Skip to main content
SpringerLink
Log in

The Occasional Perils of Reflection (Across the Midline; in Geometric Morphometrics)

  • Tools and Techniques
  • Published:
Evolutionary Biology Aims and scope Submit manuscript

Abstract

Manual landmark data collection on large samples takes a long time. Several options exist to speed the process, though each introduces problems or raises concerns of its own. For bilaterally symmetric structures (e.g., crania), some recent papers recommend limiting landmark collection to one side and the anatomical midline, then approximating the true bilateral configuration by merging the hemi-form and its reflection at the midline. However, where the midline is narrow relative to the bilateral anatomy, net midline landmark deviations from the mid-sagittal axis or plane will distort this “mirror-reflected” configuration. Here, I use a sample of bilaterally landmarked human mandibles to evaluate whether these distortions are a substantive concern at the scale of real biology. Through simulation, I introduce small mediolateral errors at the midline landmarks of the mean mandible form, then mirror-reflect one side in order to quantify and visualize the effect of midline error on mirror-reflected outcomes. I also test how faithfully mirror reflection and other reduced-landmarking strategies preserve shape and size relationships among observations characterized by the full, bilateral complement of landmarks. In both analyses, mirror reflection is shown to produce striking distortions. Mirror reflection is clearly inappropriate for these data and is likely suspect in all cases of narrow midline morphology. I also demonstrate that bilateral shape and size can be reasonably well recovered with a reflected-relabeling strategy where the landmark data consists of hemi-form landmarks plus a small number of landmarks from the specimen’s opposite side.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Data Availability

Data is provided as Supplementary Material A to the manuscript.

Code Availability

Statistical code available by request to the author.

Notes

  1. The wireframe links only the arch subset landmarks.

References

  • Adams, D., Collyer, M., & Sherratt, E. (2015). geomorph: Software for geometric morphometric analyses. R package version 2.1.6. https://cran.r-project.org/web/packages/geomorph/index.html.

  • Adler, D., Murdoch, D., & others. (2016). rgl: 3D visualization using OpenGL (Version 0.95.1441). https://CRAN.R-project.org/package=rgl

  • Benazzi, S., Fiorenza, L., Kozakowski, S., & Kullmer, O. (2011). Comparing 3D virtual methods for hemimandibular body reconstruction. The Anatomical Record,294(7), 1116–1125. https://doi.org/10.1002/ar.21410.

    PubMed  Google Scholar 

  • Bookstein, F. (1986). Size and shape spaces for landmark data in two dimensions. Statistical Science,1(2), 181–242.

    Google Scholar 

  • Boyer, D. M., Lipman, Y., St Clair, E., Puente, J., Patel, B. A., Funkhouser, T., et al. (2011). Algorithms to automatically quantify the geometric similarity of anatomical surfaces. Proceedings of the National Academy of Sciences USA,108(45), 18221–18226. https://doi.org/10.1073/pnas.1112822108.

    Google Scholar 

  • Bräuer, G., & Knußmann, R. (1988). Grundlagen der Osteometrie. In: Knußmann R (Ed.), Anthropologie. Handbuch der vergleichenden Biologie des Menschen. Band I, 1. Teil. (pp. 129–159). Stuttgart: Springer.

  • Cardini, A. (2016). Lost in the other half: Improving accuracy in geometric morphometric analyses of one side of bilaterally symmetric structures. Systematic Biology,65(6), 1096–1106. https://doi.org/10.1093/sysbio/syw043.

    PubMed  Google Scholar 

  • Cardini, A. (2017). Left, right or both? Estimating and improving accuracy of one-side-only geometric morphometric analyses of cranial variation. Journal of Zoological Systematics and Evolutionary Research,55(1), 1–10. https://doi.org/10.1111/jzs.12144.

    Google Scholar 

  • Cardini, A., Diniz Filho, J., Polly, P., & Elton, S. (2010). Biogeographic analysis using geometric morphometrics: Clines in skull size and shape in a widespread African arboreal monkey. In A. M. Elewa (Ed.), Morphometrics for nonmorphometricians (pp. 191–217). New York: Springer.

    Google Scholar 

  • Cardini, A., & Polly, P. D. (2013). Larger mammals have longer faces because of size-related constraints on skull form. Nature Communications,4, 2458. https://doi.org/10.1038/ncomms3458.

    CAS  PubMed  Google Scholar 

  • Claes, P., Roosenboom, J., White, J. D., Swigut, T., Sero, D., Li, J., et al. (2018). Genome-wide mapping of global-to-local genetic effects on human facial shape. Nature Genetics,50(3), 414–423. https://doi.org/10.1038/s41588-018-0057-4.

    CAS  PubMed  PubMed Central  Google Scholar 

  • Cole, J. B., Manyama, M., Kimwaga, E., Mathayo, J., Larson, J. R., Liberton, D. K., et al. (2016). Genomewide association study of african children identifies association of SCHIP1 and PDE8A with facial size and shape. PLoS Genetics,12(8), e1006174. https://doi.org/10.1371/journal.pgen.1006174.

