The conceptual framework of ontogenetic trajectories: parallel transport allows the recognition and visualization of pure deformation patterns

SUMMARY Ontogeny is usually studied by analyzing a deformation series spanning over juvenile to adult shapes. In geometric morphometrics, this approach implies applying generalized Procrustes analysis coupled with principal component analysis on multiple individuals or multiple species datasets. The...

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Bibliographic Details
Published in:Evolution & development 2016-05, Vol.18 (3), p.182-200
Main Authors: Piras, P., Teresi, L., Traversetti, L., Varano, V., Gabriele, S., Kotsakis, T., Raia, P., Puddu, P. E., Scalici, M.
Format: Article
Language:English
Subjects:
Animals
Biometry
Deformation
Euclidean space
Evolution & development
Mammals - anatomy & histology
Mammals - classification
Models, Biological
Morphology
Multivariate Analysis
Principal Component Analysis
Skull - anatomy & histology
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Summary:SUMMARY Ontogeny is usually studied by analyzing a deformation series spanning over juvenile to adult shapes. In geometric morphometrics, this approach implies applying generalized Procrustes analysis coupled with principal component analysis on multiple individuals or multiple species datasets. The trouble with such a procedure is that it mixes intra‐ and inter‐group variation. While MANCOVA models are relevant statistical/mathematical tools to draw inferences about the similarities of trajectories, if one wants to observe and interpret the morphological deformation alone by filtering inter‐group variability, a particular tool, namely parallel transport, is necessary. In the context of ontogenetic trajectories, one should firstly perform separate multivariate regressions between shape and size, using regression predictions to estimate within‐group deformations relative to the smallest individuals. These deformations are then applied to a common reference (the mean of per‐group smallest individuals). The estimation of deformations can be performed on the Riemannian manifold by using sophisticated connection metrics. Nevertheless, parallel transport can be effectively achieved by estimating deformations in the Euclidean space via ordinary Procrustes analysis. This approach proved very useful in comparing ontogenetic trajectories of species presenting large morphological differences at early developmental stages.
ISSN:1520-541X
1525-142X
DOI:10.1111/ede.12186