Analysis of floating and directional asymmetry

[Marcos Moura]

Dear Geomorph Community,

I'm working in Geomorph, evaluating differences between directional asymmetry (DA) and fluctuating asymmetry (FA) in bee wings from different locations.
I took photographs of the forewings, replicated each photo three times, and marked 12 landmarks on each wing.
I followed all the steps for asymmetry analysis and obtained the results normally, without any problems.
However, our main question is: is there a significant difference in asymmetry between locations?

Initially, I had thought about applying a nonparametric mean test to the generated data sets. However, as I studied and talked with other researchers, I realized that this isn't entirely correct.
I read a thread here in the Geomorph community and found an indication that I should check the permutation-based Z-score generated in the ANOVA table for each effect. Currently, there are compare.CR and compare.pls functions that analyze this effect for modularity and integration.
I've been trying to find a solution to statistically compare AF and AD between locations, but I haven't made any progress.

Do you have any suggestions?

Thank you very much!
Best regards, Marcos Moura.

[Adams, Dean [EEOB]]

Marco,

I apologize for the delayed response. I was traveling. 

As you noted, at present, geomorph and RRPP do not have 'general' Z-score comparison functions. Thus far we have provided functions to compare the strength of signal in specific attributes (e.g., compare the degree of integration or compare the degree of phylogenetic signal, etc). But conceptually, our approach is not restricted to the functions we have generated. In fact, the method is far broader, and our RRPP-derived effect sizes could be obtained from other models, and compared across those models. Your question about bilateral symmetry falls under this category. 

To make such comparisons, one needs to dive under the hood a bit, and write some code that replicates the various components and extracts the bits of interest for the two sample test. Specifically, our effect size comparisons are based on a two-sample test, which is: 

Z12 = abs(theta1 - mu1) - (theta2 - mu2) / sqrt(sd1^2 + sd2^2)

Here, theta1 and theta2 are the observed values of the test statistic, mu1 and mu2 are the mean of the empirical sampling distributions, and sd1 and sd2 are the standard deviations of those sampling distributions. Importantly, all values above are found from the transformed sampling distributions to ensure the distributions approximate a normal distribution. 

Thus, we must obtain the empirical sampling distributions from the model of interest, transform them to approximate normality, and from this extract theta, mu, and sd. Below is code (not optimized, but readable) that will do this for a single bilat.symmetry analysis, and a single component of the model (in this case, the FA component). This approach could be followed for the analysis of each of your locations, which can then be compared in pairwise fashion.  

###

library(geomorph)

data(mosquito)

gdf <- geomorph.data.frame(wingshape = mosquito$wingshape, 

                           ind = mosquito$ind, 

                           side = mosquito$side,

                           replicate = mosquito$replicate)

Y.gpa <- gpagen(mosquito$wingshape)

mosquito.sym2 <- bilat.symmetry(A = Y.gpa, ind = ind, side = side,   replicate = replicate, object.sym = FALSE, RRPP = TRUE, 

                                data = gdf)

#bilat.symmetry analysis using base-geomorph functions

PSh <- procD.lm(Y.gpa$coords ~ ind + side + ind/side, data = gdf, verbose = T)

#COMPARE: results are the same

mosquito.sym$shape.anova

anova(PSh, error = c("ind:side", "ind:side", "Residuals"))                  

######

#extract components for Z-score comparison

F.ind <- PSh$ANOVA$MS[1,] / PSh$ANOVA$MS[3,]

F.side <- PSh$ANOVA$MS[2,] / PSh$ANOVA$MS[3,]

F.indside <- PSh$ANOVA$MS[3,] / PSh$ANOVA$RSS[3,]  

# Effect sizes: the same

Z.ind <- effect.size(F.ind) #ind

Z.side <- effect.size(F.side) #side

Z.indside <- effect.size(F.indside) #ind:side

#Transformed empirical sampling distributions

F.ind.st <- geomorph:::box.cox(F.ind)$transformed

F.side.st <- geomorph:::box.cox(F.side)$transformed

F.indside.st <- geomorph:::box.cox(F.indside)$transformed

# Theta, Mu, and Sd

F.ind.st[1]

mean(F.ind.st)

sd(F.ind.st)

Dean

-- 
Dr. Dean C. Adams
Distinguished Professor
Director, Ecology and Evolutionary Biology Graduate Program
Department of Ecology, Evolution, and Organismal Biology
Iowa State University
www.public.iastate.edu/~dcadams/
phone: 515-294-3834

---

From: geomorph-...@googlegroups.com <geomorph-...@googlegroups.com> on behalf of Marcos Moura <marcose...@gmail.com>
Sent: Monday, September 15, 2025 8:43 AM
To: geomorph R package <geomorph-...@googlegroups.com>
Subject: [geomorph-r-package] Analysis of floating and directional asymmetry

 

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