Question about asymmetry results obtained with bilat.symmetry

[Alberto Martin]

Hi all,

I am exploring the directional and fluctuating asymmetry of a set of mammalian skulls using 3D landmarks. I perform the Procrustes superimposition using bilat.symmetry function with two replicates of each individual for measurement error. This is the call:

Proc <- bilat.symmetry( Dataset, ind=indiv, replicate=repli, land.pairs=M.pairs, object.sym = T )

where indiv sets the same number for the two replicates (eg., 1, 1, 2, 2, 3, 3, ....) and repli sets the two groups of replicates (eg., 1, 2, 1, 2, 1, 2, ....).

According to the shape ANOVA, both side and side:ind have a significant effect.

Afterwards, I perform principal component analyses (gm.prcomp) to explore the main directions of shape variation of symmetric component, directional asymmetry and fluctuating asymmetry. However, the PCA results obtained from Proc$asymm.shape (total asymmetric variation) are exactly the same than the ones from Proc$FA.component (fluctuating asymmetric component only, without directional asymmetry). I have cheked actual values of both datasets and they correlate almost exactly, but not completely. Therefore, I am not sure if I am doing something wrong or if this is the expected result and, if this is the case, how can I explain it (e.g., negligible effect of DA?)

I would be grateful if anyone could help me to clarify this issue.

Thanks in advance,

Best,

Alberto

[Adams, Dean [EEOB]]

Alberto,

 

That is correct; these are nearly identical, and will correlate almost perfectly.

 

For each specimen, fluctuating symmetry is the difference between its L/R values. The Asymmetric shape component is basically the same.

 

Mathematically, the only (slight difference) is that asymmetric shape is calculated from the predicted L/R differences, plus the mean shape.  Fluctuating asymmetry is the difference in the observed shapes, plus the mean and minus the average directional asymmetry.

 

The two are usually quite similar to one another; and I’m not sure that was fully appreciated in the literature.

 

Below is another empirical example for you to show it is not just your data.

 

Dean

 

## Another example

data(lizards)

gdf <- geomorph.data.frame(shape = lizards$coords,

                           ind = lizards$ind,

                           replicate = lizards$rep)

liz.sym <- bilat.symmetry(A = shape, ind = ind, rep = rep,

                          object.sym = TRUE,

                          land.pairs = lizards$lm.pairs, data = gdf, RRPP = TRUE, iter = 149)

 

liz.sym$asymm.shape

liz.sym$FA.component

 

res <- two.b.pls(liz.sym$asymm.shape,liz.sym$FA.component)

plot(res)

 

Dr. Dean C. Adams

Distinguished Professor of Evolutionary Biology

Director of Graduate Education, EEB Program

Department of Ecology, Evolution, and Organismal Biology

Iowa State University

https://faculty.sites.iastate.edu/dcadams/

phone: 515-294-3834

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[Alberto Martin]

Hi,

Thank you very much, your explanation is very clarifying.

Best

Alberto