    CAS  PubMed  PubMed Central  Google Scholar 

  • Cooke, S. B., & Terhune, C. E. (2015). Form, function, and geometric morphometrics. The Anatomical Record,298(1), 5–28. https://doi.org/10.1002/ar.23065.

    PubMed  Google Scholar 

  • Cooney, C. R., Bright, J. A., Capp, E. J. R., Chira, A. M., Hughes, E. C., Moody, C. J. A., et al. (2017). Mega-evolutionary dynamics of the adaptive radiation of birds. Nature,542(7641), 344–347. https://doi.org/10.1038/nature21074.

    CAS  PubMed  PubMed Central  Google Scholar 

  • Dow, M. M., & Cheverud, J. M. (1985). Comparison of distance matrices in studies of population structure and genetic microdifferentiation: Quadratic assignment. American Journal of Physical Anthropology,68(3), 367–373. https://doi.org/10.1002/ajpa.1330680307.

    CAS  PubMed  Google Scholar 

  • Dryden, I. L. (2018). Shapes package (Version 1.2.4). Vienna, Austria: R Foundation for Statistical Computing.

  • Frost, S. R., Marcus, L. F., Bookstein, F. L., Reddy, D. P., & Delson, E. (2003). Cranial allometry, phylogeography, and systematics of large-bodied papionins (primates: Cercopithecinae) inferred from geometric morphometric analysis of landmark data. The Anatomical Record Part A: Discoveries in Molecular, Cellular, and Evolutionary Biology,275A(2), 1048–1072. https://doi.org/10.1002/ar.a.10112.

    Google Scholar 

  • Gao, T., Yapuncich, G. S., Daubechies, I., Mukherjee, S., & Boyer, D. M. (2018). Development and assessment of fully automated and globally transitive geometric morphometric methods, with application to a biological comparative dataset with high interspecific variation. The Anatomical Record,301(4), 636–658. https://doi.org/10.1002/ar.23700.

    PubMed  Google Scholar 

  • Goswami, A., Watanabe, A., Felice, R. N., Bardua, C., Fabre, A. C., & Polly, P. D. (2019). High-density morphometric analysis of shape and integration: The good, the bad, and the not-really-a-problem. Integrative and Comparative Biology,59(3), 669–683. https://doi.org/10.1093/icb/icz120.

    PubMed  PubMed Central  Google Scholar 

  • Gunz, P., & Mitteroecker, P. (2013). Semilandmarks: A method for quantifying curves and surfaces. Hystrix, the Italian Journal of Mammology,24(1), 103–109. https://doi.org/10.4404/hystrix-24.1-6292.

    Google Scholar 

  • Gunz, P., Mitteroecker, P., Neubauer, S., Weber, G. W., & Bookstein, F. L. (2009). Principles for the virtual reconstruction of hominin crania. Journal of Human Evolution,57(1), 48–62. https://doi.org/10.1016/j.jhevol.2009.04.004.

    PubMed  Google Scholar 

  • Harvati, K. (2003). Quantitative analysis of Neanderthal temporal bone morphology using three-dimensional geometric morphometrics. American Journal of Physical Anthropology,120(4), 323–338. https://doi.org/10.1002/ajpa.10122.

    PubMed  Google Scholar 

  • Katz, D., & Friess, M. (2014). Technical note: 3D from standard digital photography of human crania—A preliminary assessment. American Journal of Physical Anthropology,154(1), 152–158.

    PubMed  Google Scholar 

  • Katz, D. C., Grote, M. N., & Weaver, T. D. (2017). Changes in human skull morphology across the agricultural transition are consistent with softer diets in preindustrial farming groups. Proceedings of the National Academy of Sciences USA,114(34), 9050–9055. https://doi.org/10.1073/pnas.1702586114.

    CAS  Google Scholar 

  • Klingenberg, C. P. (2015). Analyzing fluctuating asymmetry with geometric morphometrics: Concepts, methods, and applications. Symmetry,7, 843–934.

    Google Scholar 

  • Klingenberg, C. P., Barluenga, M., & Meyer, A. (2002). Shape analysis of symmetric structures: Quantifying variation among individuals and asymmetry. Evolution,56(10), 1909–1920.

    PubMed  Google Scholar 

  • Li, M., Cole, J. B., Manyama, M., Larson, J. R., Liberton, D. K., Riccardi, S. L., et al. (2017). Rapid automated landmarking for morphometric analysis of three-dimensional facial scans. Journal of Anatomy,230(4), 607–618. https://doi.org/10.1111/joa.12576.

    PubMed  PubMed Central  Google Scholar 

  • Maga, A. M., Tustison, N. J., & Avants, B. B. (2017). A population level atlas of Mus musculus craniofacial skeleton and automated image-based shape analysis. Journal of Anatomy,231(3), 433–443. https://doi.org/10.1111/joa.12645.

