Hi Pablo As an alternative to considering just half the skull, you can use the whole skull and extract the symmetric component of shape variation with an analysis of object symmetry. This was published by Kanti Mardia and colleagues in to somewhat technical papers:
Mardia, K. V., F. L. Bookstein, and I. J. Moreton. 2000. Statistical assessment of bilateral symmetry of shapes. Biometrika 87:285300. Kent, J. T., and K. V. Mardia. 2001. Shape, Procrustes tangent projections and bilateral symmetry. Biometrika 88:469485. There is also a paper introducing this approach in a form that should be more accessible to biologists (I hope): Klingenberg, C. P., M. Barluenga, and A. Meyer. 2002. Shape analysis of symmetric structures: quantifying variation among individuals and asymmetry. Evolution 56:19091920. (PDF file posted on my web site, http://www.flywings.org.uk ) The approach adds a reflected and relableled copy of the original configurations to the originals, and then includes both in a Procrustes analysis. You can do the reflection and relabeling steps in any statistics package that allows data manipulation or in a spreadsheet. The Procrustes analysis can then be done with any of the usual morphometrics programs. This approach avoids the problem with the landmarks on the median plane that you have with the analysis of half-skulls. Also, unlike other methods of reflecting and averaging the paired landmarks, you don't have to choose some median landmarks of which you assume that they are exactly in the median plane. I hope this helps. Best wishes, Chris *************************************************************** Christian Peter Klingenberg Faculty of Life Sciences The University of Manchester Michael Smith Building Oxford Road Manchester M13 9PT United Kingdom Telephone: +44 161 275 3899 E-mail: [EMAIL PROTECTED] Web: http://www.flywings.org.uk *************************************************************** -- Replies will be sent to the list. For more information visit http://www.morphometrics.org
