Advice on gm.measurement.error

[George lawrence]

Hello All -              

I am engaged upon a study of the evolution of head shape in horned lizards (Phrynosoma) using the array of geometric morphometric functions from geomorph. My sample consists of 3-D scans of 119 specimens from 16 of the Phrynosoma species. There is a fair amount of head shape disparity among these, a lot of which is due to differences in horn length.

I landmarked each specimen three times, in random order within species, and species were not landmarked in any order. The initial landmark configuration consisted of 72 landmarks covering the dermatocranium, mostly placed upon suture intersections or suture termini, with each horn covered by two landmarks on its base and one on the apex. I subject the entire replicate data set to a Procrustes fit and extracted the symmetric portion, subjecting it to the measurement error function gm.measurement.error, with species identity included as an argument. The output was as follows:

The magnitude of the effect size for interaction between systematic ME and groups is dismaying, as I took some pains to mix up the order in which replicates were taken; in addition, I didn’t group long-horned species or short-horned species together as I landmarked. In the SNR plot for this analysis, the individuals of each species cluster without a lot of overlap, and the short-horned species are clustered in one area while the individuals of the long-horned species are in another (non-overlapping) area, mainly defined by the systematic ME axis. This is discouraging when one is working on a phylogenetic analysis of head shape.

Horned lizards might as well be designed to potentially illustrate the Pinocchio effect, so I redid the measurement error analysis with the same data set, but with most of the landmarks designating horns removed before Procrustes fitting etc. I also wanted to see if reducing head shape disparity had an effect. The results of that analysis:

Still a large effect size for interaction.

There is only one published study so far (that I know of) using this method of assessing measurement error in GM – Umulisa et al (2025) – and they were looking at turtle shells, which are not complicated structures, and so I find it difficult to place my findings in context. My question, for anyone who’s got some perspective on this method, is whether I should consider the interaction effect size I’ve been getting as a real hinderance to further examination of phylogenetic shape change in these lizards.

Regards,

Larry Powell

[Mike Collyer]

Dear Larry,

This is a shot in the dark but have you tried the analysis without extracting the symmetric component?  If this is an object symmetry approach, don’t perform a symmetry analysis first.  If it is a matching symmetry approach, maybe perform ME analysis on just the left configurations or just the right configurations.  Whereas having an understanding of ME is important (as a basis) for interpreting asymmetry, substituting symmetric components of shape introduces an extra quantitive step that might make it difficult to evaluate measurement error that arises from digitizing.  Because the symmetric component is essentially subject means, I’m not sure if I understand what you used as data.  Regardless, I would suggest that for a ME analysis, a prior alteration, such as extracting symmetric components and using them as data, confounds the the digitizing bias you might want to assess and have taken pains to minimize with the alteration you made.  Your Rsq and Eta-sq values are really small, suggesting very little intra-subject variation.  If this is because you replace your data with estimates of subject means (symmetric component), then spurious results might be expected.

Good luck!

Mike

On Apr 4, 2025, at 1:15 AM, George lawrence <brevi...@gmail.com> wrote:

Hello All -

I am engaged upon a study of the evolution of head shape in horned lizards (Phrynosoma) using the array of geometric morphometric functions from geomorph. My sample consists of 3-D scans of 119 specimens from 16 of the Phrynosoma species. There is a fair amount of head shape disparity among these, a lot of which is due to differences in horn length.

I landmarked each specimen three times, in random order within species, and species were not landmarked in any order. The initial landmark configuration consisted of 72 landmarks covering the dermatocranium, mostly placed upon suture intersections or suture termini, with each horn covered by two landmarks on its base and one on the apex. I subject the entire replicate data set to a Procrustes fit and extracted the symmetric portion, subjecting it to the measurement error function gm.measurement.error, with species identity included as an argument. The output was as follows:

                        

The magnitude of the interaction between systematic ME and groups is dismaying, as I took some pains to mix up the order in which replicates were taken; in addition, I didn’t group long-horned species or short-horned species together as I landmarked. In the SNR plot for this analysis, the individuals of each species cluster without a lot of overlap, and the short-horned species are clustered in one area while the individuals of the long-horned species are in another (non-overlapping) area. This is discouraging when one is working on a phylogenetic analysis of head shape.

Horned lizards might as well be designed to potentially illustrate the Pinocchio effect, so I redid the measurement error analysis with the same data set, but with most of the landmarks designating horns removed before Procrustes fitting etc. The results of that analysis:

Still a large interaction effect.

There is only one published study so far using this method of assessing measurement error in GM – Umulisa et al (2025) – and they were looking at turtle shells, which are not complicated structures. I find it difficult to place my findings in context. My question, for anyone who’s got some perspective on this method, is whether I should consider the interaction effect size I’ve been getting as a real hinderance to further examination of phylogenetic shape change in these lizards.

Regards,

Larry Powell

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