sponge matrix & analysis

[Harvey E. Ballard, Jr.]

Hi, Alan:
In numerical taxonomic (= phenetic) parlance, your feature matrix is
equivalent to a character or variable matrix, where seasonal states of the
sponge you studied are essentially your Operational Taxonomic Units (OTUs)
and your measurements or qualitative observations are expressions of a
series of variables.  But there is no need to recircumscribe continuous
variables into discrete categories unless you have some particular purpose
in mind, in order to satisfactorily analyze your data using multivariate
statistical methods; and you may end up distorting the multivariate
"normal" distribution of certain variables to the extent that you end up
with artifactual rather than real separation (or merger) of some of your
observations.  (In the worst case, if most or all your variables get
squashed into categorical variable types, you also limit yourself to
certain types of analysis, other types like canonical variates analysis
being unable to accomodate these discrete variables adequately.)

With your data "OTU-by-variable" (or in your own case, your seasonal
morph-by-feature") matrix you can perform a number of useful analyses to
clarify seasonal patterns of morphological change.  Principal coordinates
analysis or nonmetric multidimensional scaling would be useful, especially
as a graphical representation of the "trajectory" of seasonal change across
all the variables you studied, and would be interpretable particularly if
you coded all individuals of each seasonal morph, or individuals observed
at a particular time, with a unique color or symbol (or both).  If most or
all your variables can be defined in "continuous" measurement terms, or you
have sufficient numbers of such variables that you could ignore qualitative
features temporarily, you might also find canonical variates analysis
helpful, in which you could assign individuals to different observation
times (=seasons?) and explore the extent and direction of multivariate
change in your measurements.

All these analyses are pretty standard, and are available in any good,
recently published textbooks.  Unfortunately, and strangely, there aren't
very many "good" textbooks with practical applications that cover all of
what I consider to be a broad-ranging battery of important multivariate
statistical methods of analysis, including ordination, scaling, clustering,
discriminant/canonical variates and canonical correlation analysis.  You
might have to dig a bit to locate one that looks valuable to you; then
you'll need to get advice on which statistical packages will be (1) user
friendly [not bloody many!] and (2) have all or most of the approaches you
hope to use.

Good luck!
Harvey Ballard

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Harvey E. Ballard, Jr., Assistant Professor, Plant Evolution and Systematics
Department of Environmental and Plant Biology
Porter Hall, Ohio University
Athens, OH 45701
(740) 593-4659 (office & lab phone)
(740) 593-1130 (fax)
email: ballardh at oak.cats.ohiou.edu