I am glad that the correspondence between Igor and Dennis were made public
and that the discussion about this topic continues. I think things have
become much clearer for me.
I agree with Asta in almost all respects. Taxonomists like practical,
diagnostic characters very much. It would be nice to see which characters
(landmarks) are of taxonomic importance. But this is not always (and in
fact, very often) the case. Let me put an example. Suppose there is an
insect taxon having two distantly related food plants (this is very common
situation). Or suppose there is a taxon with two discretely different wing
patterns but otherwise being exactly similar (also very common situation).
Suppose also that those forms are sympatric (live together in space and
time). Now, the question is not what the differences are since they can
easily been kept apart due to the discrete polymorphism. This polymorphism,
however, does not imply they are valid species, since polymorphism is such
features may be intraspecific. Thus the question is rather that does this
polymorphism correlate with morphology (in insect this mean often genital
morphology). The finding that the forms differ in genital morphology,
regardless what the differences are, is of taxonomic relevance. It speaks
for the co-existence of two biologically isolated species. In reference to
Dennis's argument ("I believe the original question that started all of
this was about discriminant functions. This is a bit different. If the goal
of a discriminant function analysis is the classification of new specimens,
then it, in a sense, matters not what you do. If the goal is
classification, then the validity of whatever is done is determined solely
by its ability to correctly classify new specimens. You could use the first
few PCAs, every third partial warp, neural networks, or tarot cards. That
which does the best job is the best of what you have tried") I therefore
conclude that in my case selecting a qualified set of partial warps in
order to classify cross-validated specimens is justified. As I found that
cross-validated specimens were classified correctly, I conclude that there
are differences, though perhaps indefinable, in analyzed genitalic outline
sections, because such a result could not be achieved by chance. All this
reasoning is basically founded on the assumption that difference in a
single partial warp tells that there is(are) difference(s) in shape, even
though this difference cannot be associated with any particular landmark.
Correct? I also assume that by comparing the consensus configuration of
forms with the overall consensus using thin-plate-splines and vector plots
I can speculate what those differences possibly are.
Well, these are difficult things I am not sure my reasoning above makes
sense. Therefore, I will be grateful for further comments, also critical
ones. I also like to warmly thank all of you who have taken part to this
discussion.
Cheers,
Marko
At 20:47 02/02/2005, you wrote:
>maybe this has been discussed already a lot but I would still dare to ask:
>
>To me it seems that for taxonomists, the use of individual partial warps
>comes largely from the need to interpret the CVA analysis and find the most
>informative characters to differentiate the species. These variables later
>can be used in further taxonomic work.
>
>In the "traditional" morphometrics one can add/remove variables one by one
>and leave the most informative ones - a widely used practice, I believe.
>
>With geometric morphometrics, for the mathematical reasons discussed before,
>one will conduct CVA on relative warp scores
>The results will tell that the most important variable for differentiating
>the two species is RW5. But this is not a variable a taxonomist would like
>to use. OK, I can go back to RW analysis and explore shape variation related
>to RW5. Still it is speculative, compared with the rigorous statistical
>procedure of selecting "traditional" variables by their within to among
>group variance (or vice versa?).
>One can also remove a certain part of landmarks manually and do the analysis
>again, but this is also subjective.
>
>Probably it does not make much sense to choose the most important landmarks,
>because the shape is analysed as a whole, in relation to other landmarks?
>There may not be one or two "the most informative" landmarks, which could be
>informative alone?
>
>Yet, I wonder whether there is there any accepted statistical procedure to
>select the most useful characters (landmarks) for species differentiation?
>
>Thanks,
>
>Asta Audzijonyte
>
>
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