Computing phylogenetic invariants for time-reversible models: from TN93 to its submodels

Phylogenetic invariants are equations that vanish on algebraic varieties associated with Markov processes that model molecular substitutions on phylogenetic trees. For practical applications, it is essential to understand these equations across a wide range of substitution models. Recent work has shown that, for equivariant models, phylogenetic invariants can be derived from those of the general Markov model by restricting to the linear space defined by the model (namely, the space of mixtures of distributions on the model). Following this philosophy, we describe the space of mixtures and phylogenetic invariants for time-reversible models that are not equivariant. Specifically, we study two submodels of the Tamura-Nei nucleotide substitution model (Felsenstein 81 and 84) using an orthogonal change of basis recently introduced for algebraic time-reversible models. This is joint work with Marta Casanellas, Jeniffer Garbett, Roser Homs, and Annachiara Korchmaros.

Arxiv link:
https://arxiv.org/abs/2505.20526