Damien,

To your first point (inter-species allometry), you are correct that it does not 
make sense when there is a significant species:size interaction. In that case, 
the data have changed one’s question: away from pairwise differences of least 
squares species means, and towards a question of pairwise differences in 
allometric slopes. (Note that when the interaction term is not significant, one 
could use the residuals from a common allometry model as you mentioned, but 
pairwise comparisons of groups using the shape~size + species and residual 
randomization will get you there as well, and avoids that additional step).

For environmental groups, the logic is precisely the same. Here one has the 
model: shape~size + env.gp + size:env.gp.  A significant interaction implies 
that the slopes within each environmental group differ, and so again the data 
have changed one’s question from that of group differences in means to group 
differences in slopes.

Dean

Dr. Dean C. Adams
Director of Graduate Education, EEB Program
Professor
Department of Ecology, Evolution, and Organismal Biology
Iowa State University
https://www.eeob.iastate.edu/faculty/adams/
phone: 515-294-3834

From: [email protected] <[email protected]> On Behalf Of 
Damien Esquerre
Sent: Monday, July 13, 2020 11:57 PM
To: [email protected]
Subject: [MORPHMET2] allometric correction

Dear morpho community,
I have a philosophical question on size correction that should start an 
interesting discussion.
When we are interested in seeing the effects of species or environmental 
variables for example, on shape, people often first remove allometric variation 
by computing the residuals of a shape ` size regression. This of course, 
doesn't make sense if there are heterogeneous slopes and species have different 
allometric trajectories (i.e. if the species*size term is significant).
What do you think would be the most appropriate way to deal with this situation 
then, if you are interested in environmental effects on shape?
Best regards,
Damien Esquerré
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