Hi Fred,

It is interesting that you are proposing to toss out CS completely in 
morphometrics, beyond its is function to bring the shape configurations to 
unit size during superimposition. In own experience (mostly derived from 3D 
microCT scans of mouse skulls and embryos), I have yet to see any set of 
landmark derived CS NOT to be highly correlated (>.9) with actually body 
weight information we collect from these organisms. In my experience, 
centroid sizes that are derived from biologically correctly scaled 
coordinate data is no worse (or better) than any size proxy that 
morphologist derive from skeletons like articular surface areas or volumes, 
or geometric means of linear measurements etc. Yes, for most cases 
landmarks are arbitrary, but so are the linear measurements. Any linear 
measurement any one claims to be reliably repeated can be represented by 
two landmarks.  

In my experience the main issue with the centroid size is that sometimes 
(often?) people do not scale them at all (regardless they are 2D or 3D 
derived) into biologically relevant units, such as mm or cm that we can 
make sense of like the mm's we measure on calipers, or osteometry boards. 
Same set of landmarks derived from two pictures of the same skull (one 
scaled by the pixel size, the other in pixel coordinates) are going to give 
CS estimates that are orders of magnitude different from each other. When 
there is that methodological inconsistency about explicitly defined units 
for coordinate data, I am not sure how keeping the size in the analysis is 
going to help. 

On Saturday, October 4, 2025 at 7:42:58 PM UTC-7 fred bookstein wrote:

> Sorry for the sheer bulk of this email, folks. My communication these days 
> is restricted to screen grabs from my iPhone. Fred B. 
>
>

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