ANALYZING PHALANGEAL FORMULAS IN TETRAPODS: DISPARITY, SYMMETRY, AND TOPOLOGICAL INSIGHTS

RASSKIN-GUTMAN, D.; FONTANARROSA, G.; DOS SANTOS, D.A.; FRATANI, J.

Valencia

Jornada; XXXVIII Jornadas de la Sociedad Española de Paleontología; 2023

Sociedad Española de Paleontología

A phalangeal formula (PF) encodes the acropodial skeletal configuration of tetrapods, indicating the sequential number of phalanges digit by digit from medial to lateral. This work is part of a broader effort involving a consortium of several laboratories whose aim is to characterize new macroevolutionary patterns as well as the theoretical conditions for the formation of PFs in tetrapods. The proposed methodology involves representing an acropodium as a two-dimensional matrix using two axes: the lateral dimension for sequential digit arrangement (X axis) and the proximodistal dimension for sequential phalanx organization within each digit (Y axis). By treating each phalanx as a discrete structural unit and observing its neighbourhood relationships, a binary square submatrix of 3 x 3 describes the phalanx’s topological neighbourhood. This approach uses the concept of pixel neighbourhood from Mathematical Morphology, exploring local rules that might influence phalanx formation during embryonic development. With binary submatrices, 512 possible motifs (2^9) arise. Applying this approach to the plesiomorphic and typical PF of the Amniota manus (2-3-4-5-3), 19 realized motifs are identified. Some motifs exhibit inherent symmetry, indicating potential axes passing through specific phalanges. Additionally, pairs of motifs at the ends of perpendicular lines regarding those axes displays specular symmetry, supporting these axes. By analysing the motifs derived by analysis of the whole pool of PF reported for tetrapods, and their configuration, the study aims to extract shared features. By doing so we aim to measure symmetry in terms of counting and topology, prioritizing the elements of the acropodium without considering other attributes such as shape and size. This represents a promising line of analysis that could lead us to study symmetry patterns that remain hidden from other form abstractions. Additionally, this approach potentially gives us insights into the topological constraints (burden) imposed on different phalanges by their location in the orthogonal manual/pedal space.