Calculating fluctuating asymmetry score for each individual

[wyf...@connect.hku.hk]

Dear all,

I am doing GMM analysis on objects with object symmetry. I wish to calculate fluctuating asymmetry (FA) scores for each specimen. From the paper "Canalization and developmental stability in the Brachyrrhine mouse" by Zelditch, I find the following formula for calculating FA score:

However, since FA10 is calculated from mean squares of an ANOVA table, I believe FA10 reflects the level of FA at group level rather than at individual level. In contrast, from the paper "Facial fluctuating asymmetry is not associated with childhood ill-health in a large British cohort study", the author stated that "The Procrustes ANOVA procedure in MORPHOJ [27] was used to calculate individual FA scores which correspond to the difference in shape between the left and right sides of the face after correction for directional asymmetry (i.e. after subtracting the mean shape asymmetry for the sample) ".

My question is how can we obtain individual FA scores from geomorph? In addition, what is the relationship between individual FA scores and group FA measure such as FA10?

Two-way mixed ANOVA was used to derive FA10. Based on my own data, I performed GPA using bilat.symmetry function with specification of ind and land.pairs arguments and object.sym=T. I extracted the resultant ANOVA table using $shape.anova but I was only returned the main effect of ind, side, and residuals. I wish to know how could I obtain the two-way mixed ANOVA table from geomorph with side as a fixed factor, ind as a random factor, their interactions included and replication included. I considered procD.lm(shape ~ ind * side, data = gdf), but I cannot specify which is fixed effect and which is random effect and I do not know how to include replication error into the model.

Thank you.

[lv xiao]

Hi, does anyone has some ideas on the issue regarding how to derive individual FA scores and how to specify two-way mixed ANOVA model in geomorph.

[Mike Collyer]

I’m answering just the two-factor mixed model question with this reply. You can perform this using procD.lm and nested.update. Also, bilat.symmetry does this inherently. I did discover a bug that might have thrown you off. The interaction term was labeled “Residuals” for non-replicated object symmetry cases. I have fixed that on our Github version.

Hope that helps!
Mike

> On Aug 24, 2018, at 5:56 AM, lv xiao <lxi...@gmail.com> wrote:
>
> Hi, does anyone has some ideas on the issue regarding how to derive individual FA scores and how to specify two-way mixed ANOVA model in geomorph.
>

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[Miriam Zelditch]

In the paper that you cite, on the Brachyrhine mouse (Willmore et al 2006), we used FA 10 as the metric for the population, for the reason given—it takes measurement error into account.  To answer the more general question that you’re asking about the relationship between metrics for individual FA and population-level metrics, two papers that thoroughly review that subject are Palmer and Strobeck 1986, and Palmer and Strobeck 2003.  There is another paper that proposes a metric for FA more specific to analyses of geometric morphometric data, Klingenberg and Monteiro, 2005.  If you plan to use the deviations of each individual from the symmetric mean, taking directional asymmetry into account, you can derive that from the FA.component returned by geomorph. As the manual says, that is the specimen-specific side deviation, adjusted for the mean directional asymmetry.  The answer to your last question, on how to obtain the two-way mixed model ANOVA from geomorph, should be more obvious now that the mislabeling of the terms in the table returned by the bilat.symmetry function is corrected.  However, it sounds like you had only two factors in your model, ind and sides, i.e., you did not specify the replicates.  If you do have replicates, you should include that factor in your geomorph dataframe and in the argument for the function, following the first example in the manual.

Willmore, K. E., M. L. Zelditch, N. Young, A. Ah-Seng, S. Lozanoff, and B. Hallgrimsson. 2006. Canalization and developmental stability in the Brachyrrhine mouse. Journal of Anatomy 208:361-372.

Klingenberg, C. P. and L. R. Monteiro. 2005. Distances and directions in multidimensional shape spaces: Implications for morphometric applications. Syst. Biol. 54:678-688.

Palmer, A.R. and C. Strobeck. 1986. Fluctuating asymmetry: measurement, analysis, patterns. Annual Review of Ecology and Systematics 17: 391–421.

Palmer, A. R and C. Strobeck. 2003. Fluctuating Asymmetry Analysis Unplugged. In: Developmental Instability (DI): Causes and Consequences (ed. Polak M), pp. 279–319. Oxford: Oxford University Press.

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Miriam Zelditch
Associate Research Scientist
Museum of Paleontology
University of Michigan
Ann Arbor, MI  48109-1079

cell: 734-353-1671
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