A resistant method for landmark‐based analysis of individual asymmetry in two dimensions

Quantitative Biology - 2016
Sebastián Torcida1, Paula N. González2, Federico Pablo Lotto3
1<!--1--> Dpto. Matemática‐Exactas UNCPBA Tandil 7000 Argentina
2<!--2--> Fac. de Ciencias Naturales y Museo UNLP‐CONICET La Plata 1900 Argentina
3<!--3--> Instituto de Veterinaria Ing. Fernando N. Dulout (IGEVET) Facultad de Cs. Veterinarias UNLP‐CONICET La Plata 1900 Argentina

Tóm tắt

BackgroundSymmetry of biological structures can be thought as the repetition of their parts in different positions and orientations. Asymmetry analyses, therefore, focuses on identifying and measuring the location and extent of symmetry departures in such structures. In the context of geometric morphometrics, a key step when studying morphological variation is the estimation of the symmetric shape. The standard procedure uses the least‐squares Procrustes superimposition, which by averaging shape differences often underestimates the symmetry departures thus leading to an inaccurate description of the asymmetry pattern. Moreover, the corresponding asymmetry values are neither geometrically intuitive nor visually perceivable.MethodsIn this work, a resistant method for landmark‐based asymmetry analysis of individual bilateral symmetric structures in 2D is introduced. A geometrical derivation of this new approach is offered, while its advantages in comparison with the standard method are examined and discussed through a few illustrative examples.ResultsExperimental tests on both artificial and real data show that asymmetry is more effectively measured by using the resistant method because the underlying symmetric shape is better estimated. Therefore, the most asymmetric (respectively symmetric) landmarks are better determined through their large (respectively small) residuals. The percentage of asymmetry that is accounted for by each landmark is an additional revealing measure the new method offers which agrees with the displayed results while helping in their biological interpretation.ConclusionsThe resistant method is a useful exploratory tool for analyzing shape asymmetry in 2D, and it might be the preferable method whenever a non homogeneous deformation of bilateral symmetric structures is possible. By offering a more detailed and rather exhaustive explanation of the asymmetry pattern, this new approach will hopefully contribute to improve the quality of biological or developmental inferences.

Từ khóa


Tài liệu tham khảo

10.1111/j.0014‐3820.2006.tb01887.x

10.1002/ajpa.22545

10.1111/j.1525‐142X.2006.00127.x

10.1146/annurev.es.17.110186.002135

10.1080/11250000409356545

Adams D. C., 2013, A field comes of age: geometric morphometrics in the twenty first century., Hystrix, 24, 7

10.1007/978-1-4757-9083-2_23

Auffray J. C., 1999, On Growth and Form: Spatio‐temporal Pattern Formation in Biology, 309

10.1007/BF02458311

10.1007/978-1-4757-9083-2_12

10.1111/j.0014‐3820.2002.tb00117.x

10.3390/sym7020843

10.1093/biomet/87.2.285

10.1007/s11692‐009‐9055‐x

10.1007/s000360050041

10.1093/sysbio/syr119

10.1002/ajpa.10174

10.1073/pnas.0508445103

10.1007/s11692‐009‐9061‐z

10.2307/2530448

10.1007/978-1-4757-9083-2_15

10.1007/s11692‐013‐9264‐1

Hampel F. R., 1986, Robust Statistics: The Approach Based on Influence Functions

10.1002/0471725250

10.1093/biomet/69.1.242

10.2307/2411306

10.1086/285728

10.1093/icb/icn076

Zelditch M. L., 2004, Geometric Morphometric for Biologists.

10.1080/10635150119110

10.1007/BF02291478

10.2307/2992207

Bookstein F. L., 1991, Morphometric Tools for Landmark Data: Geometry and Biology

Weiszfeld E., 1937, On the point for which the sum of the distances to n given points is minimum., Tohoku Math. J., 43, 355

10.1016/0898‐1221(94)90109‐0

Thông tin
Thông tin xuất bản

Quantitative Biology

Thông tin tác giả