Dear Louis, I have had this problem in systematics where after performing a PCA and inspecting the clustering pattern on a pair of axes you ask yourself the question: are there really two groups or am I imagining this pattern?
Kernel Density Estimation of principal components might provide you with GRAPHIC answer. However, beware that this is in no way a statiscal test but can be rather convincing. Confidence ellipses might also help you determine de degree of overlap between groups. Another approach to this kind of problem is model based clustering. This pattern recognition technique allows automatic recongtion of groups based on the structure of the variance-covariance matrix. Both approaches have been implemented by Michel Baylac and extended by Baylac and myself, and can easily be performed under R. Here are some references: Baylac, M.; Villemant, C. & Simbolotti, G. 2003. Combining geometric morphometrics with pattern recognition for the investigation of species complexes. Biological Journal of the Linean Society 80: 89-98. Cordeiro-Estrela, P.; Baylac, M.; Denys, C. & Marinho-Filho, J. 2006. INTERSPECIFIC PATTERNS OF SKULL VARIATION BETWEEN SYMPATRIC BRAZILIAN VESPER MICE: GEOMETRIC MORPHOMETRICS ASSESSMENT Journal of Mammalogy 87: 1270-1279. Cordeiro-Estrela, P.; Baylac, M.; Denys, C. & Polop, J. Accepted. Combining geometric morphometrics and pattern recognition to identify interspecific patterns of skull variation: case study in sympatric Argentinian species of the genus it Calomys (Rodentia: Cricetidae: Sigmodontinae) Biological Journal of the Linnean Society. sincerely, Pedro --- morphmet <[EMAIL PROTECTED]> wrote: > Dear morphometricians, > > I have the following problem: > > I have performed a PCA of shape (relative warps analysis) on a set of > mouse mandibles from animals of different geographic origins. Now in a > plot of PC1 vs PC2, I can "see" that PC1 sorts specimens into broadly > overlapping clusters corresponding to the respective origins of the > mice, while PC2 (and the other PCs) do not. The problem is now that the > overlaps of the "population" clusters are rather broad so the question > is how different they actually are. Also, I have several "populations", > so it looks like a continuum of overlapping clouds. > Could you recommend a means to quantify and/or somehow test the actual > differences between "populations" along PC1? > > Louis Boell > > ------------------------------------------------------------------------ > Machen Sie Ihre E-Mail-Kontakte zu Messenger-Freunden! Einfacher > Adressimport! > <http://redirect.gimas.net/?cat=hmtl&n=M1007AI&d=http://messenger.live.de/ersteschritte_adressimport.html> > > -- > Replies will be sent to the list. > For more information visit http://www.morphometrics.org > > _______________________________________________________ Pedro Cordeiro Estrela Dr.Sc. Departamento de Genetica - Universidade Federal do Rio Grande do Sul Campus do Vale - Bloco III Av. Bento Gon�alves, 9500 - Agronomia Porto Alegre, RS 91501-970 / Caixa Postal 15.053 Brasil. TEL: +55 (51) 3308.6726 (cod. Porto Alegre) ________________________________________________________ __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com -- Replies will be sent to the list. For more information visit http://www.morphometrics.org
