Dear Professor Bookstein, I'm sorry for my delayed response. Thank you very much for your detailed explanation of my question about form analysis. I heard about Boas coordinates, and it seems that using them is the right approach. Thank you for your suggestion.
Regarding my study, I'm not evaluating any specific hypothesis, but rather conducting an exploratory analysis to assess how well my taxa differ in terms of shape and form. Thank you for your additional suggestions on using Boas coordinates in PCA, PLS, and landmark plotting. These procedures appear to be a bit more complex and iterative than the conventional methods used to find major axes of shape or form variation. Thank you for the references mentioned. I know all of them except your 2018 textbook, to which I do not have access. I assume computing Boas coordinates using the R package geomorph would look like this simple script: boas <- simplify2array(lapply(1:length(Y.gpa$Csize), function(j) Y.gpa$coords[,,j] * Y.gpa$Csize[j])). I know you mentioned that the use of an arbitrary number of landmarks and their positions without specific biological meaning also plays a role. So, I suspect that this script lacks a term to include fixed landmarks. Like Murat, I'm also impressed by your opinion that CS, at least as used in the common Procrustes analysis, lacks biological meaning. I think this requires a much more detailed explanation for the GMM community, who still use the common procedures and theories proposed 40 years ago. Again, thank you very much for your detailed explanation and for your suggestions. With kind regards, Pablo El sáb, 4 oct 2025 a las 23:43, fred bookstein (<[email protected]>) escribió: > Sorry for the sheer bulk of this email, folks. My communication these days > is restricted to screen grabs from my iPhone. Fred B. > > -- > You received this message because you are subscribed to the Google Groups > "Morphmet" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion visit > https://groups.google.com/d/msgid/morphmet2/4FBA2804-28B4-4FE4-8E7C-117A19448FCC%40gmail.com > . > > > > -- > You received this message because you are subscribed to the Google Groups > "Morphmet" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion visit > https://groups.google.com/d/msgid/morphmet2/4FBA2804-28B4-4FE4-8E7C-117A19448FCC%40gmail.com > . > > > > -- > You received this message because you are subscribed to the Google Groups > "Morphmet" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion visit > https://groups.google.com/d/msgid/morphmet2/4FBA2804-28B4-4FE4-8E7C-117A19448FCC%40gmail.com > . > > > > -- > You received this message because you are subscribed to the Google Groups > "Morphmet" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion visit > https://groups.google.com/d/msgid/morphmet2/4FBA2804-28B4-4FE4-8E7C-117A19448FCC%40gmail.com > . > > > > -- > You received this message because you are subscribed to the Google Groups > "Morphmet" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion visit > https://groups.google.com/d/msgid/morphmet2/4FBA2804-28B4-4FE4-8E7C-117A19448FCC%40gmail.com > . > > > > -- > You received this message because you are subscribed to the Google Groups > "Morphmet" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion visit > https://groups.google.com/d/msgid/morphmet2/4FBA2804-28B4-4FE4-8E7C-117A19448FCC%40gmail.com > . > > Sent from my iPhone > > -- > You received this message because you are subscribed to the Google Groups > "Morphmet" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion visit > https://groups.google.com/d/msgid/morphmet2/4FBA2804-28B4-4FE4-8E7C-117A19448FCC%40gmail.com > . > -- You received this message because you are subscribed to the Google Groups "Morphmet" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/morphmet2/CANPrD1jMTJ57iPrxmzaH2hgG%2B-bWbpZHz_1w61MEbAdMZpfzQg%40mail.gmail.com.
