I agree with Jim. However, this discussion does beg the question of what the 
status of landmark, semilandmark, or indeed pixel brightness configurations 
within multivariate spaces is? Very similar spaces have been used in the area 
of theoretical morphology to conduct various sorts of experiments dealing with 
the nature of morphological evolution, especially the development of patterns 
based on null models to which empirical patterns can be compared. Moreover, 
machine learning specialists are now using morphologies generated artificially, 
in ways that aren’t very different from the ways in which such visualisations 
can be created by morphometricians, to train their AI systems. McGhee 
distinguishes "theoretical morphospaces” derived from graphics equations (e.g., 
Raup’s coiling models) from (what he terms) the “empirical morphospaces” we 
deal with as morphometricians and that lie at the heart of this conversation. 
But are the two really that different? If so, why and in what cases? If not 
what does that mean for the ways in which we might use such spaces? I’ve long 
found this an interesting question to ponder. Any thoughts from the community?

Norm MacLeod

> On 15 May 2017, at 18:28, F. James Rohlf <f.james.ro...@stonybrook.edu> wrote:
> What is important is not the fact that one is going +/- one standard 
> deviation along each axis. When shape changes are subtle one may need to go 
> beyond the observed range to make it more obvious to the eye what the changes 
> are. Exactly how far one goes away from the mean is arbitrary. It is a 
> visualization – not statistics.
> ----------------------
> F. James Rohlf New email: f.james.ro...@stonybrook.edu
> Distinguished Professor, Emeritus. Dept. of Ecol. & Evol.
> & Research Professor. Dept. of Anthropology
> Stony Brook University 11794-4364
> WWW: http://life.bio.sunysb.edu/morph/rohlf
> P Please consider the environment before printing this email


Professor Norman MacLeod
The Natural History Museum, Cromwell Road, London, SW7 5BD
(0)207 942-5204 (Office Landline)
(0)785 017-1787 (Mobile)

Department of Earth Sciences, University College
London, Gower Street, London WC1E 6BT, UK

Nanjing Institute of Geology & Palaeontology,
Chinese Academy of Sciences, 39 Beijing, Donglu, Nanjing, China

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