Biology Reference
In-Depth Information
After applying morphometric techniques to the data, there is still the problem of inter-
pretation. Even if the data meet the designated criteria, the samples might not come from
different species
they could come from geographically differentiated populations that
were sampled only at the extremes of their range (e.g. the most northern and the most
southern localities). Had they been sampled throughout the entire range, it might turn out
that there is no statistically significant difference between geographically adjacent popula-
tions. Conversely, they might not meet the criterion but, nonetheless, be distinct species; it
is just that the distinguishing features do not lie in shape. CVA provides a useful method
for discrimination, but finding that samples can be discriminated is only part of the
answer to the first taxonomic question.
As Viscosi and Cardini (2011) nicely demonstrate, structures that are repeated within
an individual, such as leaves on a tree, add even more layers of complexity to this prob-
lem. Variability of repeated structures is not just a concern of botanists; many animal taxa
also have repeated structures (e.g. eye facets, body segments, vertebrae), and colonial
organisms like bryozoans and corals also have repeated individuals. Not only might
repeated structures vary within an individual or colony, perhaps as a function of position
within the individual, the pattern of intra-individual variation might have an ontogeny of
its own. Intra-individual variation may also differ between individuals in response to all
the same factors that might account for inter-individual variation. Even with all these
potential layers, the question of “are species different?” still can be answered by well-
reasoned application of convention morphometric methods.
Although CVA can be useful for answering both the first part of the taxonomic question
(Are they different?), and the second part (In what are they different?), it is important to
bear in mind the limitations discussed in Chapter 6. Those limitations mean that the likeli-
hood that CVA will produce a discriminant function that is entirely an artifact of rotating
and rescaling the data increases with the number of variables. But rather than reduce or
eliminate semilandmarks and lose potentially informative shape data, cross-validation can
be used to confirm reliability of the discrimination. Indeed, cross-validation should be
used for large sets of landmarks even if no semilandmarks are used.
Whether taxonomic differences are discovered by CVA or other analyses, combinations
of shape variables may not be the most useful descriptions of those differences for the biol-
ogist comparing specimens in the field or in the museum. If it is intended to be useful for
field biologists, no purpose is served by writing a key that requires digitizing specimens,
entering their data in a CVA, and allocating them to species according to the discriminant
function. Although that could be considered a merely technological limitation, a taxonomic
key serves a pragmatic purpose and therefore must be useful. The key must be applicable
to the specimens in hand, under the conditions when they are in hand, while still account-
ing for potential sources of intraspecific variation. These requirements make writing a use-
ful key a challenging problem, but turning a geometric analysis into a useful key adds no
further difficulties. That can be done by using geometric morphometrics to determine the
shape variables that best discriminate, then translating them into terms of traditional mor-
phometric variables that can be measured with calipers or rulers. For example, if relative
body depth discriminates between species, two lengths can be calculated from the land-
mark coordinates; one for the depth measured between two landmarks (such as anterior
bases of the dorsal and anal fin), and one between the landmarks that capture standard
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