Anatomical insights into fish terrestrial locomotion: A study of barred mudskipper (Periophthalmus argentilineatus) fins based on µCT 3D reconstructions.

Mudskippers are a group of extant ray-finned fishes with an amphibious lifestyle and serve as exemplars for understanding the evolution of amphibious capabilities in teleosts. A comprehensive anatomical profile of both the soft and hard tissues within their propulsive fins is essential for advancing our understanding of terrestrial locomotor adaptations in fish. Despite the ecological significance of mudskippers, detailed data on their musculoskeletal anatomy remains limited. In the present research, we utilized contrast-enhanced high-resolution microcomputed tomography (µCT) imaging to investigate the barred mudskipper, Periophthalmus argentilineatus. This technique enabled detailed reconstruction and quantification of the morphological details of the pectoral, pelvic, and caudal fins of this terrestrial mudskipper, facilitating comparison with its aquatic relatives. Our findings reveal that P. argentilineatus has undergone complex musculoskeletal adaptations for terrestrial movement, including an increase in muscle complexity and muscle volume, as well as the development of specialized structures like aponeuroses for pectoral fin extension. Skeletal modifications are also evident, with features such as a reinforced shoulder-pelvic joint and thickened fin rays. These evolutionary modifications suggest biomechanically advanced fins capable of overcoming the gravitational challenges of terrestrial habitats, indicating a strong selective advantage for these features in land-based environments. The unique musculoskeletal modifications in the fins of mudskippers like P. argentilineatus, compared with their aquatic counterparts, mark a critical evolutionary shift toward terrestrial adaptations. This study not only sheds light on the specific anatomical changes facilitating this transition but also offers broader insights into the early evolutionary mechanisms of terrestrial locomotion, potentially mirroring the transformative journey from aquatic to terrestrial life in the lineage leading to tetrapods.

Stiffness of the human foot and evolution of the transverse arch.

The stiff human foot enables an efficient push-off when walking or running, and was critical for the evolution of bipedalism1-6. The uniquely arched morphology of the human midfoot is thought to stiffen it5-9, whereas other primates have flat feet that bend severely in the midfoot7,10,11. However, the relationship between midfoot geometry and stiffness remains debated in foot biomechanics12,13, podiatry14,15 and palaeontology4-6. These debates centre on the medial longitudinal arch5,6 and have not considered whether stiffness is affected by the second, transverse tarsal arch of the human foot16. Here we show that the transverse tarsal arch, acting through the inter-metatarsal tissues, is responsible for more than 40% of the longitudinal stiffness of the foot. The underlying principle resembles a floppy currency note that stiffens considerably when it curls transversally. We derive a dimensionless curvature parameter that governs the stiffness contribution of the transverse tarsal arch, demonstrate its predictive power using mechanical models of the foot and find its skeletal correlate in hominin feet. In the foot, the material properties of the inter-metatarsal tissues and the mobility of the metatarsals may additionally influence the longitudinal stiffness of the foot and thus the curvature-stiffness relationship of the transverse tarsal arch. By analysing fossils, we track the evolution of the curvature parameter among extinct hominins and show that a human-like transverse arch was a key step in the evolution of human bipedalism that predates the genus Homo by at least 1.5 million years. This renewed understanding of the foot may improve the clinical treatment of flatfoot disorders, the design of robotic feet and the study of foot function in locomotion.

Curvature-induced stiffening of a fish fin.

How fish modulate their fin stiffness during locomotive manoeuvres remains unknown. We show that changing the fin's curvature modulates its stiffness. Modelling the fin as bendable bony rays held together by a membrane, we deduce that fin curvature is manifested as a misalignment of the principal bending axes between neighbouring rays. An external force causes neighbouring rays to bend and splay apart, and thus stretches the membrane. This coupling between bending the rays and stretching the membrane underlies the increase in stiffness. Using three-dimensional reconstruction of a mackerel (Scomber japonicus) pectoral fin for illustration, we calculate the range of stiffnesses this fin is expected to span by changing curvature. The three-dimensional reconstruction shows that, even in its geometrically flat state, a functional curvature is embedded within the fin microstructure owing to the morphology of individual rays. As the ability of a propulsive surface to transmit force to the surrounding fluid is limited by its stiffness, the fin curvature controls the coupling between the fish and its surrounding fluid. Thereby, our results provide mechanical underpinnings and morphological predictions for the hypothesis that the spanned range of fin stiffnesses correlates with the behaviour and the ecological niche of the fish.

Craig's XY distribution and the statistics of Lagrangian power in two-dimensional turbulence.

We examine the probability distribution function (PDF) of the energy injection rate (power) in numerical simulations of stationary two-dimensional (2D) turbulence in the Lagrangian frame. The simulation is designed to mimic an electromagnetically driven fluid layer, a well-documented system for generating 2D turbulence in the laboratory. In our simulations, the forcing and velocity fields are close to Gaussian. On the other hand, the measured PDF of injected power is very sharply peaked at zero, suggestive of a singularity there, with tails which are exponential but asymmetric. Large positive fluctuations are more probable than large negative fluctuations. It is this asymmetry of the tails which leads to a net positive mean value for the energy input despite the most probable value being zero. The main features of the power distribution are well described by Craig's XY distribution for the PDF of the product of two correlated normal variables. We show that the power distribution should exhibit a logarithmic singularity at zero and decay exponentially for large absolute values of the power. We calculate the asymptotic behavior and express the asymmetry of the tails in terms of the correlation coefficient of the force and velocity. We compare the measured PDFs with the theoretical calculations and briefly discuss how the power PDF might change with other forcing mechanisms.