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3 de diciembre de 2008

Relationships between shape variables

En la lista de Morphmet ha surgido esta muy educada e interesante cuestión.
Espero sea de utilidad a los lectores del blog.

Relationships between shape variables
Date: Tue, 2 Dec 2008 16:59:21 -0800 (PST)
From: Brendan McCane <[EMAIL PROTECTED]>


I have a rather technical question (i.e. I'm interested in the
underlying technique rather than software that can do it). Here is the

Given a sample of images (say lateral images of the human facial
skeleton), we locate quite a number of landmarks (actually
semi-landmarks or slid-landmarks) with landmarks coming from many
different structures. I'd like to test for relationships between the
structures - i.e. do changes in this structure (e.g mandible) , produce
corresponding changes in that structure (e.g. upper dentition). Of
course I can do a Procrustes analysis, followed by a PCA and visually
see how the structures co-vary along the principal axes, but I am
interested in something a little less qualitative, perhaps more along
the lines of a hypothesis test. I was thinking perhaps of canonical
correlation analysis between different sets of structures, but I haven't
seen much work using this technique in shape analysis. Does anyone have
any advice or pointers to other work?


Brendan McCane, Head of Dept, Email: [EMAIL PROTECTED]
Department of Computer Science Phone: +64 3 479 8588/8578.
University of Otago Fax: +64 3 479 8529
Box 56, Dunedin, New Zealand.

From: Dennis E. Slice <[EMAIL PROTECTED]>
References: <[EMAIL PROTECTED]>

The answer you seek can be found in Partial Least-Squares Analysis. See
below to get you started.

Bookstein, FL, P Gunz, P Mitteroecker, et al. 2003. Cranial
integration in Homo: singular warps analysis of the midsagittal plane in
ontogeny and evolution. JOURNAL OF HUMAN EVOLUTION 44, no. 2 (February):

Mitteroecker, P, and F Bookstein. 2007. The conceptual and statistical
relationship between modularity and morphological integration.
SYSTEMATIC BIOLOGY 56, no. 5 (October): 818-836.

---. 2008. The evolutionary role of modularity and integration in the
hominoid cranium. EVOLUTION 62, no. 4 (April): 943-958.

Rohlf, FJ, and M Corti. 2000. Use of two-block partial least-squares
to study covariation in shape. SYSTEMATIC BIOLOGY 49, no. 4 (December):

Best, dslice
From: Chris Klingenberg <[EMAIL PROTECTED]>
Organization: University of Manchester
References: <[EMAIL PROTECTED]>

Hi Brendan

Probably the most widespread technique for this is PLS. A good review of
the technique is the following paper:
Rohlf, F. J., and M. Corti. 2000. The use of two-block partial
least-squares to study covariation in shape. Systematic Biology 49:740–753.

PLS has been used for landmarks in separate configurations, for which
separate Procrustes fits are used. A couple of examples of this:

Tabachnick, R. E., and F. L. Bookstein. 1990. The structure of
individual variation in Miocene Globorotalia. Evolution 44:416–434.

Bastir, M., and A. Rosas. 2005. Hierarchical nature of morphological
integration and modularity in the human posterior face. American Journal
of Physical Anthropology 128:26–34.

A different option is the approach of using a single Procrustes fit for
all landmarks, and then a PLS analysis among sets of landmarks within
the configuration. Examples include:

Klingenberg, C. P., and S. D. Zaklan. 2000. Morphological integration
between developmental compartments in the Drosophila wing. Evolution

Bookstein, F. L., P. Gunz, P. Mitteroecker, H. Prossinger, K. Schaefer,
and H. Seidler. 2003. Cranial integration in Homo: singular warps
analysis of the midsagittal plane in ontogeny and evolution. Journal of
Human Evolution 44:167–187.

Statistical testing is usually done via permutation methods.

I hope this is useful.

Best wishes,

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