Dear All,
this (links and abstract below) is out right now in Evol.Biol., with
many thanks to Benedikt for being such a great editor (plus more thanks
to all those who read it and helped with comments etc.!).
One of the two main Procrustes approaches that produce data for analyses
of modularity and/or integration seems to lead to very high rates of
false positives in some of the most common tests used in the main
programs/packages.
The study has some simulations and explore a variety of cases (plus a
few more in the R-script mentioned in the paper, and written by a
reviewer). It happens all the time in those data (unless one uses such a
small N relative to p, the number of variables, that unsurprisingly
nothing is significant). However, it is mostly an empirical study and
will require more work to understand how serious and general the issue
is. This is clearly said in the paper, that also says (but I'd like to
stress it) that:
1) the problem is not Procrustes but the way the data are used after
Procrustes;
2) the alternative approach does not produce false positives, but may
have low power and other issues (said multiple times but not a question
addressed by the study), which is why there is no recommendation in
favour of one or the other approach.
It might well be that in practice, if data have a real and strong
covariance, the problem will have just a small effect. But it seems to
be there all the time and there might be cases where it becomes much
more serious.
I hope it may be useful for those interested in that type of evo-devo
studies.
Cheers
Andrea
FINAL VERSION:
https://link.springer.com/article/10.1007%2Fs11692-018-9463-x
ALMOST (few differences!) FINAL PREPRINT:
https://www.biorxiv.org/content/early/2018/07/19/371187
Integration and Modularity in Procrustes Shape Data: Is There a Risk of
Spurious Results?
Abstract
Studies of morphological integration and modularity are a hot topic in
evolutionary developmental biology. Geometric morphometrics using
Procrustes methods offers powerful tools to quantitatively investigate
morphological variation and, within this methodological framework, a
number of different methods has been put forward to test if different
regions within an anatomical structure behave like modules or, vice
versa, are highly integrated and covary strongly. Although some
exploratory techniques do not require a priori modules, commonly modules
are specified in advance based on prior knowledge. Once this is done,
most of the methods can be applied either by subdividing modules and
performing separate Procrustes alignments or by splitting shape
coordinates of anatomical landmarks into modules after a common
superimposition. This second approach is particularly interesting
because, contrary to completely separate blocks analyses, it preserves
information on relative size and position of the putative modules.
However, it also violates one of the fundamental assumptions on which
Procrustes methods are based, which is that one should not analyse or
interpret subsets of landmarks from a common superimposition, because
the choice of that superimposition is purely based on statistical
convenience (although with sound theoretical foundations) and not on a
biological model of variance and covariance. In this study, I offer a
first investigation of the effects of testing integration and modularity
within a configuration of commonly superimposed landmarks using some of
the most widely employed statistical methods available to this aim. When
applied to simulated shapes with random non-modular isotropic variation,
standard methods frequently recovered significant but arbitrary patterns
of integration and modularity. Re-superimposing landmarks within each
module, before testing integration or modularity, generally removes this
artifact. The study, although preliminary and exploratory in nature,
raises an important issue and indicates an avenue for future research.
It also suggests that great caution should be exercised in the
application and interpretation of findings from analyses of modularity
and integration using Procrustes shape data, and that issues might be
even more serious using some of the most common methods for handling the
increasing popular semilandmark data used to analyse 2D outlines and 3D
surfaces.
--
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
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