Hi Christy,
there's probably two main ways of doing that and they're to some extent
related.
1) Comparing angles of vectors. Besides MorphoJ's approach to this,
there are other resampling approaches and some of these are described in
Zelditch et al.'s Green Book and others in papers by the Viennese group
(Mitteroecker et al.'s papers on developmental trajectories and
size-shape spaces) and by O'Higgins et al..
2) The MANCOVA approach, which is well described in the Green Book. With
this, you'll find both parametric versions as well as resampling approaches.
In the Yellow Book (Hystrix 2013, link in my signature), there are at
least a couple of papers which are relevant: one is by Sheets and
Zelditch and the other one by Mitteroecker et al. I'd give a look also
at the recent review on allometry by Klingenberg (2016).
Especially with static allometry, you might need very large samples to
get reliables estimates. We explored somewhat this, years ago, in
Cardini & Elton, 2007, Zoomorphol. Also, for evolutionary allometries
and other comparative analyses, you should take phylogeny into account
(PGLS and the like - see papers by Rohlf, Adams etc.).
Besides P values, I would carefully check how different R2 of the models
you're comparing are and would also carefully inspect the visualizations
(do they suggest similar patterns across groups?).
Good luck.
Cheers
Andrea
On 19/08/16 02:34, Christy Hipsley wrote:
Dear Morphmet community,
I'm working with a big GM data set of 92 species and would like to
statistically compare levels of static, evolutionary, and ontogenetic allometry
to assess levels of constraint in phenotypic development.
For static and evolutionary allometry, I have regressions (shape on size for species) and
size-corrected PCAs. I am wondering what is the best way to directly compare those in a
statistical framework. I originally compared PC axes between the two data sets using the
"Compare Vector Directions" option in MorphoJ, but this seems a bit
complicated. Is a simple ANCOVA between the 2 regressions appropriate? They are at least
by eye nearly identical.
I also have regressions for growth series of 21 of those species, but I'm not
sure how those could be directly compared to static or evolutionary allometry.
If I do a regression of shape on size for that data set, pooled by species, the
R2 is slightly higher, which I expect since it is sampling over the entire
postnatal development (from hatchling to adult). However there is a strong
trend for some of the species to be significantly down-shifted along the
y-axis, although the slopes remain statistically the same (tested using MANCOVA
in GeoMorph).
Thanks for any advice on how to compare these levels or if it even makes sense
to compare ontogenetic allometry to either of the others.
Christy
-----------------------------
Christy Anna Hipsley
University of Melbourne/Melbourne Museum
--
Dr. Andrea Cardini
Researcher, Dipartimento di Scienze Chimiche e Geologiche, Università di Modena
e Reggio Emilia, Via Campi, 103 - 41125 Modena - Italy
tel. 0039 059 2058472
Adjunct Associate Professor, School of Anatomy, Physiology and Human Biology,
The University of Western Australia, 35 Stirling Highway, Crawley WA 6009,
Australia
E-mail address: alcard...@gmail.com, andrea.card...@unimore.it
WEBPAGE: https://sites.google.com/site/alcardini/home/main
FREE Yellow BOOK on Geometric Morphometrics:
http://www.italian-journal-of-mammalogy.it/public/journals/3/issue_241_complete_100.pdf
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MORPHMET may be accessed via its webpage at http://www.morphometrics.org
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