i.e. different compositions. To answer this question, several
well-known proximity measures are considered and applied to two data sets,
one of which is used in a simulation exercise where "shape"
differences have been eliminated by randomization. For any data set and
any proximity measure, a quantification is achieved of the proportion of
"size" variance and "shape" variance that the measure
is capturing, as well as the proportion of variance that confounds
"size" and "shape" together. 3. The results
consistently show that the Bray-Curtis coefficient incorporates both
"size" and "shape" differences, to varying degrees.
These two components are thus always confounded by this proximity measure
in the determination of ordinations, clusters, group comparisons and
relations to environmental variables. 4. There are several implications of
these results, the main one being that researchers should be aware of this
issue when they choose a proximity measure. They should compute the
"size" and "shape" components for their particular
data sets, since this can radically affect the interpretation of their
results. It is recommended to separate these components: analysing total
abundances or other measures of "size" by univariate methods,
and using multivariate analysis on the relative abundances where size has
been specifically excluded.