Modelling evolutionary tempo and mode using formal morphological spaces and Markov chain principles

Abstract

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 ofLepidosaurian phalangeal formulae (PFs). This approach involves quantifying the frequencies of morphological changes along an evolutionarytrajectory. The five meristic characters encoded by PFs are particularly valuable in revealing evolutionary patterns, owing to their discrete natureand 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. Thisculminates in a diagram accounting for the phylogenetic dynamic of evolution traversing across different regions of morphospace. The methodinvolves 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 linksMarkovian chains and evolutionary trajectories to formally define parameters that describe the underlying transitions of morphological change.Among other results, we found that (a) PF evolution exhibits a clear trend towards reduction in the phalangeal count and that (b) evolutionarychange tends to occur significantly between morphologically similar PFs. Notwithstanding, although minor but not trivial, transitions betweendistant formulas -jumps- occur. Our results support a pluralistic view including stasis, gradualism, and saltationism discriminating their prevalence in a target character evolution.