    PubMed  PubMed Central  Google Scholar 

  • Mantel, N. (1967). The detection of disease clustering and a generalized regression approach. Cancer Research, 27(1), 209–220.

    CAS  PubMed  Google Scholar 

  • Marcus, L. F., Bello, E., & Garcia-Valdecasas, A. (1992). Contributions to morphometrics. Madrid, Spain: Consejo Superior de Investigaciones Cientificas.

    Google Scholar 

  • Mardia, K. V., Bookstein, F. L., & Moreton, I. J. (2000). Statistical assessment of bilateral symmetry of shapes. Biometrika,87(2), 285–300.

    Google Scholar 

  • Mitteroecker, P. (2018). Semilandmarks in biology. In MORPHMET. https://groups.google.com/a/morphometrics.org/forum/#!forum/morphmet.

  • Mitteroecker, P., & Bookstein, F. (2011). Linear discrimination, ordination, and the visualization of selection gradients in modern morphometrics. Evolutionary Biology,38(1), 100–114.

    Google Scholar 

  • Mitteroecker, P., & Gunz, P. (2009). Advances in geometric morphometrics. Evolutionary Biology,36(2), 235–247. https://doi.org/10.1007/s11692-009-9055-x.

    Google Scholar 

  • Nicholson, E., & Harvati, K. (2006). Quantitative analysis of human mandibular shape using three-dimensional geometric morphometrics. American Journal of Physical Anthropology,131(3), 368–383. https://doi.org/10.1002/ajpa.20425.

    PubMed  Google Scholar 

  • Pavličev, M., Mitteroecker, P., Gonzalez, P. M., Rolian, C., Jamniczky, H., Villena, F. P., et al. (2016). Development shapes a consistent inbreeding effect in mouse crania of different line crosses. Journal of Experimental Zoology Part B - Molecular and Developmental Evolution,326(8), 474–488. https://doi.org/10.1002/jez.b.22722.

    Google Scholar 

  • Percival, C. P., Devine, J., Darwin, B. C., Liu, W., van Eede, M., Henkelman, R. M., & Hallgrímsson, B. (2019). The effect of automated landmark identification on morphometric analysis. Journal of Anatomy, 234, 917–935. https://doi.org/10.1111/joa.12973.

    PubMed  PubMed Central  Google Scholar 

  • R Core Team. (2019). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/.

  • Rohlf, F. J. (2000). Statistical power comparisons among alternative morphometric methods. American Journal of Physical Anthropology,111, 463–478.

    CAS  PubMed  Google Scholar 

  • Rohlf, F.J., & Bookstein, F. (Eds.). (1988). Proceedings of the Michigan morphometrics workshop (Vol. 2). Ann Arbor, MI: University of Michigan Museum of Zoology.

  • Rohlf, F. J., & Marcus, L. F. (1993). A revolution in morphometrics. Trends in Ecology and Evolution,8(4), 129–132. https://doi.org/10.1016/0169-5347(93)90024-j.

    Google Scholar 

  • Rohlf, F. J., & Slice, D. E. (1990). Extensions of the Procrustes method for the optimal superimposition of landmarks. Systematic Zoology,39(1), 40–59.

    Google Scholar 

  • Savriama, Y., & Klingenberg, C. P. (2011). Beyond bilateral symmetry: Geometric morphometric methods for any type of symmetry. BMC Evolutionary Biology,11(1), 280.

    PubMed  PubMed Central  Google Scholar 

  • Slice, D. E. (2005). Modern morphometrics. In D. E. Slice (Ed.), Modern morphometrics in physical anthropology (pp. 1–45). New York: Kluwer Acad./Plenum.

    Google Scholar 

  • Slice, D. E. (2007). Geometric morphometrics. Annual Review of Anthropology,36, 261–281.

    Google Scholar 

  • Watanabe, A. (2018). How many landmarks are enough to characterize shape and size variation? PLoS ONE,13(6), e0198341. https://doi.org/10.1371/journal.pone.0198341.

    CAS  PubMed  PubMed Central  Google Scholar 

  • Zelditch, M. L., Swiderski, D. L., & Sheets, H. D. (2014). Geometric morphometrics for biologists: A primer (2nd ed.). New York: Elsevier Academic Press.

    Google Scholar 

Download references

Acknowledgements

The author thanks Timothy D. Weaver and the members of the Hallgrímsson lab for comments on an early version of this manuscript.

Funding

None for this project.

Author information

Authors and Affiliations

  1. Department of Cell Biology & Anatomy, Cumming School of Medicine, University of Calgary, Calgary, AB, Canada

    David C. Katz

Authors
  1. David C. Katz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to David C. Katz.

Ethics declarations

Conflict of interest

The author has no conflicts of interest.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary file1 (TXT 128 kb)

Supplementary file2 (PDF 417 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Katz, D.C. The Occasional Perils of Reflection (Across the Midline; in Geometric Morphometrics). Evol Biol 47, 164–174 (2020). https://doi.org/10.1007/s11692-020-09501-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11692-020-09501-1

Keywords

Search

Navigation