morphmet
Fri, 06 Nov 2009 23:26:35 -0800
-------- Original Message -------- Subject: Re: Morphological disparity and landmark variation Date: Tue, 3 Nov 2009 01:33:33 -0800 (PST) From: andrea cardini <alcard...@interfree.it> To: morphmet@morphometrics.org Dear Murat, please, read my answers below. At 14:47 02/11/2009 -0500, you wrote:
-------- Original Message -------- Subject: Morphological disparity and landmark variation Date: Mon, 2 Nov 2009 09:58:55 -0800 (PST) From: Murat Maga <m...@u.washington.edu> To: morphmet@morphometrics.org Hi all, I have 3 sample groups, each of which have 5-12 individuals. Two of those are subspecies, and the third is a cross between them. I want to estimate (1) what is the most morphologically different of these three groups, and (2) for that group, which LMs are driving the difference from the other groups. All of these groups are really similar, and I am looking for small shape changes.
To really be able to say which the landmarks are that make these groups different is not going to be easy. This is because the variation you describe and test refers to the landmark configuration as a whole and changes are always in terms of relative positions of all landmarks. You could possibly think about some kind of 'experiment' where you exclude subsets of landmarks, do a discriminant analysis each time and compare the classification accuracy among these subsets. Even this way, it's unlikely to be straightforward and you will also have to take into account that you're running multiple tests on more or less the same kind of data. If you have a priori hp about which regions of the structure could be more different (which probably require some hp of modularity), you could then split the structure and compare those regions (with no landmarks in common) in terms of discriminatory power and variance, and I suspect this would a bit more sensible. Maybe first you would also test whether the regions behave as modules at least in a statistical sense. To my limited experience, despite the statistical power and effectiveness of visualizations, Procrustes based geometric morphometrics is not ideal if your aim is to find 'dimensions' within a structure which maximally contribute to differences among groups. I am not sure if other methods, including traditional morphometrics, may help in this respect.
For (1) I looked into the Morphological Disparity (MD) equation provided in Zelditch et al. (2004) and got confused a bit. Definition says the measure of distance(or at least one of them) can be the Procrustes distance between the average shape of an individual species and the grand mean of all groups. I can, of course, calculate a mean shape for each of my groups using 3 separate GLS, and then calculate the grand mean from those three means. They also suggest to calculate a confidence interval for MD using bootstrapping with resampling with replacement. My understanding is, I bootstrap one group, take the new group mean shape, calculate a new MD for that group, rank them, toss the upper and lower 2.5%. to get a 95%. Provided that this correct, here are the parts that I am confused about: While bootstrapping, should I also calculate a new grand mean of groups?
I've done it a number of times but not very recently. A few papers where I think we did it are reported below. Yes, I'd say that the idea is that you repeat each step of the disparity analysis in the pseudosamples created by bootstrapping. Franklin D., Cardini A., Oxnard C. E. - A Geometric Morphometric Study of Population Variation in Indigenous sub-Saharan African Crania. American Journal of Human Biology, DOI 10.1002/ajhb.20908. Cardini A., Elton S., 2009, - The radiation of red colobus monkeys (Primates, Colobinae): morphological evolution in a clade of endangered African primates. Zoological Journal of the Linnean Society, 157: 197-224. Nowak K., Cardini A., Elton S., 2009 - Evolutionary acceleration in an endangered African primate: speciation and divergence in the Zanzibar Red Colobus (Primates, Colobinae). International Journal of Primatology, DOI 10.1007/s10764-008-9306-1. Cardini A., Elton S., 2008 - Variation in guenon skulls I: species divergence, ecological and genetic differences. Journal of Human Evolution, 54: 615-637. Cardini A, Thorington Jr. R. W., P. D. Polly, 2007 - Evolutionary acceleration in the most endangered mammal of Canada: phylogenetic signal and cranial divergence in the Vancouver Island marmot (Rodentia, Sciuridae). Journal of Evolutionary Biology, 20: 1833-1846. MOST OF THESE PAPERS, PROBABLY ALL OF THEM EXCEPT THE FIRST ONE, AREAVAIALABLE ON THE WEB. PLEASE, FOLLOW INSTRUCTIONS IN MY ELECTRONIC SIGNATURE.
Obviously, the group mean for the bootstrapped sample is not going to be identical to my original mean for that group, and that should have some effect on the grand mean of groups.
... Which also will have to be recalculated every time, if I am correct. Should I worry about this, or stick
with the grand mean from the original analysis? Also when I do resampling, should I resample the individuals or LMs?
You resample the individuals if you want to estimate the error due to sampling individuals within populations. Bootstrapping landmarks does not make much sense, I suspect, as one would be simulating a case where a given landmark (in exactely the same position) can be there 2 o 3 times or more, which is probably a non-sense at least in a biological structure. As I mentioned before (but I am not sure I would follow this route), one could jacknife landmarks. Then you're excluding bits of information and you're doing something analogous to examine errors due to character sampling in a phylogenetic analysis.
For (2), I was thinking I can take the pooled sample, calculate the Euclidean Distance of each LM (for each individual) from the consensus shape in tangent projected coordinates which will let me calculate LM difference means for each group. But then I couldn't figure out what to do with that. I guess I can calculate some sort of ratio, but would that really give me what I want?
If you still talking about the disparity analysis, you do everything using Procrustes shape distances. Those could be approximated by Euclidean distances (between GPA superimposed configurations) in the tangent space. For 2D data, I think that the analysis can be done using the IMP series. For 3D data, I used to do everything using batch files in NTSYS and a bit of manual computation in Excel.
Am I totally off the track?
One of the problem you may have is that samples are small. Especially if you have many landmarks, that's not ideal. You'll have problems with sample size also with other methods like discriminant analysis and the like. Resampling stats helps but is not a solution to every problem. Increasing sample size sometimes is the only option. Good luck. Cheers Andrea
Best, Murat -- A. Murat Maga, PhD Senior Fellow University of Washington Dept. Pediatrics, Division of Craniofacial Medicine 1959 NE Pacific St. HSB RR234 Seattle, WA 98195 (206) 616-9703 -- Replies will be sent to the list. For more information visit http://www.morphometrics.org
Dr. Andrea Cardini Lecturer in Animal Biology Museo di Paleobiologia e dell'Orto Botanico, Universitá di Modena e Reggio Emilia via Università 4, 41100, Modena, Italy tel: 0039 059 2056532; fax: 0039 059 2056535 Honorary Fellow Functional Morphology and Evolution Unit, Hull York Medical School University of Hull, Cottingham Road, Hull, HU6 7RX, UK University of York, Heslington, York YO10 5DD, UK E-mail address: alcard...@interfree.it, andrea.card...@unimore.it, andrea.card...@hyms.ac.uk http://hyms.fme.googlepages.com/drandreacardini http://ads.ahds.ac.uk/catalogue/archive/cerco_lt_2007/overview.cfm#metadata More on publications at: http://www.cons-dev.org/marm/MARM/EMARM/framarm/framarm.html LOOK FOR BIBLIOGRAPHIA MARMOTARUM, CLICK ON THE LETTER C AND LOOK FOR "CARDINI" (p. 8-9 until March 2009) http://hyms.fme.googlepages.com/dr.sarahelton-publications LOOK FOR "CARDINI" -- Replies will be sent to the list. For more information visit http://www.morphometrics.org