Substitution Models in Phylogenetic Reconstruction from Molecular Data: Theoretical Principles, Implementation and Selection Methodologies, Limits of Results Interpretation, and Recent Advances

Richard Murdoch Montgomery

Substitution models constitute the mathematical foundation of modern phylogenetic inference, providing the probabilistic framework necessary for reconstructing evolutionary relationships from molecular sequence data. These models describe the stochastic processes governing nucleotide or amino acid changes over evolutionary time through continuous-time Markov chains, enabling maximum likelihood and Bayesian approaches to phylogenetic reconstruction. This comprehensive review examines the theoretical principles underlying substitution models, from the foundational Jukes-Cantor model to sophisticated general time-reversible frameworks, whilst addressing critical aspects of model selection, parameter estimation, and computational implementation. We analyse the mathematical formulations of key models including JC69, K80, F81, HKY85, and GTR, presenting their rate matrices, transition probabilities, and equilibrium conditions in formal notation suitable for publication. Through computational illustrations and graphical analyses, we demonstrate the behaviour of these models under varying parameter conditions and evolutionary scenarios. The article critically evaluates model selection