Phalangeal Formula of Lepidosauria

Evolutionary tempo and mode summarize ancient and controversial subjects of theoretical biology such as gradualism, convergence, contingence, trends, and entrenchment. We employed an integrative methodological approach to explore the evolutionary tempo and mode of Lepidosaurian Phalangeal Formulae (PFs). This approach involves quantifying the frequencies of morphological changes along an evolutionary trajectory (ET). The five meristic characters encoded by PFs are particularly valuable in revealing evolutionary patterns, owing to their discrete nature and extensive documentation in the literature. Based on a pre-existing dataset of PFs from 649 taxa (35 Lepidosauria families, including fossils), from which there exists a unique repertoire of 53 formulations, our approach simultaneously considers phenetic and phylogenetic data. This culminates in a diagram accounting for the phylogenetic dynamic of evolution traversing across different regions of morphospace. The method involves enumerating phenotypical options, reconstructing phenotypes across the phylogeny, projecting phenotypes onto a morphospace, and constructing a flow network from the frequency of evolutionary transitions between unique phenotypic conditions. This approach links Markovian chains and evolutionary trajectories to formally define parameters that describe the underlying transitions of morphological change. Among other results, we found that: (i) PF evolution exhibits a clear trend toward reduction in the phalangeal count, and that (ii) evolutionary change tends to occur significantly between morphologically similar PFs. Notwithstanding, although minor but not trivial, transitions between distant formulas jumps occur. Our results support a pluralistic view including stasis, gradualism, and saltationism discriminating their prevalence in a target character evolution.

Methods
The phalangeal formulae data set was compiled using information from specialized literature and own records from x‐rays, cleared and stained specimens, and dried osteological specimens. The sample included members of 33 extant families within Squamata belonging to every main clade (Gekkota, Scincoidea, Lacertoidea, Anguinomorpha, Iguania, and Serpentes), the extinct family Aigialosauridae (Anguimorpha), members of the Stem clades of extant representatives (Stem Gekkotan and Stem Serpentes) and members (both extinct and extant) of the squamatan sister group Rhynchocephalia (Sphenodontidae).