-------- Original Message -------- Subject: Re: Comparing Segments of Developmental Trajectories Date: Tue, 13 Mar 2012 07:00:14 -0400 From: ppi...@uniroma3.it To: morphmet@morphometrics.org CC: morphmet <morphmet@morphometrics.org> Hi all, Piras et al (2011) higlighted (using real data) that checking for the obliquity is very important when comparing ontogenetic trajectories, as pointed out by Huttegger and Mitteroecker (2011). In fact, if obliquiy severly affects the data, angles are incommensurable and any angle computation (such as euclidean distances computed between full vectors of regression coefficients of per-group regressions between shape (Proc. Coords) and size-among other strategies) loose sense. I used a "visual inspection" of obliquity by plotting (3d) AT THE VERY LEAST the first two PCA scores computed on predicted values (acronimized here to fore in PCAonpred) coming from per-group multivariate regressions between shape and size. They should develop on the SAME direction. However, even plotting solely the first 3 or 4 PCAonpreds against each other (using 3d plots o scatterplot matrices) is useful to check for obliquity. This is the reason of why Andrea claimed for a "low power" of angle calculation. Obliquity is a BIG problem not only for studies on ontogenetic trajectories but also for ANY type of multivariate regressions conparison. It could be nice to develop a specific strategy to assess if the obliquity affecting a given dataset is trascurable or not..... Maybe in the presence of a severe obliquity, one can manage the problem by applying angle comparisons to the bivariate relationship between allometric vector computed in morphoJ (maybe by performing a "pooled within group regression") and size. This becomes a classical pairwise comparison between regression coefficients of per-group univariate regressions. One can consider the allometric vector as the best APPROXIMATION of the actual group-specific trajectories. Now....the problem of Michelle is not only to check for obliquity for the full developmental interval but to look for it in A SERIES of developmental intervals. Maybe using predicted shapes at given size values (I assume here that what you call "developmental variable" is size) you can compare if procrustes distances between groups get larger or smaller for avery step you decided to partionate the full size interval (i.e. 10 intervals). I'm not sure about the biological meaning of this operation, however. Or.....if your dataset OF ANY GROUP consists of many individuals FOR ANY INTERVAL (often it is highly difficult to find this situation), you can track the course of DEVELOPMENTAL COVARIANCE MATRIces as described by Mitteroecker and Bookstein (2009). However, the sample size of any group for any interval must be large and this condition is rarely met in experimental biological studies. Maybe this last strategy is what actually Michelle is looking for when partitioning the full size interval into smaller sub-intervals. Is your dataset appropriate? I hope this helps Paolo Mitteroecker P, Bookstein FL (2009) The Ontogenetic Trajectory of the Phenotypic Covariance Matrix, with Examples from Craniofacial Shape in Rats and Humans. Evolution 63 (3), 727-737 Huttegger, S. & Mitteroecker, P. 2011. Invariance and meaningfulness in phenotype spaces. Evol. Biol. 38: 335352. Piras P, Salvi D, Ferrara G, Maiorino L, Delfino M, Pedde L, Kotsakis T. 2011. The role of post-natal ontogeny in the evolution of phenotypic diversity in Podarcis lizards. Journal of Evolutionary Biology, 24: 27052720. -------- Original Message -------- Subject: Re: Comparing Segments of Developmental Trajectories Date: Tue, 13 Mar 2012 05:12:10 -0400 From: andrea cardini <alcard...@gmail.com> To: morphmet@morphometrics.org Hi Michelle, Sarah Elton and I, years ago, explored a little bit how variable angles were when sample size got smaller. We did not do the tests of significance but found quite a big variation. The reference is below and it is available also in my webpage: Cardini A., Elton S., 2007 - Sample size and sampling error in geometric morphometric studies of size and shape. Zoomorphology, 126: 121-134. My guess is that statistical power will be very low. Within a developmental stage, trajectories are not unlikely to be almost circular (with variation 'squeezed' just a little bit in a given direction): to get accurate angles, one will then need really big samples. Cobb and O'Higgins, if I remember well, also explored the issue with a similar approach but they were comparing ontogenetic trajectories (all stages) across species. Those trajectories will be much more 'stretched' and smaller samples might still be reasonably accurate. I can find the ref. but I am sure you already know the paper. Good luck. Cheers Andrea At 23:29 12/03/2012 +0100, you wrote:
-------- Original Message -------- Subject: Comparing Segments of Developmental Trajectories Date: Mon, 12 Mar 2012 18:15:09 -0400 From: Michelle Singleton <msingle...@midwestern.edu> To: morphmet@morphometrics.org Dear Colleagues, As part of a study of ontogenetic shape change in a group of related species, I wish to compare patterns of shape change between successive developmental stages. My intention was to compare angular differences between species vectors obtained from multivariate regression of Procrustes residuals on my developmental variable. When I apply this approach to the full developmental series (juvenile to adult) I get interspecies angles comparable to those obtained by myself and others in prior studies, but when I look at individual segments (e.g., Stage 1 to Stage 2) the resulting angles are very large, apparently because the amount of variation between stages is too small to allow accurate vector estimates, although the smaller sample sizes probably contribute as well. The large angles do, nevertheless, return the same qualitative result (in terms of relative vector similarity) as the angles for the full ontogenetic series. My questions are: 1) have I correctly identified the source of the discrepancy in angle magnitudes? 2) can permutation significance tests based on these angles be meaningful; or, 3) is this the wrong approach and is there perhaps a more appropriate method for this comparison? Many thanks for your thoughts on this problem. Best regards, Michelle -- Michelle Singleton, Ph.D. Professor of Anatomy Midwestern University 555 31st Street Downers Grove, IL 60515 Phone: 630.515.6137 <tel:630.515.6137> Fax: 630.515.7199 <tel:630.515.7199> e-mail: msingle...@midwestern.edu <mailto:msingle...@midwestern.edu>
Dr. Andrea Cardini Researcher in Animal Biology Dipartimento di Biologia, Universitá di Modena e Reggio Emilia, via Campi 213, 41100, Modena, Italy tel: 0039 059 2055017 ; fax: 0039 059 2055548 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 Adjunct Associate Professor Centre for Forensic Science , The University of Western Australia 35 Stirling Highway, Crawley WA 6009, Australia E-mail address: alcard...@gmail.com, andrea.card...@unimore.it, andrea.card...@hyms.ac.uk, andrea.card...@uwa.edu.au Webpage: http://sites.google.com/site/hymsfme/drandreacardini Datasets: http://ads.ahds.ac.uk/catalogue/archive/cerco_lt_2007/overview.cfm#metadata Editorial board for: Zoomorphology: http://www.springer.com/life+sciences/animal+sciences/journal/435 Journal of Zoological Systematics and Evolutionary Research: http://www.wiley.com/bw/journal.asp?ref=0947-5745&site=1 Hystrix, the Italian Journal of Mammalogy: http://www.italian-journal-of-mammalogy.it/ -- Paolo Piras Center for Evolutionary Ecology and Dipartimento di Scienze Geologiche, Università Roma Tre Largo San Leonardo Murialdo, 1, 00146 Roma Tel: +390657338000 email: ppi...@uniroma3.it
