Estimating body volumes and surface areas of animals from cross-sections

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Zoological Science

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Introduction

where a and b are semi-major and semi-minor axes respectively. It is noteworthy that this formula represents an ellipse when k equals 2. It was recently implemented in R and represents the latest study on 2D volumetric-density approaches (Motani, 2023). The new version can read bitmaps and generate a superellipse for every pixel along the sagittal axis. All superellipses are then combined into a 3D mesh, then Paleomass can calculate the cubic pixels (for volume) or square pixels (for surface area) that the mesh contains (Motani, 2023). The strength of this method is that it can generate intervals to bracket true animals with different k-values. Paleomass is good at estimating the volumes and surface areas of marine vertebrates, and it uses an equation for hydrodynamic foils, which includes a parameter that controls relative thickness, to approximate their fins (Motani, 2023).

Materials and Methods

Data collection

Body volume calculation

where l is the distance from Bs to Bk1. Then let

where mk is the mass of the kth subslab, and xk is the distance from the centroid of the kth subslab to the anteriormost base of the slab, i.e.,

Body surface area calculation

where l is the distance from Bs to Bk1. Then let

Validation and comparison

when the calculation underestimates the true value, the error rate is negative; when overestimating, the error rate is positive. The mean error is calculated as:

Working examples

Software application

Results

Discussion

Conclusion

Supplemental Information

Detailed results of the validation tests.

DOI: 10.7717/peerj.17479/supp-1

Detailed reconstruction process of the T. rex model.

DOI: 10.7717/peerj.17479/supp-2

Additional Information and Declarations

Competing Interests

The author declares that they have no competing interests.

Author Contributions

Ruizhe Jackevan Zhao conceived and designed the experiments, performed the experiments, analyzed the data, prepared figures and/or tables, authored or reviewed drafts of the article, and approved the final draft.

Data Availability

The following information was supplied regarding data availability:

The raw data are available in the Supplemental Files and a tutorial on CSM is available at Zenodo: Ruizhe Jackevan Zhao. (2024). Cross-sectional Method (v1.1). Zenodo. https://doi.org/10.5281/zenodo.10974317.

Funding

The author received no funding for this work.

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