Ruizhe Jackevan Zhao’s research while affiliated with Northwest University and other places

Background Body mass and surface area are among the most important biological properties, but such information is lacking for some extant organisms and most extinct species. Numerous methods have been developed for body size estimation of animals for this reason. There are two main categories of mass-estimating approaches: extant-scaling approaches and volumetric-density approaches. Extant-scaling approaches determine the relationships between linear skeletal measurements and body mass using regression equations. Volumetric-density approaches, on the other hand, are all based on models. The models are of various types, including physical models, 2D images, and 3D virtual reconstructions. Once the models are constructed, their volumes are acquired using Archimedes’ Principle, math formulae, or 3D software. Then densities are assigned to convert volumes to masses. The acquisition of surface area is similar to volume estimation by changing math formulae or software commands. This article presents a new 2D volumetric-density approach called the cross-sectional method (CSM). Methods The CSM integrates biological cross-sections to estimate volume and surface area accurately. It requires a side view or dorsal/ventral view image, a series of cross-sectional silhouettes and some measurements to perform the calculation. To evaluate the performance of the CSM, two other 2D volumetric-density approaches (Graphic Double Integration (GDI) and Paleomass) are compared with it. Results The CSM produces very accurate results, with average error rates around 0.20% in volume and 1.21% in area respectively. It has higher accuracy than GDI or Paleomass in estimating the volumes and areas of irregular-shaped biological structures. Discussion Most previous 2D volumetric-density approaches assume an elliptical or superelliptical approximation of animal cross-sections. Such an approximation does not always have good performance. The CSM processes the true profiles directly rather than approximating and can deal with any shape. It can process objects that have gradually changing cross-sections. This study also suggests that more attention should be paid to the careful acquisition of cross-sections of animals in 2D volumetric-density approaches, otherwise serious errors may be introduced during the estimations. Combined with 2D modeling techniques, the CSM can be considered as an alternative to 3D modeling under certain conditions. It can reduce the complexity of making reconstructions while ensuring the reliability of the results.

Body size is the key to understanding many biological properties. Sizes of extinct animals are usually estimated from body reconstructions since their masses can not be weighed directly. Plesiosaurs were Mesozoic marine reptiles that were diverse in both body plan and size. Attempts to estimate body masses of plesiosaurs were rare in the past two centuries, possibly due to lack of knowledge about their postcranial anatomy and body shapes in life. The burst of plesiosaur studies in the past two decades has greatly expanded our cognition of their physiology, taxonomy, potential behavior and even soft body outlines. Here I present a comprehensive review of relevant knowledge, and propose a uniform set of methodology for rigorous body reconstruction of plesiosaurs. Twenty-two plesiosaur models were constructed under these criteria, and they were subsequently used as samples to find proxies for body mass. It is revealed that multiple skeletal elements are good indicators of plesiosaur size. This study offers scaling equations for size estimation, enabling quick acquisition of body mass information from fragmented fossils. A summary of body size evolution of different plesiosaur clades is also provided.

Body mass and surface area are among the most important biological properties, but such information are lacking for some extant organisms and all extinct species. Numerous methods have been developed for body size estimation for this reason. There are two main categories of mass-estimating methods: volumetric-density approaches and extant-scaling approaches. In this paper, a new 2D volumetric-density approach named cross-sectional method is presented. Cross-sectional method integrates biological cross-sections to obtain volume and surface area accurately. Unlike all previous 2D methods, cross-sectional method processes true cross-sectional profiles directly rather than approximating. Cross-sectional method also has the advantage over others that it can deal with objects with gradually changing cross-sections. It generates very accurate results, with errors always lower than 2% in all cases tested.